Standard cosmological model. Big Bang. Forming the structure of the universe.

5.4. Standard cosmological model. Big Bang.
Forming the structure of the universe.

Physical cosmology
So far in previous §5.2 and 5.3 we have focused on models of the universe mainly in terms of structure - geometric properties - spacetime of the general theory of relativity as the physics of gravity, while we made only some general assumptions about its "material content". We now proceed to the concretization of the material content of the universe - physical cosmology, which shows how the physical properties of mass - matter - substance - particles - radiation - co-determine the global structure and evolution of the universe. Conversely, how gravitational forces control the behavior of matter - the formation, motion and transformation of particles, the synthesis of nuclei and atoms, the formation of galaxies and clusters of galaxies. This comprehensive view provides a plausible explanation for the origin, construction, and evolution of the universe, which leads to a cosmos consistent with current astronomical observations. By applying the proven laws of physics *) to the entire universe, earlier speculative cosmology has become an exact physical science.
*) A specific exception, however, are the very initial moments of the origin of the universe (see below "Stages of the evolution of the universe", passage "Very early universe"), for which we do not yet have these "verified laws of physics". So far, these are more hypotheses, anticipating perhaps the future "new physics " ..?..

Expansion of the universe
Current cosmology shows us that our expanding universe was younger, denser, and hotter in the past. A common feature of almost all the above-mentioned cosmological models is the beginning of their evolution in a very dense (theoretically point-singular) and hot phase - the so-called "big bang", followed by a rapid expansion of the universe.
The name "big bang" is used in two senses :
1.In a narrower sense for the initial (hypothetical) singularity and the subsequent "quantum" period of a very early rapidly expanding universe.
Note, however, that initial singularity is not necessary, the inclusion of quantum interactions in the universe model may remove the singularity (discussed below and in §5.5 "Microphysics and cosmology. Inflationary universe.").
2.In a broader sense for the whole initial period when the substance in space was in a hot ionized plasma state , ie until the end of the radiation era (listed below).
Note:The very term "big bang " paradoxically comes from the opponent of this concept of F.Hoyl, as a somewhat derogatory expression, which, however, proved concise in a positive sense and was widely accepted...
The name "bang" can be associated with a sound effect. In today's almost empty space (in a vacuum), the classic sound does not spread. However, in the early hot universe filled with a dense plasma of electrons, photons, and byryons (protons and neutrons), regions with higher and lower plasma densities could form, between which pressure differences and reverse gravitational forces could cause oscillations similar to sound waves in the air (see section "Fluctuations and acoustic oscillations in plasma" below).
The grandiose phenomena in the creation of the universe also probably "resonated" gravity - they vibrated the "web" of the curvature of space-time as a primordial gravitational waves ...
In its beginnings, the Universe was extremely hot and dense; it graduallyexpanded, adiabatically cooled, and increasingly complex structures formed in it (discussed in more detail below). From the initial chaotic and unstructured clutter of fields, the basic elementary particles gradually "condensed" - electrons and quarks, which merged into protons and neutrons, which then grouped into atomic nuclei (initially only deuterium, tritium, helium and several light elements) and later in atoms. From them, galaxies, stars, planets condensed by gravitational contraction ...
This basic claim of relativistic cosmology - apart from Hubble's observation of galaxy moving away (redshift) - was decisively supported by the discovery of relic radiation (see below "Microwave background - a unique messenger reports on the early Universe") indicative of the fact that the universe in the past undergone a very hot and dense phase. The Big Bang, it is not a common localized explosion comming from a certain center, but an explosion taking place at the same time everywhere in the entire existing space, which caused that each particle of matter to begin to rapidly move away from all other particles [273]; together with the mass expands itself space *) - resp. expanding is a dynamic property of the "free" space-time itself --> the particles of matter are carried by it. From this perspective, therefore, there is not a mechanical movement, so that the relative speed of the particles in the cosmological expansion may be superluminal (without violating the laws of the special theory of relativity) .
*)What actually expands as the universe expands? (and what doesn't expand!)
The universe expands from all its points - there is no center of expansion. We perceive expansion the same in every place in the universe, and it will seem to us that we are in the middle of expansion, that galaxies are moving away from us (but it is a mistake). And the farther an object we observe, the faster it moves away from us.
The cause of the expansion of matter (now observed as the divergence of galaxies) is the global expansion of space itself which the galaxy pulls with it. Light waves also "stretch" when the space expands, they lengthen their wavelength - they undergo a "redshift" in their spectrum, "reddening". In connection with the concept of general expansion of the universe, interpreted as expansion of space and modeled using an inflating balloon with galaxies drawn on its surface (§5.3, texts around Fig.5.2), the following paradoxical objection may arise :
  "When expanding space, as clusters of galaxies and possibly galaxies move away from each other during the expansion of space, even the stars in the galaxy should gradually move away from each other, planets from stars in their orbit, the standard of meter should be extended in the same proportion, electron orbits should increase in atoms, etc. If that were the case, there actually would be nothing to relate to the expansion of the universe, all spatial scales would change the same, the expansion of the universe would be unobservable - fictitious".
  However, this is in fact not. Objects that have their own internal integrity do not expand. In particular, the electron orbits in atoms with the expansion of the universe does not change: they are not bound by gravity, but electrically, while within the locally inertial system these electric forces do not depend in any way on the gravitational background. Furthermore, when we formulated the basic starting points of the cosmological model in §5.1, we modeled the matter filling the universe as an ideal "gas" whose "molecules" are clusters of galaxies. Only these largest bound structures will "listen" to the global structure of spacetime and participate in cosmological expansion, always as a whole - not separately in parts. Smaller bound systems - galaxies, star and planetary systems, atoms, or molecules - formed and evolved under the influence of their internal binding forces; we can introduce an approximate locally inertial system, in which the laws of physics will not be affected in any way by the global cosmological gravitational field of the expanding universe. Thus, not only the sizes of atoms, but also the distances of stars or the orbits of planets do not change with cosmological expansion. Here, too, the aforementioned analogy with gas molecules applies: when we open a container with compressed gas, all molecules will move away from each other during its expansion, but the (electrically bound) molecules themselves will not enlarge.
  The oft-cited analogy of an expanding universe with an inflating balloon, on the surface of which galaxies or clusters of galaxies are drawn, is therefore somewhat misleading; when inflating a balloon, the drawn galaxies on its surface would also expand. The model should be clarified in the sense that galaxies (after their formation) should not be painted on the surface of the balloon, but on small discs of paper, each of which would be glued at one point in the proper place to the balloon. Then we would get a realistic picture of receding galaxies, whose own dimensions would not change with expansion (they would change, possibly, only due to the actual dynamics of galaxy evolution). An even simpler one-dimensional concise model is a flexible clothesline to which clothes pegs are attached. If we stretch the elastic cord, the clothes pegs will move away from each other. However, the size of the pegs will not change, but only the spatial distances between them.
Note: Of course, such illustrative models are not applicable in the initial stages of the early universe, when no bound structures like galaxies (or even atoms) existed. And then also in the case. the final stages of a closed universe ...
From a standard physico-mechanical point of view, the expansion of the universe means that all galaxies are moving away from each other. However, within general-relativistic cosmology, a different view is preferred: from a global point of view, no galaxy moves (we do not consider their local peculiar motions here). All galaxies have their fixed spatial coordinates, they do not move. The observed "expansion" is caused by changing the metric tensor g_ik, that describes the distances between these fixed coordinates. The GTR cosmological model expresses the temporal dynamics of changes in the metric tensor, that represents the expansion of the universe *), even though the galaxies themselves are not move relative to the coordinates. And the global mass distribution in turn affects - through the equations of the gravitational field - the dynamics of the space-time metric tensor, in turn...
*)In the most frequently used Robertson-Walker-Fridman metric (5.22), the time dependence (evolution of the universe) is contained in the scale factor a(t).

Spatial finiteness or infinity of the universe ?
Although the universe cannot have any particular spatial boundary (what would be beyond it?), it does not follow that it must be infinite. This was discussed in the previous §5.3 on cosmological models and can be clearly demonstrated by moving on the surface of a sphere that has a finite surface, but when moving along it we do not encounter any boundary. In a dynamic universe, we cannot generally see the whole Universe, but only that part of it - the observable universe, from which it was enough to reach the light during the existence of the universe. The boundaries of the observable universe are referred to as the particle horizon or the light horizon (causality issues and different types of horizons were analyzed in more detail in §3.3 "Cauchy's problem, causality and horizons"); indicates where the farest can be seen with a telescope or any other observation or detection device. Although we do not see more distant areas at the moment, this does not mean that they do not exist: if we wait long enough, light will reach us from these distant areas of space *). Similar to the horizon observed at sea - we know that the ocean continues beyond the horizon, just as the universe does not end beyond the light horizon ...
*)However, with the rapid accelerated expansion of the universe, this light will never "catch up" with us...

The beginning of time ?
What preceded big bang *), the nature of the big bang itself and the phenomena immediately folowing it (t < ~10^-43s) contemporary physics is not able to understand. In the singularity, space and time "don't work" - it doesn't make sense left and right, up and down, sooner and later. Prepositions "before" or "after" lose their meaning. Only the so-called quantum cosmology can perhaps help to answer the mystery of how a real universe with three spatial dimensions and one temporal dimension emerged from such "non-spatiality" and "timelessness" (§5.5). As the real beginning - the origin - of the universe can effectively be considered not a hypothetical singularity, but a stage of inflationary expansion of the very early universe.
*) What was before the big bang?
All our experience of what is happening in the world around us leads us to an intuitive idea of cause and effect. Especially in the field of physical phenomena, it does not happen that some events "just happen" - without a cause that precedes the consequence. This gives rise to the opinion that "something" must have created the universe! And then immediately the question arises, where did the "something" come from..?.. - and so it could still back, to infinity. To avoid such a series of unsolvable questions, some refer to this impenetrable mystery to the "supreme instance" - to God as the creator of the Universe.
Within Fridman's cosmological models, no period before the initial singularity t = 0 has any physical meaning - the solution cannot be analytically extended to areas t <0; at the same time as the universe, time also "originated". Similarly to thermodynamics, where it exists an absolute zero of temperature and a temperature lower than 0 °K does not make sense *), "absolute zero of time" t = 0 appears here as a moment before which, in principle, a chain of causes and consequences cannot be observed. So there was not any "before" - with the big bang, time itself began. Or another analogy: asking, "What was before the Big Bang?" is similar to asking, "What's north of the North Pole?", or "Where can you sink deeper than the center of the globe?". Certain possibilities of explaining (or circumventing) this fundamental cosmological and philosophical problem will be outlined in §5.5.
*) The temperature of a body is a measure of the motion of particles of matter and the absolute zero of the thermodynamic Kelvin scale is defined so that all movements of atoms and molecules cease (except for "zero" oscillations given by quantum relations of uncertainty). We cannot have a negative temperature less than an absolute 0 °K, as this would mean that the particles of matter "less than they do not move" - this does not make sense ..!..
All questions about what happened before the beginning~formation of the universe, what will happen after its end~extinction, or what lies beyond the boundaries of the universe are just our human artificial constructions. It is difficult for us to imagine things and events without beginnings and ends, because our brains are set to reflect things and events that have beginnings and ends - we see the beginning and end of the day (sunrises and sunsets), we watch stories with beginnings and endings, life beginning with birth and ending with death. We then project this linear structure onto the entire universe; we tend to place limits even on systems that are actually boundless in space and time...
Already in the introductory §1.1, passage "Space and Time", we intended over some general scientific and philosophical-gnoseological aspects of the nature of time. In the following discussion, we completely abandoned the idea of absolute time and unequivocally adhered to the operationalist conception of time which leads to relative time. In the current stage of development of the universe, in today's everyday life, we measure time using (almost) uniform periodic events such as the Earth's rotation, the Earth's orbit around the Sun, pendulum movements, cesium-137 radiation, and so on. However, all such "standards" of time are useless under conditions where the universe was so dense and hot that there were no planetary systems or atoms. We must define time using typical phenomena at a given stage in the evolution of the universe (perhaps at the time of (re) combination of electrons with nuclei, the unit of time could be one oscillation of the radiation of a hydrogen atom). Towards the beginning of the universe, it is becoming more and more difficult, in the very initial singularity t=0 (or quantum foam) it is then impossible.
In a standard cosmological model there is no time period before the big bang, because there is no object (body or particle) by whose motions the time could be measured. The universe did not form in time, but together with time *).
*) Current note: However, some new alternative hypotheses to the process of origin and evolution of the earliest phases of the universe, including the concept of the beginning of time, introduce new research in superstring theories - see "Astrophysical and Cosmological Consequences of Superstring Theory" in §B.6 "Unification of Fundamental Interactions. Supergravity. Superstrings.".
The discussion of the question of conservation or non-conservation of energy in cosmology is in §5.1, the passage "Energy and the law of conservation of energy in an expanding universe".

Stages of the evolution of the universe
The theory involving the idea of the Big Bang and the subsequent expansion of the hot, gradually cooling, universe is now already considered a standard cosmological model. The global structure and evolution of the universe is governed by gravity, but the specific properties of matter and the formation of structures in the universe are given by the laws of hydrodynamics, thermodynamics, elementary particle physics, atomic and nuclear physics. The physical cosmology, which deals with this issue, leads to a comprehensive understanding of the evolution of the universe and the global structure of spacetime.
More details on physical cosmology can be found in the book literature, eg [288], [200], [215], [250], [273].
The standard cosmological model is now extended by the implementation of hidden - dark matter and energy, often denoted by the abbreviation LCDM - Lambda Cold Dark Matter. It contains cold dark matter, which binds galaxies and clusters of galaxies by its gravitational effects (see below "Formation of the large-scale structure of the universe" and in more detail §5.6, passage "Future development of the universe. Hidden-dark matter."). And it also contains dark energy, expressed by the cosmological constant "Lambda" L, which in the late stages of evolution causes the acceleration of universe expansion (discussed in §5.6, the passage "Accelerated expansion of the universe? Dark energy?").
The course of the early stages of the evolution of the universe practically does not depend on whether k = -1, 0, or +1, ie whether the universe is open (negative curvature), flat or closed (positive curvature of space). The time component of the curvature of spacetime (proportional to ä²/a²) is much larger in the early stages than the spatial curvature (proportional ±1/a²), so the sign of spatial curvature does not matter much here. All three variants (k = -1, 0, +1) of Friedman's model lead for small t to the same approximate law of expansion (5.31) a(t) ~ t^1/2 for dominant radiation and (5.30) a(t) ~ t^2/3 for dominant substance; the mass-energy density decreases according to the universal law r(t) ~ t^-2, in which the coefficient of proportionality depends only on the equation of state.
The reason why neither the course of specific physical processes in the early universe does not depend on its global geometric structure, is the existence of the horizon. During evolution, the size of the universe is proportional to t^1/2, or t^2/3, while the distance of the horizon is proportional to t . Towards the beginning of the universe, therefore, the radius of the horizon decreases faster than the size of the universe - the earlier the moment, the smaller part of the universe is enclosed within the horizon. Thus, for each place (each particle) there is a certain maximum "zone of influence", which is so small in the early universe that it does not reflect the difference between the positive and negative spatial curvature of a closed or open universe in physical processes. This means that in the early universe, the finiteness or infinity of space is not as important to physical events as it might seem at first glance. Only in the later stages of evolution, when the horizon expands accordingly, does the sign and magnitude of the curvature of space begins to mankifest itself - substantial differences arise in the rate of expansion and in the overall nature of evolution between the closed and open model.

Very early universe
Quantum effects of the space-time geometry cause, that the evolution of the universe can be observed not from the time "t = 0", but only from the time about t_P » 10^-43sec. after the Big Bang. In shorter times, due to quantum fluctuations, spacetime loses its usual local topological properties, so the continuity of causes and consequences cannot be observed here.
Origin of physical laws ?
It can also be hypothesized that the current laws of physics (classical and quantum) are a "conserved remnant" of chaotic processes, that took place shortly after the creation of the universe..?.. What we now perceive as matter, energy, space-time, was at that moment intertwined in an interpenetrating unity. It was perhaps just a kind of boiling "false vacuum", from which virtual pairs of particles and antiparticles emerged like waves or excitations and then disappeared again. In the end, these basic particles themselves may also be composed of a vacuum of specially configured space-time geometry (§B3 "Geometrodynamics. Gravity and topology." And §B4 "Quantum geometrodynamics"). Metaphorically, it can be said that "Everything came out of nothing" ...
In an attempt to understand the earliest stages of the evolution of the universe, the very beginning of the Big Bang, we come across ignorance of physical laws, according to which particles and fields behaved at immense densities and energies. Newertheless, some hypotheses have been developed, according to which, at least tentatively, the early moments of the big bang can be divided into some presumed significant stages and landmark milestones, how with time t there is a sharply expansion of the universe and a rapid decrease of the energy E ~ temperature T of interacting particles :
-> Era of "Chaos" (t » 0 - 10^-43s, temperature and density cannot be talked about here)
The origin of the universe begins with a hypothetical singularity, from which the time "t=0" is defined. According to quantum-gravitational notions, however, it was not a real (mathematical) singularity, but the universe was formed by a chaotically fluctuating topological space-time "foam". This era ended with the expiration of Planck's time of 10^-43 seconds. In the very early stages of evolution, it can be assumed that the universe was completely amorphous, not yet having any structure, there were no elementary particles. All four known physical interactions (gravitational, electromagnetic, strong and weak) behaved as a single unified unitary "prime-field" or "superfield" (cf. §B.6 "Unification of fundamental interactions. Supergravity. Superstrings."), which ruled the physics of the universe. Even here, however, probably hidden there specific quantum fluctuation fields and properties of the nascent space-time, which later became the "seeds" for the formation of large-scale structure of the universe, the formation of clusters of galaxies, and each galaxy.
-> Planck time; separation of gravity (t»10^-43s, r»10⁹⁴g/cm³, T»10³² °K, E»10¹⁹GeV)
This very initial era ended with the lapse of the Planck time of 10^-43 seconds. During this period, the gravitational interaction was separated from the original "prime-interaction". From the chaos of the original "topological foam" a causal structure of spacetime emerged, some laws of physics began to apply. Electromagnetic, nuclear strong and weak interactions still formed one whole, in the terminology of unitarization now called "great unification" GUT (this stage is therefore sometimes called the GUT epoch). Two forces ruled the physics of the universe: gravity and the GUT force.Gravity became decisive for the global structure and dynamics of further evolution of the universe, and later for the formation of larger and smaller structures in the universe.
-> Inflationary expansion
In the time around 10^-34-10^-35s, a sharp inflationary expansion of the universe could occur here, when the size of the universe grows exponentially with a factor of about 10⁴³ (the hypothetical mechanism and course is discussed in the following §5.5 "Microphysics and cosmology. Inflationary universe."). After inflation, the expansion slows significantly (to the normal value of the Friedman expansion). Inflationary expansion helps explain why the spacetime of the universe is globally so smooth and flat.
-> Separation of strong interaction (t » 10^-35s, T » 10²⁷°K, E » 10¹⁴GeV)
After the end of the inflationary expansion, there is a separation of the strong interaction from the original unified GUT. The physics of the universe is governed by 3 forces: gravity, strong and electroweak forces. The universe is dominated by high-energy radiation, with particles from quarks, leptons, intermediate field particles, and X and Y bosons, causing quarks to transform into leptons and vice versa. The X and Y particles continuously break down into quark-antiquark, antiquark-lepton, quark-antilepton pairs. And during the interactions of quarks and leptons (+ their antiparticles), X and Y particles are formed again, which are thus in thermodynamic equilibrium with quarks and leptons.
-> Extinction of X, Y leptoquarks (t » 10^-30s, T » 10²⁵°K, E » 10¹² GeV)
When the energy ~ temperature falls below the threshold value for the spontaneous formation of X and Y particles, these leptoquarks decay irreversibly into quarks-antiquark, antiquark-lepton, quark-antilepton. The processes of mutual transformation between leptons and quarks quickly cease and are no longer possible later. The transformation between leptons and quarks is slightly asymmetric (CP-invariance is not preserved), the direction of antiquark àlepton and antilepton àquark slightly predominates: baryon asymmetry is established - the predominance of matter over antimatter (will be discussed below in the section "Standard cosmological model", passage "Baryon asymmetry of the universe").

Rapid mutual separating of fundamental physical interactions in the very early universe (left part of graph). In the right part of the graph, the times of some later important astrophysical processes are approximately marked.
The relative strength of individual types of interactions depends on the type of test particles. On the vertical axis on the right, two protons at a nuclear distance of ~ 10^-13cm were chosen for approximate values; is normalized to the gravitational force.

-> Separation of weak interaction (t » 10^-10s, T » 10¹⁵°K, E » 100 GeV)
The symmetry of the hitherto uniform electroweak interaction is violated due to Higgs fields and their quantum Higgs bosons, which separates the weak interaction from the electromagnetic one. Since this phase, the four independent interactions that we know now operate in nature and space: gravitational, electromagnetic, strong and weak interactions.The matter of the universe is made up of high-energy radiation, quarks, leptons, intermediate field particles, in constant formation and extinction at high energies.
Formation of rest mass of particles:In the first trillionth of a second after the Big Bang, the universe was a wild mix of particles without a rest mass that flew at the speed of light. Then, by interacting with the Higgs field, some species of particles gained rest mass, became the building blocks of the atoms of matter, and eventually formed the universe as we know it.
-> Quark trapping - hadron formation (t » 10^-6s, T » 10¹³°K, E » 1 GeV)
In the first millionths of a second, the substance of the universe consisted of an exotic so-called quark-gluon plasma (see below). As the temperature ~ energy decreases, the effective distance between the quarks increases above »10^-13cm. The strong interaction with gluons firmly connects quarks into pairs - mesons and into triples - baryons (from the point of view of nuclear physics it is discussed in §1.3, passage "Quark structure of hadrons" in the book "Nuclear physics and physics of ionizing radiation"). This ended the period of free quarks in the quark-gluon plasma, the quarks are still perfectly "trapped" in hadrons - the hadron era of the early universe begins.
We will discuss the subsequent stages of the evolution of the universe in more detail later in this chapter. Here we will only present a brief overview diagram of the entire global evolution of the universe :

A brief schematic diagram of the origin and evolution of the universe according to the standard cosmological model LDCM.
The gradual cooling of the hot early universe is depicted by colors smoothly transitioning from white around the big bang, through yellow to red, gradually darker, to black.
It's just symbolic, it's not exactly the colors of the light emitted at that time...

Standard cosmological model
The standart cosmological model begins to study the evolution of the universe only from somewhat later moments t_min » 10^-6s (just from the above-mentioned hadron era ), because current physical theories are not able to reliably describe situations where mass density significantly exceeded nuclear density *); on some attempts to describe the earliest period using grandunification theories, see the following §5.5 "Microphysics and cosmology. Inflationary universe.".
*) Quark-gluon plasma
However, nuclear physics assumes that just before the beginning of the hadron era, the substance probably had a quark form called quark-gluon plasmas. The matter of the universe consisted mainly of quarks and antiquarks, along with high-energy photons, electrons, positrons, neutrinos, antineutrins, constantly evolving and annihilating. As the temperature-energy decreased, the quarks bound to baryons (3 quarks) and mesons (quark-antiquark) due to a strong interaction mediated by gluons - the quark-gluon plasma had a hadronization (as mentioned in the last point of the previous paragraph).
It is described in more detail in the book "Nuclear physics and physics of ionizing radiation", §5.1 "Elementary particles and accelerators", part "Quark structure of hadrons", passage "Quark-gluon plasma - 5th state of matter".
The initial assumption of the standard cosmological model is that the rapid expansion of the universe began from a homogeneous and isotropic state of very high density and temperature. In the first moments of expansion, the temperature was so high (>10¹² °K) that there was a complete thermodynamic equilibrium between photons, electrons, positrons, muons, neutrinos, protons, neutrons, mesons, hyperons and possibly other hypothetical particles. After a few seconds, when the temperature dropped to about 10¹⁰°K (and the density of the substance to about 10⁵g/cm³), all baryons annihilated with antibaryons (except for a small remainder - "baryon asymmetry"), mesons and hyperons disintegrated, neutrinos stopped interacting with other particles. With a further decrease in temperature from 10¹⁰ to 10⁹ °K (and substance density from 10⁵ to 10^-1 g/cm³) in the period of about 10 - 1000 sec., protons and neutrons could combine to form atomic nuclei of light elements (especially helium, in small amounts deuterium, tritium, helium-3, lithium ...). After a substantial drop in temperature below about 3000 °K, over a period of about 400,000 years, electrons fused with protons and helium nuclei to form the neutral hydrogen and helium atoms, of which the present universe is essentially composed.
From a space-time perspective, the universe has a globally homogeneous and isotropic Robertson-Walker metric

which, however, is slightly disturbed on a smaller scale by perturbations generated by mass-energy inhomogeneities. In §5.3, we formulated the basic Fridman equation (5.23a) for the rate of expansion of the universe in the form :

where W_xxx are the contributions of the individual components of matter ~ energy to the dynamics of expansion: W_rad from relativistic particles and radiation, W_m from non-relativistic matter, W_k from the curvature of space and W_L from the cosmological constant - "vacuum energy" (parameter H₀ » 67 km s^-1/Mpc is the current value of the Hubble constant).
For our purposes of physical cosmology, in the sum of the contributions on the right side of equation (5.40) we divide the omega-parameter of the gravitational mass "m" into the sum of W_m = W_b + W_dm of the baryon density "b" *) and the dark mass density "dm". This is especially important for analysis at the interface of the lepton and radiation eras, where baryon density played a crucial role in primordial nucleosynthesis. In the early stages of the universe, at high temperatures and energies of particles and quantum radiation, there were interactions and transmutations of particles, during which the densities of different types of matter (and thus the individual parameters of Omega) changed. The density of neutrinos W_n is sometimes added to the mass parameters, which could have been significant especially in the lepton era (neutrinos are discussed in detail in the section "Neutrinos - "ghosts" inter-particles" §1.2 monograph "Nuclear Physics, ionizing radiation").
*) The electron density is also efficiently incorporated in this baryon density, since the number of electrons required to provide charge neutrality is equal to the number of protons, which in terms of mass represents a proportion of only about 10^-3. Thus the electron density is too small, so it need not be separately considered. After the era of radiation are, due to electric attractive force, electrons generally bound protons of baryon mass.
The values of these and other cosmological parameters(corresponding to the current space) will be listed in the table below in the section "Values of cosmological parameters".

The history of the adiabatically expanding (and thus cooling) universe within the standard model is usually divided into four significant stages, partially intertwined, according to the physical processes that currently dominate :

Baryon asymmetry of the universe
According to standard physical ideas, the same number of particles and antiparticles should initially be formed at the beginning of the universe. All experiments in nuclear physics show that in all particle interactions there is always a combined production of particles and antiparticles, in a ratio of 1:1. The law of conservation of the number of leptons and baryons applies (particles are taken with a "+" sign, antiparticles "-").
In the present universe, however, we observe practically only our "ordinary" matter (sometimes called koinomatter, from the Greek koinos = ordinary, common), not antimatter. Everything living and inanimate that we see here on Earth, planets, stars and the most distant galaxies in the universe, is composed almost exclusively of matter. The question arises, "What happened to antimatter?" - why do we see an almost absolute asymmetry between matter and antimatter? Or from the opposite point of view: "Why is there any matter in the universe at all?" - why is it not filled only with radiation created by the annihilation of all particles and antiparticles?
On the explanation of the asymmetry of matter and antimatter - why the universe is now only a matter - can be viewed essentially from two aspects :
¨ Particles and antiparticles (baryons and antibaryons) was established in hadron era of the same amount. Due to slightly different properties of antimatter (violation of CP symmetry) the annihilation proceeded slightly asymmetrically, whereby all antibaryons annihilated and a small amount of non-annihilated baryons remaining (1:10⁹).
¨ Slightly more particles (by 1:10⁹) were formed than antiparticles - due to asymmetry in the separation of electroweak interactions ("leptokvars" X, Y). After the annihilation, only the small excess of baryons remained.
The relevant discussion from the point of view of nuclear physics is in the section "Antiparticles - antiatoms - antimatter - antiworlds" in §1.5 of the monograph "Nuclear physics and physics of ionizing radiation".
Is antimatter the same as matter ?
In virtually all "normal" processes and particle interactions, the law of conservation of lepton and baryon numbers is met (see §1.5 "Elementary particles and accelerators" in the monograph "Nuclear physics and physics of ionizing radiation"). The ratio between the amount of matter and antimatter is therefore maintained with high accuracy not only in the present universe, but also in all the processes taking place in earlier stages, beginning with the hadron era. Matter and antimatter appear to us to be the same - except for the opposite signs of el. charges and some other quantum numbers have the same properties. Nevertheless, antimatter differs slightly from matter in behavior - asymmetric production and decay of some "exotic" particles and antiparticles (it was found experimentally mainly in K and B mesons). This hidden difference between matter and antimatter, generated in the earliest stages of the separation of basic interactions, eventually resulted in a hadon asymmetry in the hadron era.
The baryon asymmetry of the universe therefore had to be "established" before the beginning of the hadron era - during strongly nonequilibrium phase transitions, in which the electroweak and strong interaction separated (in time »10^-35 s), or during another phase transition separating the electromagnetic and weak interaction (in time »10^-10s). According to current theories of elementary particles, baryon asymmetry may have arisen from the decay of some "exotic" particles, in which does not preserve CP-symmetry *) (see the passage "CPT symmetry of interactions" of §1.5 in the mentioned monograph). These could be Higgs bosons, calibration bosons X and Y (leptoquarks), or hadrons (mesons and baryons) containing c-quarks and b-quarks - these are all just hypotheses..!... These particles, now "exotic" for us, could have been present in large numbers at the beginning of the hadron era. In order not to be able to "erase" the baryon asymmetry of the substance at a certain moment by the action of other subsequent processes without preserving the baryon number, it is important that the baryogenesis process takes place in a strongly nonequilibrium state, in the rapid expansion stage; in the next §5.5 "Microphysics and cosmology. Inflationary universe." we will see that this non-equilibrium state, leading to an effective "conservation" baryon asymmetry can be inflationary expansion of the early universe.
*)Due to certain specific situations - symmetry breaking interactions in the early moments of the evolution of the universe - the amount of mass slightly prevailed over antimatter, there was a slight baryon asymmetry of the universe. More or less random quantum fluctuation thus caused the victory of matter over antimatter in our very early universe. In the hypothetical other universes, the opposite could have been the case - quantum fluctuations at the appropriate moment occurred on the other side, and such a universe would be from antimatter - "antiuniverse" . From our point of view, this eventual victory of antimatter would not necessarily mean anything. In the anti-universe, exactly the same laws of physics would work, the universe would develop in the same way. Only everything would be made of antimatter - which we would call matter...

The quantitative ratio of baryon asymmetry is estimated at 1:10⁹ - there is a billion +1 nucleons per billion antinucleons. Except for this one nucleon, all 10⁹ nucleons and antinucleons, annihated each other. From this slight excess of nucleons, all the matter we observe in the universe has formed - the atoms of interstellar gas, galaxies, stars, planets, and we humans. Everything else was transformed into radiation and light particles (photons, neutrinos) scattered in space (it is from the ratio of the density of standard baryon matter and the density of the relic radiation quanta that the excess is estimated to be 1:10⁹).

Balance between neutrinos and electrons are maintained mainly by reactions e^- + e⁺ <-> n_e + n^~_e, whose effective cross section for relativistic electrons of energy E is about s » g²E²/h⁴c⁴, where g is a constant weak interactions. Neutrinos and their role in space are discussed in detail in §1.2, section "Neutrino - the 'ghosts' among particles" of the book "Nuclear physics and physics of ionizing radiation", about their interactions and detection in the passage "Neutrino interaction with particles and matter".
In the period around t » 0.2 s, the effective cross section decreases so much that neutrinos practically stop interacting with other particles and with each other. Neutrinos, whose "temperature" at that time reached about 10¹⁰°K, thus became permanent it separated from the rest of matter and continued to move freely through space without noticeable interactions; due to the expansion of the universe, the neutrino radiation gradually "cooled by a redshift" to the current temperature of about 1°K (we cannot detect these low-energy relic neutrinos). The only thing that neutrinos continue to contribute to the evolution of the universe, is the contribution of their mass-energy to the total gravitational field of the universe (if the rest mass of the neutrino is nonzero, this post could even be decisive - see §5.6 "The future of the universe. The arrow of time."). Electrons and positrons are in equilibrium with radiation, on average the same number of annihilations e^- + e⁺ r 2g electron-positron pairs for photons g and the formation of electron-positron pairs from photons g à e ^- + e ⁺. At this stage, the universe is filled mainly with electron-positron plasma.
The importance of the first seconds
During the first second of the universe's existence, the physical foundations for the entire further evolution of the universe were formed - for the creation of primordial atomic nuclei, the formation of atoms, the emergence of stars and galaxies, planets, the chemical evolution of matter in the universe. The further continuation of processes in the universe - within the framework of these physical laws - then depended on the rate of expansion of the universe and later on specific, largely random, local densities of matter (including dark matter) in coproduction with the local gravity excited by this matter. Places with a somewhat higher density of primordial gas began to attract and pack more and more gas from the surroundings, which eventually resulted in the formation of stars. These areas, in addition to random formation, increasingly occurred in places of earlier fluctuations, persisting after small primordial (will be analyzed below). And on large-scale scales, these local processes combined into galaxies and clusters of galaxies, observed now.
Dynamics of expansion, temperature and density in the early universe
Lepton era and radiation era, ie a period of about 10^-⁴sec. up to 380,000 years, was an epoch essentially controlled by radiation, during which the universe expanded at a speed a(t) ~ t^1/2. Fridman's equation (5.23a) is simplified here to

where r_g is the radiation density (in terms of photon energy, it was initially really gamma, later the energy dropped to the UV region). The expansion of the universe then takes place according to the dependence :

where H_o = 87.7 km s^-2 Mpc^-2 is the current value of the Hubble parameter.
Since the radiation temperature decreases inversely to the scale factor during expansion: T_g ~ a ^-1 , the time dependence of the temperature is T(t) = g. T ^-1/2, where the coefficient g is given by the effective number of thermodynamic degrees of freedom for bosons and fermions. For the situation at the interface of the lepton and radiation eras (after e^- - e⁺ annihilation) , the temperature during the expansion of the universe decreases with time t_[sec.] as :

It is plotted on the upper horizontal axis of thermodynamic temperature in Fig.5.4 of primordial nucleosynthesis.
The mass-energy density r in the radiation dominant period changes differently for matter and radiation with the expansion of the universe. For a substance component such as baryons (and also dark matter), the shape dependence is r_B ~ a ^-3, while the radiation component varies as r_g ~ a ^-4. The mass-energy density changes with time as r ~ t ^-3/2. It depends on the temperature as

These laws of cosmological expansion of the universe, in combination with the properties and interactions of nucleons, are applied in the primordial cosmological nucleosynthesis :

Initial cosmological nucleosynthesis
Protons and neutrons from the hadron era (which remain due to baryon asymmetry after annihilation of baryons with antibaryons) will now, at the interface of the lepton and radiation eras, become the basis for the formation of the first simple atomic nuclei - primordial nucleosynthesis (which will be described in detail below). The number and representation of different types of emerging nuclei depends on the "competition" between the rates of the respective nuclear reactions and the rate of universal expansion of the universe. The rate of nuclear reactions is directly proportional to the density of nucleons. As the universe expands, the density of nucleons decreases, but the density of photons decreases at the same rate. An important parameter of the "material content" of the universe is therefore the ratio of the density of the number of nucleons n_B and the density of the number of photons n_g, which is called the relative baryon density :

It is denoted by the Greek letter h and, due to its very small value, its decimal multiple h₁₀ = (n_B/n_g) .10¹⁰. After e^- e⁺ annihilation, this ratio is exactly maintained throughout the evolution of the universe. Baryon density is an important parameter of the universe within the standard cosmological model, its significance for initial nucleogenesis will be discussed below in the section "Baryometry of the early universe".
At the beginning of the Lepton era, when the temperature was still very high, tens of billions of degrees (ie the kinetic energy of particle collisions of tens of MeV), protons and neutrons were constantly mutually converted by reactions

Electrons, positrons and neutrinos were emitted and absorbed in the process of beta and inverse beta decay (these transformations take place by mechanisms of weak interaction - transmutations of quarks in protons and neutrons - see §1.2, passage "Mechanism of beta transformation", Fig.1.2.5 in the book "Nuclear physics and ionizing radiation"). Due to the slightly higher mass, neutrons transformed into protons faster than protons into neutrons, so the number of neutrons gradually decreased - Fig.5.4 on the left.
At the thermodynamic temperature T (expressed in energy units [keV]) , the equilibrium ratio of neutrons to protons is

where Dm = m_n -m_p = 1.29 MeV is the difference in mass of the neutron and proton. At high temperatures of tens of MeV at the beginning of the Lepton era, the n/p ratio was close to 1:1. As the energy T decreased due to the expansion of the universe, the n/p ratio gradually decreased, but at the same time the rate of the above-mentioned mutual transformations between protons and neutrons decreased. The neutrinos - by their interactions - separated from other particles, most positrons anihilated with electrons. Weak interactions of mutual transformation of protons and neutrons in time around 1sec. stopped (figuratively speaking, "frozen"), at a ratio value (n/p) = 0.166, ie about 1/6. Only the slow radioactive decay of neutrons into protons with a half-life of 13 min. remained *), which is internal, without the participation of electron-positron plasma, independent of temperature. Thanks to this radioactive decay, in a time of about 100 sec. (temperature T = approx. 80keV), when the initial nucleosynthesis was intensive, the ratio (n/p) furthemore dropped somewhat to approx. 1/7.
*) Instability - radioactivity - of neutrons
Free neutrons are unstable - by beta^- -radioactivity n ® p + e^- + n' are converted into protons, electrons and (anti)neutrinos with a half-life of about 13 minutes. Formation of primary helium, deuterium and possibly other elements by fusion reactions of protons and neutrons therefore had to take place in less than about 1000 seconds after the big bang. The period of the first formation of elements - primordial nucleogenesis - was very short. In times of less than tens of seconds, the substance had too high a temperature to hold the nucleus together. In later times, the universe was again too sparse and neutron-deficient for effective collisions, in which protons and neutrons would combine into atomic nuclei ...
The complete disappearance of neutrons was prevented by the fact, that due to the decrease in space temperature at time t @ 10s to about 3.10⁹°K, protons and neutrons could begin to merge into stable helium nuclei (via deuterium and tritium), as discussed in more detail below. Primordial cosmological nucleosynthesis occurred - Fig.5.4 on the right.
In the early times of the Lepton era, when the density and energy of photons were very high (many MeVs), protons and neutrons "bathed" in a stormy sea of high-energy gamma photons (there were many billions of photons per nucleon). If in this situation protons and neutrons would collide to form deuterons ²H, high-energy gamma would immediately break them - photodissociate, before the capture of another proton or neutron could form heavier nuclides (similar dissociation would be caused by high-energy protons). No nucleogenesis takes place here.
Towards the end of the Lepton era at ~10 sec., with a drop in temperature to about 3.10⁹°K, when the kinetic energy of the particles during collisions was already lower than the binding energy of nucleons in the nuclei (than 0.22 MeV for deuterium), coult by reaction p + n ® ²H + g start to form deuterium D º ²H, without decaying again (photodissociated) by collisions with high-energy particles (especially gamma-photons). The resulting deuterium nuclei could then further react with other protons and neutrons, until in the final phase helium ⁴He was formed (see eg J.Peebles [199]). At the same time, some other light nuclei were formed, but to a much lesser extent; the ⁴He core is strongly bound and thus significantly more stable than other light elements - D, ³He, Li, B, Be.
Due to the above-mentioned lepton interactions, the ratio of the number of protons to neutrons decreased to about 7: 1 until the period of nucleosynthesis of light nuclei. If we limit ourselves to helium, then for every 14 protons and 2 neutrons, 1 helium nucleus of ⁴He₂ could have formed and 12 protons remained free in the form of ¹H₁ hydrogen. Thus, the ratio of N(H): N(He) was 12:1. Since the helium nucleus is four times heavier than hydrogen, the weight ratio of hydrogen to helium m(H) : m(He) is 3:1, so that the weight of helium formed would be about 1/4 of the total weight of the baryon mass, which is in good agreement with the observed the average chemical composition of matter in space (about 2% more helium comes from nucleogenesis in stars).
From the nucleon composition of helium ⁴He₂ from 2 protons and 2 neutrons follows a simple relation for the relative amount of helium with respect to hydrogen :

which may arise from a substance with a certain p/n ratio.
In the "fire furnace" of a hot substance at the end of the Lepton era, with the mentioned drop in temperature, a chain of reactions takes place between protons, neutrons and the newly emerging nuclei of light elements :

initial reaction : _l p + n ® ²H₁sD + g _c			(5.49)
p + D ® ³He₂ + g	.......................	n + D ® ³H₁sT + g
n + ³He ® ⁴He₂ + g		p + T ® ⁴He₂ + g
D + D ® n + ³He , D + D ® ⁴He + g , D + D ® p + T , D +³He®⁴He + p , D + T®⁴He₂ + n
³He +³He ®⁴He + 2p , T + T ® ⁴He + 2n , ³He + T ® ⁴He + p + n , ³He + T ® ⁴He + D
³He + ⁴He ® ⁷Be + g , T + ⁴He ® ⁷Li + g , n + ⁷Be ® p + ⁷Li , p + ⁷Be ® ⁸B + g ,
p + ⁷Li ® ⁴He +⁴He , n + ⁷Be ® ⁴He +⁴He

... these reactions can take place also in the opposite direction ...

The reactions of the initial nucleosynthesis of light nuclei proceeded very rapidly, as the density of nucleons was enormous and the cosmological expansion continuously "adjusted" their kinetic energies to values at which the high cross sections of the respective nuclear reactions.
The number of atomic nuclei produced by these reactions is due to a complex combination of a number of factors - the frequency of collisions given by nucleon density, the effective cross sections of reactions for different energies, which changed rapidly with time due to cosmological expansion. It combines nuclear physics investigating through experiments on accelerators the nuclear reaction *) and their effective cross sections at different energies, with model analyzes of astrophysics - here the cosmology of structure and dynamics of evolution (expansion rate) of the early universe. Figuratively, the final composition of the substance from the initial nucleosynthesis was the result of a massive "sprint race" between the rates of nuclear reactions and the rate of expansion of universe ...
*)Primordial nucleosynthesis reactions are analyzed in detail in the extensive work of Wagoner et al. [266], [267]. In general, nuclear reactions are discussed, for example, in §1.3 "Nuclear reactions and nuclear energy of the book "Nuclear physics and physics of ionizing radiation".
The synergy of these particle-nuclear reactions, together with rapid cosmological expansion and reduction of energy and particle density, leads to "chemical" evolution the substance content of the early universe according to the graphic representation in Fig.5.4. The more complex dynamics of some curves - with a local decrease - for tritium and lithium-7, is caused by the participation of these nuclei in other reactions (when the appropriate energy is reached for the increased effective cross section), leading to their temporary decline.
Some details of the initial nucleogenesis according to Fig.5.4 are the subject of further nuclear-astrophysical research. In experiments on accelerators, particle interactions and nuclear reactions between light nuclei are studied and their effective cross sections are specified. These results are applied to the model distribution of particles (protons, neutrons, electrons) and the distribution of their energies during cosmological expansion. The specific shapes of the curves in Fig.5.4 may thus change somewhat (in some analyzes, e.g. absent said local decrease in time of about 07.10 ³ sec. the curves ³ H and ⁷ Li) ..?..
Furthermore the fusion of nuclear reactions with the final result primordial nucleosynthesis somewhat later in time also applied radioactivity beta. Free neutrons are converted into protons, electrons and (anti) neutrinos n ® p + e^- + n' with a half-life of about 13 minutes, so that the remaining neutrons (which did not fuse) quickly disappeared. Tritium ³H with b^- radioactivity ³H º T ® ³He + e + n' with a half-life of 12.3 years is transformed into helium-3, the original content of which according to Fig.5.4 is thus slightly increased at the beginning of the radiation era. Similarly, beryllium-7 is unstable, with electron capture (EC) ⁷Be + e^- ® ⁷Li + n is converted to lithium-7 with a half-life of 53.2 days, the resulting proportion of which also increases *).
*) The problem of spectrometrically measured considerably lower proportion of lithium-7 in space is not yet fully explained, about 3 times less than predicted primordial nucleosynthesis ..?..
With further decrease the temperature below ~10⁹°C (3 min. after the Big Bang), the production of helium, as well as initial production of extremely small quantities of other elements, has definitely stopped. The kinetic energy of the particles decreased, and matter in the universe was already too sparse to effectively collide, in which protons and neutrons would coalesce into larger nuclei (after all, free neutrons almost disappeared at that time).
In terms of time, therefore, this "space primordial nuclear reactor" had a very short duration: only during the decisive time period of about 10 ÷ 1000 sec. were favorable conditions for the formation of element cores. After 10 minutes from the beginning of the universe, almost all free neutrons disappeared (they were incorporated into nuclei mainly ⁴He) and the thermodynamic temperature - kinetic energy - fell below about 50keV. Due to the repulsive Coulomb barrier, low-energy protons and newly formed atomic nuclei were no longer capable of nuclear reactions - nucleogenesis "froze" (let us not be surprised that it is freezing at a temperature of 100 million degrees..!.). In this short period of primordial nucleogenesis, therefore, only the lightest (simplest) nuclei were formed - hydrogen (protons were there before), deuterium, helium, lithium, beryllium. Primordial nucleogenesis at the end of the Lepton era is also sometimes called "big-bang nucleogenesis" (BBN).
Detailed analyzes [266], [267], taking into account all possible nuclear reactions, lead to the "chemical evolution" of the early - pregalactic, pre - stellar - universe shown in Fig.5.4. These nuclear reactions ultimately result in the composition of the substance stabilizing approximately 3 minutes after the onset of expansion so that for every 12 free protons there was one helium nucleus; the number of nucleons was established at 87% of protons and 13% of neutrons (bound in the nuclei of light elements, mainly helium). About 25% by weight of helium ⁴He ºa was thus formed (in the terminology of nuclear physics and radioactivity, nucleus of helium-4 is often called alpha particles) and the other 75% remains in the form of hydrogen ¹H, wherein the percentage result very little dependent on the specific baryon mass density (analysis was performed for n_B/n_g in a wide range (1 ÷ 10) . 10^-10).

Fig.5.4. "Chemical evolution" of the early universe, ie the time dependence of the relative representation (quantity, abundance) of protons, neutrons and light elements - helium, deuterium, lithium, beryllium - arising from nuclear reactions of nucleosynthesis in the early hot universe at the end of the Lepton era and the beginning of the radiation era.
To clearly display a large range of values of the relative representation of the various emerging elements, the scale on the vertical axis is combined: in the area of relative content 0.1-1 it is linear, for lower values it is logarithmic.
The basic horizontal axis at the bottom is time (logarithmic). It is plotted on the two upper horizontal scales temperature on the one hand by thermodynamic degrees Kelvin [°K] x 10 ⁹, on the other hand by the kinetic energy of particles in [keV].

Nucleosynthesis of further elements behind ⁴He already depends significantly on the actual density of baryons at a given temperature, but in general it can be said that nuclei heavier than helium could only be formed in very small amounts, because there are not sufficiently stable nuclei with 5 and 8 nucleons. This "gap" interrupts the chain of two-particle interactions pa, na, aa, leading to the formation of heavier nuclei. If the helium nucleus captured a neutron or proton, a highly unstable nucleus with mass 5 would be formed, and when two helium nuclei merged, an unstable nucleus with mass 8 was formed. Such unstable nuclei decay rapidly before they can trap next protons, neutrons or a-particles in the already diluted substance, which would turn them into heavier stable nuclei. And in the earlier period, when the density was sufficient, heavier nuclei could not form due to the high temperature and kinetic energy of the particles, which would immediately "break" them.
Reactions of helium ⁴He with deuterium ²H , tritium ³H or other helium ⁴He are required to bridge the gap "5". Coulomb's electrical repulsive barrier between these positively charged cores reduces the effective cross section - suppresses the reaction rate. Therefore, only a very small amount of lithium ⁷Li could be formed by the reaction of ³H(a,g)⁷Li and beryllium ⁷Be by reaction of ³He(a,g)⁷Be. And the gap "8" at already reduced temperatures and densities here in the relevant amount are not able to overcome any reactions - the production of heavier elements no longer occurs...
When in about 10⁴sec. the temperature drops to about 100 million degrees, all nuclear reactions cease, the representation of the elements no longer changes. Only the remaining free neutrons continue their radioactive decay until their complete disappearance (and the radioactive beta transformations of tritium and beryllium-7 continue for many years).The primary nucleosynthesis is over..!..
The " baryometry " of the early universe ?
An important free parameter of the standard cosmological model is baryon (nucleon) density - the initial ratio of the number of baryons to photons n_B/n_g at the interface of the hadron and lepton era, which then maintains throughout the further expansion of the universe. It decides on the representation of elements that arise during primordial cosmological nucleosynthesis. By analyzing the representation of light elements in space, we can basically determine this important parameter. Deuterium D º ²H can serve as the main sensitive "baryometer" of the early universe. All the deuterium we observe in nature must have been formed in the Big Bang - in primordial nucleosynthesis, not in the stars (on the contrary, it burns quickly in the stars), so it has a pregalactic origin. No known stellar or galactic process can produce significant amounts of deuterium. The higher the density of baryons in the early universe, the more frequent nuclear collisions, and the more effectively deuterium (which is an "intermediate" in the synthesis of hydrogen to He) was coupled to helium by nuclear reactions. At high densities, almost all deuterium would fuse rapidly to helium, while at lower densities more "fossil" deuterium would remain. Based on the measurement of deuterium content, the baryon (nucleon) density was determined to be n_B/n_g = 6.1 x 10^-10.
Helium⁴He is not usable as a direct "baryometer" of the early universe, as its representation is almost independent of baryon density. ....
Helium³He is in principle usable, but somewhat problematic as a baryometer, because in fusion reactions in stars it is both burned to⁴He, and new helium-3 is formed during proton-proton fusion.
Similarly, lithium ⁷Li.Their observed representation depends on the type of stars and convection models from the interior to stellar atmospheres. If measured on old stars with low metallicity, it can be used as an auxiliary "baryometer" (cf. also the passage "Other destinies of primordial elements" below).
Production of light elements (except helium) - especially deuterium, or also He³ and Li⁷ - strongly depends on the mean mass density (nucleon concentration) during the period of nuclear synthesis. Therefore, by measuring the relative proportion of these light elements in the interstellar matter, it is possible to determine the ratio of the number of photons and nucleons, which in the period of nucleosynthesis affected the rate of reactions - to perform some kind of nuclear "diagnostics" of "Baryometry" early universe. Using the current temperature of relic cosmic background, the average density of the universe can then determined. Observations ultaviolet absorption lines in the spectra of bright hot stars (and also radiation l = 91.6 cm of transitions in the superfine structure of D) has been found that the proportion of deuterium in interstelar gas is about ~2.5 . 10^-5, which according to the standard model correspond to density mass at present time r » 5.10^-31g/cm³, ten times lower than critical.
Thus, no conventional form of baryon matter seems to be able to explain the observed relatively slow rate of cosmological expansion (or even to make the universe closed). The predominant part of the observed gravitational matter is thus "something" that is indifferent to nuclear reactions - a kind of hidden-dark matter; its essential part cannot be formed by ordinary matter composed of atoms whose nuclei are formed by baryons (cf. the discussion of the non-baryonic nature of hidden matter in §5.6 "The Future of the Universe. Arrow of Time. Hidden Matter.", part "Hidden-Dark Matter").
Sequence of the origin of elements in space
The original view of the founder of the concept of the hot beginning of the universe, G.Gamov, that all elements of Mendeleev's periodic table were "cooked" in the earliest hot universes at high densities and temperatures, proved to be partially erroneous. There may arise a lightweight core - excluding hydrogen and deuterium only helium ^4,3He, lithium ^6,7Li, beryllium ⁹Be, boron traces ^10,11B. Heavier elements were not enough to form in the early stages of the universe, because the rapid expansion of the universe caused the initial very high temperatures and densities of matter to drop sharply, so that further nuclear reactions prectically ceased *). It can be said that in the early moments the universe was too hot to form heavier elements, while in later times it was too sparse and cold. Further nucleosynthesis could continue by fusion thermonuclear reactions only after to star formation, in the interiors of which (where hydrogen initially combines to helium) there is a long-term sufficient density and temperature for helium to further merge into carbon (a + a ® Be⁸, Be⁸ + a ® C¹²; unstable ⁸Be is not enough to decay before capturing another particle a) and in later stages of evolution of massive stars to other heavier elements (as discussed in more detail §4.1, section "Thermonuclear reactions inside stars", passage "Helium combustion").
*) Note: If the universe remained denser and hotter for a little longer, all light elements (their protons and neutrons) would merge into heavier nuclei, eventually into iron, and there would be no terrmonuclear fuel left for later stars ...
Thus, the galaxy and the first stars formed from a "precursor" consisting of about 75 % hydrogen and 25 % helium. This prediction of the composition of the primordial substance, which allows to explain the basic representation of elements in nature, is a great triumph of nuclear astrophysics and hot space theory, because it is in good quantitative agreement with the results of chemical composition analysis of stellar atmospheres and ionized interstellar gas zones. Relevant spectrometric measurements have shown that the helium content of our galaxy and several other nearby galaxies is about 28%, which is almost 20 times more helium than could be formed by thermonuclear reactions inside stars *). The bulk of the existing helium must therefore have a pregalactic, cosmological ("primordial") origin, while virtually all heavy elements have been synthesized inside the stars - see §4.1, 4.2 (and also the passage "Formation of nuclei and the origin of the elements" in the book "Nuclear Physics, ionizing radiation").
*) 10¹¹ stars forming a typical galaxy with a mass ~4.10⁴⁴g and a luminosity ~10³⁷J/sec, radiated over the lifetime of the galaxy ~10¹⁰ years approx. 3.10⁵⁴J; it was created about 10⁶⁶He nuclei (the syntheses of one core of He⁴ released energy of 2,5.10^-12J) with a total weight of ~7.10⁴²g, which is only about l,7% by weight.
Another fates of primordial elements in space
After the completion of primary cosmological nucleosynthesis (and the rapid radioactive decay of tritium and beryllium) the chemical composition of matter in an expanding universe remains unchanged throughout the radiation era; and even long later, after recombination and the formation of neutral atoms in the era of matter. From the substance of this original composition, stars of the 1st generation were formed, in the period of about 100-200 million years from the beginning of the universe. Only in stars, where gravity re-compressed matter to high densities and temperatures, could a new stage of nuclear reactions of nucleosynthesis begin - the continuation of the chemical evolution of the universe.
The current number of light elements differs somewhat from its original representation from primordial nucleogenesis due to the later chemical evolution of the universe (whereas different objects - stars, galaxies - could have been affected differently by this development). These are mainly nuclear reactions in stars, to a lesser extent also reactions caused by cosmic ionizing radiation *) in interstellar matter and star atmospheres.
*) In the era of radiation and the beginning of the era of matter, in the expanding and cooling universe, there was no ionizing radiation. Only thermonuclear reactions in stars and their supernova explosions emitted high-energy particles into space - cosmic rays that are able to cause nuclear reactions in substances in space.
The first generations of stars formed from a gas whose elemental composition was created in primary nucleosynthesis - corresponds to Fig.5.4 (after early radioactive decay of tritium ³H and beryllium ⁷Be). During gravitational contraction, after sufficient compression and heating of the star's interior, nuclear reactions were started (discussed in more detail in §4.1, part "Evolution of stars" - "Thermonuclear reactions inside stars"), the most important of which is thermunuclear fusion of hydrogen to helium at approx. 10⁷ °K. Part of the hydrogen ¹H is consumed as a "fuel" and its amount decreases, while helium ⁴He increases as flue gas or "ash"; in the next sequence of fusion reactions, part of the helium is then burned to carbon and heavier elements, depending on the mass of the star. The gases ejected by the stars then partially return to the interstellar matter after each cycle of evolution an increasing contribution of helium and less hydrogen - and an increasing contribution of heavier elements (metallicity increases).
However, even before that, at lower temperatures from 10⁶ degrees, weakly bound deuterium nuclei are converted to helium-3 by reactions with protons D + p ® ³He + g - deuterium is destroyed in the stars! As the universe evolves and primordial gas is "recycled" by future generations of stars, deuterium declines. Other primordial elements lithium-7, beryllium, boron, which burn in stars even at relatively low temperatures from 10⁶°K, have a similar fate (relevant reactions are given in §4.1, part "Evolution of stars", passage "First nuclear reaction at the beginning of the star's evolution"). However, apart from primordial synthesis and reactions in stars, a small amount of light elements, such as ^6,7Li, ⁹Be, ^10.11B, can be formed by nuclear and spalation (cleavage, comminuted) reactions of cosmic radiation quanta with atoms of the interstellar medium (e.g. beryllium-7,10 are formed in trace amounts in the Earth's atmosphere as cosmogenic radionuclides).
Helium-3 isburned to helium-4 in the hot interiors of stars by the reactions ³He + ³He ® ⁴He + 2 ¹H. However, at the same time, new helium-3 is formed as an intermediate of ²D + ¹H ® ³He + g in a proton-proton fusion reaction. The resulting trend in helium-3 content in space depends on what part of this newly synthesized ³He returns to the interstellar medium and what part is consumed ("burned") for the ongoing sequences of thermonuclear reactions..?..
The balance of loss (or increase) of primordial elements in the spectra of stellar radiation also affects convective flow, through which the substance moves from the relatively colder upper layers to the inner much warmer inner regions (where combustion occurs) and vice versa. With a powerful and deep convective flow, the content of lithium and beryllium in the atmospheres of stars decreases rapidly.
Atoms in cosmic bodies and in space
At the current stage, only about 7% of all atoms (or atomic nuclei and electrons) in the universe are part of stars, planets and other cosmic bodies. The ajority, 93%, remains sparsely dispersed in interstellar matter - gases, dust, nebulae.

The lepton era lasts (approx. 10 s.) until the temperature drops below T » 5.10⁹°K, when k.T » 0.5 MeV @ m_e .c², no new leptons are formed. Then most of the electron-positron pairs annihilate to the quantum of gamma radiation, leaving a small excess of electrons (same as the excess of protons) necessary to ensure charge neutrality of the universe. These electrons will then later (in the era of matter) be electrically attracted to the nuclei and will serve to form the atomic shells of the elements.

The intense scattering of photons on the remaining electrons causes a temperature balance between matter-plasma and radiation, the electrons forming a kind of "cosmic fog". The substance in space was in a plasma state, electromagnetic radiation interacted intensively with the substance - it was scattered, absorbed and re-emitted, in different directions and with different energies. Most of the energy ~ mass of the universe was formed by electromagnetic radiation. When the temperature drops below T » 3000 °K, the photon energy decreases to such an extend that they are no longer capable of ionizing the hydrogen, so that it can proceed unhindered (re)combination *) electrons with protons: originally free electrons were captured and bound to hydrogen and helium nuclei to form electrically neutral atoms. This produces gaseous hydrogen (and helium), which is already transparent to existing electromagnetic radiation (average wavelength approx. 700 nm). There was a phase transition of the substance from plasma to gaseous state. The space-time region where this transition occurred is referred to as the last scattering surface (LSS) sphere of light before its separation from matter - plasma. This light radiation followed the expansion of the universe and thus extended its wavelength to the current length of about a millimeter - relict electromagnetic radiation in the microwave region (its properties are discussed below in the section "Microwave relic radiation - messenger of early space news").
*)Terminological note: The commonly used name "recombination" is somewhat inadequate here. This name is used in "terrestrial" physics and chemistry for a situation where in a substance originally composed of neutral atoms, ionization and subsequent recombination of electrons and positive ions occurs. However, in the early universe, no neutral atoms existed before, the state of full ionization was original and default, the prefix "re" is out of place. Therefore, instead of the word "recombination", the term "combination" or ^"deionization" is more appropriate here..?..

Fluctuations and perturbations in cosmic matter
A substance that fills the universe, although on a large scale it is basically globally homogeneous, shows on a smaller scale local inhomogeneities - fluctuations, perturbations. In terms of origin, these may be perturbations :
- Primordial , which were generated in a very early universe (probably in the inflation phase, see the following §5.5) and have since evolved "passively" - changed only by the action of gravity and cosmic expansion.
- Later , which can be continuously formed at different times and places in the universe by various processes ("actively"), in a substantially random way ....
In terms of the nature and internal structure of inhomogeneities (and thermodynamics) in a multicomponent system (in matter, a set of particles), here we mean a perfect fluid - plasma - composed of matter density r_m and radiation density r_r, there can be perturbances of two basic types :
- Entropic , in which there are local changes in the equation of state due to changes in the relative number (densities) of different types of particles in the system, without changing the total mass-energy density. Entropic perturbation consist in change dr_m = - d r_r. Entropic perturbations are also called "isorurvature", because the overall density of the system remains constant and does not change the curvature of space.
- Adiabatic , where the mass-energy density changes locally. The change is described by the relation dr_r/r_r = (4/3). (dr_m/r_m). Adiabatic perturbations are also perturbations of curvature, because they gravitationally cause inhomogeneities in spatial curvature.
From a geometrical point of view, the fluctuations of the curvature of spacetime can be of two types :
- Scalar fluctuations , caused by inhomogeneities in the distribution matter. It is assumed that the initial origin of these inhomogeneities could be in the quantum fluctuations of the model scalar field (f) which induced the inflationary expansion of the very early universe. Microscopic fluctuations increased to a macroscopic level by inflation and later developed as nuclei for the formation of large-scale structures, clusters of galaxies and galaxies (§5.5, passage "Germinal inhomogeneities and large-scale structure of the universe").
- Tensor fluctuations , caused by gravitational waves originating from the turbulent events of the very early periods of the universe (gravitational waves in the general theory of relativity describe the relationships between tensor quantities - components of the metric tensor and the curvature tensor; it is discussed in detail in §2.7 "Gravitational waves ). These gravitational waves do not have to be bound directly to matter. They cause quadrupole deformations of the metric, they could cause special polarization (B-mode) of relic microwave radiation (it has not yet been proven, from a cosmological point of view, this type of fluctuations is probably negligible) .
The fluctuation (perturbation, local inhomogeneity) of the cosmic mass can be expressed as the relative difference of the local actual density from the average: dr(x,t) = [r(x,t) - <r>]/<r>, where r(x, t) is the instantaneous density at a point with coordinates x at time t (in a companion cosmological frame of reference) and <r> is the average density of matter in a large surrounding region. From the point of view of the evolution of structures in the universe, the relative representation of primordial fluctuations of various magnitudes is very important - the spectrum of these fluctuations. To quantitatively evaluate the spectrum of fluctuations, a Fourir analysis is performed : the fluctuations dr(x, t) decompose into a superposition of harmonic functions dr(x,t) = _kSd_kr.e^-ik.x, whose representation is described as a function of d_kr(k) using the wave coefficient k (in the Fourier frequency domain). The size of the fluctuations is then described using "power spectrum" P(k) ~ (k³/4p²).|d_kr|². The spectrum of density fluctuations is then modeled using the power function P(k) = P₀(k) . k^ⁿ^s^{^-1}. The exponent n_s is called spectral index of fluctuations. For n_s = 1 it is a flat spectrum - scale invariant fluctuations, in which all magnitudes of fluctuations are evenly represented (as Harrison and Zeldoviè assumed) .
For the cosmological formation of a large-scale mass structure, it also depends on the normalized spatial "density" of mass fluctuations P(k), for which quantification was introduced as the mean square fluctuation of matter in a sphere with a radius of 8 h^-1 Mpc; is denoted s₈ (radius 8 h ^-1 Mpc was chosen because it roughly corresponds to the typical scale of massive clusters of galaxies). Value s₈ comes out around 0.8. ....... ......
Inhomogeneities of matter in the universe induce changes - perturbations, fluctuations of the gravitational field, or fluctuations of the curvature of space. And the amplitude of the fluctuations of the space curvature is quantified by means of the parameter D_R², which expresses the magnitude of the changes in the curvature of the space induced by the fluctuations of the mass-energy density. Similar to inhomogeneities in mass density (spectral fluctuation index and mean square mass fluctuation) is quantified using Fourier harmonic analysis in the frequency k-region. The normalization scale k₀ is chosen to be 0.002 Mpc ^-1 ....
Note: In technical materials from the analysis of microwave relic radiation, this parameter D_R²is sometimes denoted A_s and the normalization scale is given ..... ...
Density acoustic oscillations in plasma matter
Let's stay for a while in the period of the early hot universe filled with dense plasma electrons, photons and baryons (protons, neutrons, later helium nuclei). There was a strong electromagnetic interaction between them, the plasma behaved like a compressible liquid. In this dynamic, rapidly expanding environment, fluctuations and perturbations *) could create areas with higher and lower plasma densities, between which pressure differences and the inverse forces of gravity could cause oscillations, similar to sound waves in the air (plasma waves are also known from laboratory experiments) .
*)In addition to tubulences, baseline fluctuations and perturbations in plasma could predominantly come from the primordial inflationary expansion of stochastic quantum fluctuations in the inflationary epoch - cf. drive you in §5.5 "Microphysics and cosmology. Inflationary Universe." passage "Germ inhomogeneity and large-scale structure of the universe".
These "acoustic waves" moved outward from the hyperdensity region, at a rate dependent on the density and temperature of the plasma(the speed of plasma wave propagation is estimated here at about c/2) . This velocity v_s ("sound" velocity) in the mixed photon-baryon plasma is: v_s² = dp/dr = ^{^.}p_g/(^{^.}r_g + ^{^.}r_B), where p is pressure, r is density, the upper dots denote the time derivative, the indices g and B denote the photon and byryon components. Substituting for time derivatives of pressure and densities (from Fridman and equation of state) it is possible to obtain the relation v_s²= (4c²r_g/3)/(4r_g + 3r_B) = (c²/3)/(1 + 3r_B/4r_g). The higher the density of baryons r_B, the lower the speed of "sound" v_s . After recombination, the photons stopped interacting with the plasma, releasing the pressure in the plasma density wave, stopping its expansion and "freezing" at the appropriate site. The distance the wave thus traveled before recombination is sometimes called the "sound" horizon d_s = a . n (v_s/a) dt, where a is a scale factor (integrated over the duration of the radiation dominant plasma era). Plasma density oscillations imprinted certain traces on the mass distribution of the early universe. Tiny inhomogeneities have expanded with cosmological expansion to nearly 500 million light-years in the present universe.
These "frozen" areas of increased density then attracted more mass than slightly thinner areas. The resulting small inhomogeneities in the early universe acted as gravitational "seed-germs" to build later large structures in the matter era. These inhomogeneities later formed galaxies and clusters of galaxies.
Even before recombination, these "acoustic fluctuations" left inhomogeneities of relic radiation. The resulting inhomogeneities (at the level of only millikelvins) have recently been shown in the angular spectrum of temperature fluctuations of relic radiation, see below the section "Relic microwave radiation", Fig.G5.CMB c).
Note: These plasma density-wave oscillations are also called baryon acoustic oscillations (BAO), because the main mass component of the plasma are baryons, which are also the basis - atomic nuclei - visible and absorbing matter in space.

After "recombination" or "deionization", the era of free electrons has ended, the substance is "transparent" to electromagnetic radiation and thus the radiation is separated from the substance; the energy of the photons of this radiation has since decreased only due to the expansion of the universe, independent of the behavior of matter. The period of the early hot universe, the Big Bang, is over. The longest era of the universe is coming :

How and when does radiation or matter dominate the universe ?
We can look at this question from two perspectives :
1.Gravitational prevalence - influence on the dynamics of cosmological expansion,
according to equation (5.40), where the relative representation of the energy carried by the radiation (and relativistic particles) W_rad leads to the time dynamics of expansion a(t) ~ t^1/2, while the energy of matter (formed by non-relativistic particles) W_m causes cosmological expansion according to a(t) ~ t^2/3. In the evolution of the universe in the Lepton era, radiation clearly dominates and the dynamics of cosmological expansion is a(t) ~ t^1/2. In the following era of radiation, this is initially also true, but later the radiation gradually dilutes due to expansion and a larger proportion of the substance gradually acquires, so that the dynamics of expansion gradually changes from a(t) ~ t^1/2 to a(t) ~ t^2/3. At a time of about 50,000 years, which is still deep in the era of radiation, when the substance is opaque, the dominance of the substance with the dynamics of expansion a(t) ~ t^2/3 begins to prevail.
2.Physical significance
for events taking place in matter that fills the universe. The interface between the era of matter and radiation here is a decrease in the energy of radiation quanta below the ionization level of hydrogen atoms, about 3000 °K, when electrons could bind to atoms and physically separate photon radiation from gaseous matter. This then led to astrophysical processes leading to the creation of a rich structure of the universe.
In this chapter dealing with physical cosmology, criterion 2 will be especially important for us.

The first millions of years of this matter era, the pre-galactic period, can be described as the Dark Ages - the initial massive flash of the Big Bang has faded, and as a result of the expansion of the universe, its wavelengths have shifted from the original g -radiation to infrared radiation. The darkness of the space filled with cooling gas, infrared, and microwave radiation, had not yet been illuminated by any stars.
During this period, which lasts about 200 million years, seemingly nothing dramatic happened, the universe expanded and became significantly colder. However, gravity was already secretly working on the most important process of the matter era, which is the densification of huge clouds of hydrogen and helium, leading to the creation of distinctive large-scale structures in space - formation of galaxies and clusters of galaxies, in which the first stars later formed *).
*)The stars of the first generation, which originated in the period around 100-200 million years after the Big Bang, from the dense clouds of hydrogen and helium (other elements were practically not yet in the universe at the time), probably had quite large masses of about 100-300 M_¤, possibly up to 1000 M_¤! According to the laws of stellar evolution, they therefore evolved very rapidly (§4.1 "Gravity and evolution of stars") - after about 3-5 million years (the most massive perhaps lived only hundreds of thousands of years) they exploded as supernovae (or hypernovae) and introduced heavier elements into the interstellar matter, which were formed in them by thermonuclear fusion. The next generation of stars formed from this substance, enriched with heavier elements, no longer reached such masses - the presence of heavier elements stimulates the earlier ignition of thermonuclear reactions, so that the star is not enough to "pack" such an amount of matter from a sparse cloud; their lifetimes were hundreds of millions of years to several billion years. Our Sun probably formed as a 3rd generation star made of material enriched after the explosion of 2nd generation stars (and previously 1st generation).
After the formation of the first stars, the dark period ended and the universe became bright again (already for the second time) - but with a different radiation from the first one from the big bang: now it was radiation coming from the heated gases of stars, driven mainly by the energy of fusion thermonuclear reactions in the interior of stars (§ 4.1, section "Thermonuclear reactions in the interior of stars"). This radiation reionized the gases in space, is still created and illuminates space even now. After the thermonuclear fuel was used up (which only took on the order of millions of years), these stars then provided gas enriched with heavier elements for later stellar generations.

Formation of the large-scale structure of the universe
Contemporary astrophysics assumes that due to the gravitational shrinkage (condensation) of local gas densities, which were located in an otherwise globally homogeneous universe, large clusters of gas and emerging stars - galaxies - were formed.
The etymological meaning of the word "galaxy" comes from ancient Greek, where "galaxias kyklos" meant "milk circle", then the only known large grouping observed in the universe - our Milky Way. At the time, however, it was not known that it was a huge grouping of billions of stars. Only a faint - "milky - glowing nebula was observed, a curved stripe stretching across the night sky.
Weak initial inhomogeneities (i.e. local deviations of metric, density of matter and fields, speed, or entropy) must have already existed in the early stages of the universe (discussed above in the section "Fluctuations and acoustic oscillations in plasma matter"). This led to small differences in temperatures that we can observe even now in the cosmic microwave background. However, these perturbations were so small that their influence on global processes, such as the course of expansion or primordial nucleosynthesis, can be neglected. However, some regions of the universe expanded a bit more slowly, eventually stopped expanding and began to contract. However, in the post-recombination period, due to the gravitational attraction of the surrounding matter, the "amplitudes" of these fluctuations of the increased density are growing considerably. In areas with higher density, cosmic matter has become more and more concentrated over time due to gravitational attraction. Gradually, individual large clusters of matter, weighing in the order of ~10¹⁴ M_¤ (germs of galaxy clusters) are formed - Fig.5.5, to the center of gravity of which, due to gravity, massive gas currents are directed. During this adiabatic compression, the gas heats up and turbulence and shock waves are created. If the generated heat radiates, the contraction can continue. J.B.Zeldovich showed [288] that over time such compactions acquire the shape of discs, a kind of gigantic "pancakes". Due to gravitational instability, these formations then disintegrate into individual galaxies: the entire "pancake" gradually transforms into a cluster of galaxies. Two opposing processes are the most important for gravitational instability: gravity trying to concentrate matter into compact shapes, and pressure trying to balance all inhomogeneities in the distribution of matter. And also centrifugal forces during rotation.

Fig. 5.5. Demonstration of two-dimensional computer modeling of the emergence of the large-scale structure of the universe (A.Melott, 1982).
Left: The initial state is an almost homogeneous distribution of particles shown by crosses. Middle: In the presence of small initial perturbations, particles gradually begin to clump together due to gravity.
Right: Finally, the particles are arranged in a "network-like" structure, containing significant densifications and, conversely, extensive almost empty areas.

The detailed physical processes of galaxy formation and clustering are very complex - three-dimensional nonlinear hydrodynamics combined with gravity and radiation heat transfer physics (see, for example, the detailed review in [200]) - and are therefore not yet fully developed. However, the observed distribution of galaxies in space and the existence of large "voids" of ~ 100´100´100 Mpc support the scenario that large-scale structures of matter in space have evolved from initial small perturbations by gravitational instabilities. One of the computer simulations of such a process is shown in Fig.5.5. Originally an almost homogeneous distribution of matter due to gravitational instabilities, it gradually acquires a fibrous structure of some kind "cosmic cobweb". At the scales of hundreds of millions of light-years, the distribution of matter in the universe resembles a complex network full of fine fibers whose intersections or "nodes" consists of clusters of galaxies (see below). These densified nodes gradually "eat" the mass of fibers by gravitaty, which enlarges the clusters (they can also approach each other) and, on the contrary, large voids are created in the surroudings, almost without galaxies ...

The role of dark matter ?
The possibility is currently being investigated whether the "germ deposits" for the formation of large-scale structure of the universe could form dark matter (§ 5.6, part "Future evolution of the universe. Hidden-dark matter."), which is five times more abundant in the universe than atomic (baryonic) substances. This is because dark matter is almost not interact with high-energy radiation and particles, so it could begin to clump gravitationally much earlier after the Big Bang than conventional "luminous" matter. Clouds of ordinary matter, hydrogen, and helium would then accumulate around these densities of dark matter by gravity. The first galaxies, formed by the clustering of already sufficiently cooled gas, would thus not form in random places, but in areas of dark matter concentration that had previously formed ..?..
Deep vacuum in cosmic space
Matter left over from initial expansion during further evolution was subject to many gravitational contractions and collapses that created galaxies, stars, planets, and other astronomical objects. These processes left a deep vacuum between the formed structures. However, the space that is located between bodies in space - cosmic space - is not completely empty, but contains a very low density of particles (electrons, protons, hydrogen and helium atoms, electromagnetic radiation, magnetic field, neutrinos); according to current astrophysical ideas, also dark matter and dark energy (§5.6, section "Future evolution of the universe. Hidden-dark matter." and "Dark energy and accented expansion of the universe"). This interstellar and intergalactic matter, despite its very low density, with huge spatial volumes, plays an important role in the global cosmological evolution of the universe!

Structure and evolution of galaxies
Galaxies are vast systems of large numbers of stars (in the order of hundreds of billions), nebulae, interstellar gas and dust, held together by gravitational pull. Galaxies also contain magnetic fields, cosmic ray particles, electromagnetic waves from radio waves to hard gamma rays. According to current astronomical knowledge, the gravitationally dominant part of galaxies is probably dark, non-radiant matter (see §5.6, section "Future evolution of the universe. Hidden-dark matter."). If so, galaxies formed in some kind of "deep pools" of gravitationally condensed dark matter ..?..
Early galaxies
The original galaxies immediately after their formation (for several million years) were chaotic mictures of moving clouds of gas and dust and gradually formig stars. Over the course of a billion years, they were gradually formed into the current relatively regular spiral and elliptical shape by a co-production of the physical laws of mechanics and gravity.
The gravitational force directed to the center of the galaxy is balanced by the centrifugal force of the orbital motion of stars, gas, and other material in approximately the same direction - the galaxy as a whole rotates around an axis passing through its center. In addition to random movements in different directions and speeds, the total orbital motion around the gravitational center ("center of gravity") of the galaxy predominates. Therefore, most galaxies have the global shape of a flattened disk.
The primordial galaxies after their formation were significantly smaller than the currently observed galaxies - they were not yet able to accumulate a large amount of matter. However, due to the high density of gas, many stars soon began to form in them. Giant stars with relatively short lives were formed, but also stars of solar masses and small red dwarf stars with long lifetimes. Stars are formed in galaxies all the time, but at different rates. In the primordial galaxies, first-generation stars from hydrogen and helium formed very quickly, but many of them soon exploded as supernovae. The gases enriched with heavier elements then formed new stars of subsequent generations. There could have been a temporary exhaustion of the "fuel"-gas and thus the suppression of star formation. In the next stages, when gas clouds accumulated again, attracted from the surroundings or ejected by the previous generation of stars, the activity increased again. In large galaxies, these temporal fluctuations of activity-star formation occur only in relatively small areas, the overall average activity remains roughly the same. In long time periods of the order of tens of billions of years, however, it naturally decreases, in about 10¹⁵years all available thermonuclear fuel will be exhausted, new stars will no longer be formed, only white dwarfs and small infrared stars will shine in the galaxy.
Black holes
"Small" stellar-mass black holes commonly form in the gravitational collapse of stars greater than about 10 M_¤ after all thermonuclear fuel has been consumed. During the collisions of a large amount of cold gas at the time of the formation of the first galaxies, however, very massive cumulations could be formed, which collapsed directly - without igniting thermonuclear reactions - into large black holes, which could then eventually form supermassive black holes through collisions and the packing of additional material. This scenario could explain the astrophysical mystery of how such giant black holes could form relatively quickly in the center of galaxies (§4.8, passage "How did supermassive black holes form?"). Gigantic black holes would thus not form by merging large numbers of collapsed stars as previously thought, but would form independently of the stars, simultaneously with them, if large amounts of dense, cool gas were available.
Or even perhaps even before the first stars were formed in the galaxy..?.. In that case, supermassive black holes could become the seeds of galaxies, because they would start packing on themselves the surrounding gas, from which they would then start to form around them stars and their grouping - a new galaxy would gradually form. This scenario would be a contribution to the discussion on "Which came first: the galaxy or its central giant black hole?".
Relation between mass and speed of galaxy rotation - Tully-Fisher dependence
The greater the mass of the galaxy, the faster it must rotate to balance its attractive gravity by centrifugal force. And massive galaxies have more stars and therefore shine more than small galaxies - the mass of a galaxy is proportional to its luminosity. The dependence between the luminosity L of galaxies and their maximum rotational speed v_max based on astronomical observations of spiral galaxies was empirically measured in 1977 by R.B.Tully and J.R.Fisher. This dependence has a simple power form
L ~ (v_max ) ^b ,
where the exponent b has somewhat different values depending on the wavelength band of the observed radiation: b = 3.0 in the B-band around l = 400nm, b = 3.2 in the I-band l = 800nm, b = 4.2 in the H-band around l = 1200nm. A similar dependence on rotation is expected even for the total (baryon) mass of the galaxy, which should be proportional to the rotational speed in the power of 3.5-4. The speed of a galaxy's rotation can be measured by the Doppler broadening of the spectral lines. This makes it possible to determine the absolute luminosity of the galaxy L; we then compare this with the observed brightness ("stellar size") to obtain the resulting distance of the galaxy. The Tully-Fisher relation can thus be used as one of the methods for determining the distance of spiral galaxies *), is one of the "steps" of distance scales in astronomy (§4.1, passage "Determining the distances of cosmic objects - a basic condition of astrophysics").
*) For elliptical galaxies, the analog Faber-Jackson relation L ~ s⁴ applies approximately between the luminosity L and the central dispersion s orbital velocities.
Shapes of galaxies
With its distinctive and diverse structure, galaxies are among the most interesting and, from an aesthetic point of view, also the most beautiful formations (along with some nebulae), which we can see with larger telescopes in the night sky *).
*) These beautiful formations - galaxies, gas dust nebulae, "planetary" nebulae, supernova remnants, multiple star systems - have been hidden from earlier generations. They are not visible to the eyes or smaller binoculars, only large telescopes and modern observation devices allow you to see these objects with all the beautiful details, not only in the optical field, but also in the field of radio waves, infrared, UV, X-ray and gamma radiation. Even more important than the aesthetic experience, however, is the contribution of detailed observation of distant cosmic objects to the knowledge of the structure and evolution of the universe, its parts and the properties of matter in general.!..
According to the shape and appearance of a galaxies we can be divided into three basic groups: spiral, elliptical andirregular. Many spiral galaxies also have a so-called bar - a narrow band of brighter stars stretching across the inner part of the galaxy. "Our" home galaxy, the Milky Way, also has a spiral shape *).
*) It has the shape of a flat disk with a diameter of about 120,000 light-years and a (central) thickness of about 2,000 light-years, it contains almost 400 billion stars. With our solar system, we are inside the galactic disk, about 26,000 light-years from its center. We observe our galaxy from a cross section: it appears to us as a bright band - the "Milky Way" - stretching through the night sky.

Until recently, astronomers thought that the shapes and structures of galaxies were unchanging over long time scales, and that galaxies own them that these structures slowly rotate as a whole along with the rotation of the galaxy. However, analysis of more detailed observations of the structure of various spiral galaxies in particular in the 1960s led astronomers to a different notion: that spiral arms and bars are not permanent galactic structures, but are only transient oscillations or waves of higher density "galactic material" in which stars are temporarily more concentrated than in surrounding places. During the course of evolution, these formations probably arise and disappeared again (Ch.-Ch.Lin and F.H.Shu were the first to deal with the behavior of density waves in galaxies and their mathematical modeling in 1966). This process takes place over time periods of hundreds of millions of years, so we see only "instant shots" of the structure of galaxies; if we could accelerated observe a series of such images taken over many millions of years, we would see an impressive dynamic process in which the structure and appearance of galaxies would change dramatically..!..
In the beginings, the galaxies are probably born as a more or less amorphous rotating disk of gas, dust, and gradually emerging stars. Individual stars and clouds of gas orbit the center of the galaxy in roughly elliptical orbits, which, however, do not have a Kepler character. The gravitational field of the galaxy is not centrally symmetric - it is not dominated by one distinct central body *), but the main part of matter is distributed continuously in space. This leads to a significant precessionelliptical orbits, which do not close into an exact ellipse at the end of the cycle, but always it turns by a certain angle, form a kind of rosette (analogous situation as in §4.3, passage "Precession of an elliptical orbit in the Schwarzschild field", Fig.4.12, only the cause is different) .
*) There is probably a massive black hole in the center of most galaxies, but it generally forms only a small fraction of the galaxy's mass (for active galaxy nuclei and quasars, see §4.8 "Astrophysical significance of black holes", section "Thick accretion disks . Quasars").
If the stellar orbits are randomly oriented and rotate at significantly different speeds, no galactic structure is formed. Computer simulations show (........) that under certain circumstances the orbits of stars and other substances may be partially "synchronized", and mutual gravity may temporarily fix this state; most elliptical paths then rotate at the same speed, with each ellipse being slightly turned relative to the adjacent ones. In places where ellipses meet, the concentration of stars is highest. The axes of the orbits are gradually rotated more and more, creating an area of increased density in the shape of a spiral curved line. If the orbits of the stars near the center of the galaxy are approximately aligned with their axes, an area of increased density will be created along their major axis - it will appear as a bar.
This kinematic mechanism of galactic structures is only one of the possibilities. Other aspects, such as the role of angular momentum-carrying galactic gas or intergalactic gas flowing from the surrounding universe, remain to be explored.
About the origin and evolution of stars within galaxies is discussed in more detail in §4.1 "The role of gravity in the formation and evolution of stars", section "Star formation" and "Evolution of stars".

Giant black holes in the center of galaxies
In the center of most galaxies (and perhaps in all..?..) is a massive black hole with a mass of about 10⁶ - 10¹⁰ M_¤. Although it generally makes up only a small fraction of the galaxy's mass, it may be dominant in astronomical observations. In the distant universe, we often observe active galaxy nuclei and quasars (see §4.8 "Astrophysical Significance of Black Holes", section "Thick accretion disks. Quasars"), which are one of the most energetic processes in the universe. However, due to the galaxy's own dynamics and late evolution, this central black hole probably has no significant effect, but could have participated in the process of galaxy formation - if it already existed at that time..?.. Central black holes in galaxies, including possible ways of their formation, are discussed in §4.8, section "Thick accretion disks. Quasars".

Gravitational interactions and "collisions" of galaxies
The enormous mass of galaxies, made up of billions of stars, creates strong and extencive gravitational fields in the surrounding universe, through which particularly "neighboring" galaxies interact with each other through attractive forces. In the simplest case, this can affect the trajectories of galaxies in space - cause peculiar movements of galaxies, which can in some areas outweigh the general cosmological expansion and instead of moving away from each other, cause them to approach and eventually collide. The structure of some galaxies can thus be significantly influenced by phenomena related to close interactions of galaxies - attractive and tidal forces, penetration, collision or merger of galaxies, galactic "cannibalism" (absorption of a smaller galaxy by a larger galaxy).

As long as two "neighboring" galaxies are at a great distance >about 300,000 light years apart (in the picture on the left), there is only a slight mutual gravitational interaction, which can be manifested only by small changes in their shape. When approaching to a distance closer than about 150,000 light years apart, gases and individual stars from the peripheral regions begin to flow between the two galaxies and gravitational radial and tidal forces gradually distort the shapes of the galaxies. Many stars from both original galaxies now follow new trajectories influenced by new gravitational effects. At close approach, the spiral shapes become distorted by tidal forces. Each star will orbit around its current local center of gravity; this teaches its affiliation with one galaxy or the other, or later with a giant galaxy formed by the merger of the two. The penultimate picture on the right shows the irregular galaxy NGC 6052, which is located in the constellation Hercules about 230 million light years away. It was observed as early as 1783 by W.Herschel as a faint irregular nebula. However, a detailed image taken by the WFPC2 camera on the Hubble Space Telescope has now shown that NGC 6052 is actually composed of two galaxies that are in the process of mutual colliding and merging, lasting for many millions of years! Spectrometrically, components with opposite directions of motion are observed. The last image on the right shows two deformed galaxies long after a high-speed collision; they flew through each other, now moving away from each other, but are so far connected by filaments of ionized hydrogen gas about 400,000 light-years long.
In the distant past of several billion years, galaxy collisions were probably very common, since the distances between them were much smaller than they are now. The large number of observed irregular galaxies is evidence of these frequent collisions. The final result of the interaction or collision of two galaxies depends on a number of circumstances, primarily :
->On the size and type of both galaxies and the amount of interstellar gas, depends the details of the formation of the resulting local structures.
->The mutual orientation of both galaxies - whether they collide first with their peripheral disks, or "flat" with their nuclei.
->The impact parameter of the collision - whether they collide only peripherally or directly "head-on". With an impact parameter significantly larger than the radius of the galaxies, the paths of movement of both galaxies will only be curved, and they will continue their movement in changed directions, with only a slight influence on their internal structure and dynamics. A significant interaction or even a collision can only occur with an impact parameter close to or smaller than the sum of the radii of both galaxies.
->The collision speed relative to the escape velocity from the gravitational field of one or the other galaxy or from the resulting galaxy after the merger. At slower collision speeds relative to the escape velocity, the result will be a large, merged irregular galaxy that will remain bound at the collision site. At high collision speeds, higher than the escape velocity, the two galaxies will intersect, distort their shape, and continue moving apart (last image on the right) at reduced speed and in changed directions. A certain remnant may sometimes detach and remain near the collision site. There are certainly many such irregular galaxies after mutual collisions, but their assignment to the original galaxies is now problematic.
At first glance, the collision of two galaxies could seem like a huge cosmic catastrophe. However, the opposite is true! The distances between the stars in the galaxies are so huge (several light-years) that the probability of the stars colliding is negligible (no stars will collide), nor will the planetary systems be affected. The two colliding galaxies just penetrate each other and "mix" (this interweaving is gradual, it takes millions of years). If our Milky Way collided with the galaxy in Andromeda (which is likely to happen in the distant future, > 4 billion years; at that time, life will probably no longer exist on Earth), we on Earth and in the Solar System would not feel anything, we would only observe new stars... When galaxies collide, however, vast clouds of interstellar gas collide, thereby thickening and gradually condensing, which triggers the formation of a large number of new stars.
Atoms of the interstellar gas would initially collide with each other at high speed, causing them to be excited and ionized, the emission of fast electrons, accompanied by the emission of radio waves.
For spiral galactic structures, the collision processes are mostly destructive - gravitational perturbations "detune" the orbits of stars, leaving behind an elliptical or irregular galaxy, without a spiral structure. Many stars are gravitationally ejected out of the galaxy.
Clusters of galaxies
Individual galaxies are usually not lonely and isolated in large areas of space, but are grouped into larger systems called clusters of galaxies (the formation of galaxy clusters in the early periods of the substance era was discussed above in connection with Figure 5.5). Our Milky Way galaxy is part of the so-called Local Group of Galaxies, containing about 50 nearest galaxies within a radius of about 7 million light-years. And it is included in the Virgo Cluster of Galaxies about 50 million light-years across, containing more than 1,000 galaxies. A galaxy clusters are further grouped into gigantic superclusters of galaxies, spanning over 100 million light years and containing hundreds of thousands of galaxies.
Galaxies are (partially) gravitationally bound in galactic clusters and superclusters. They perform two types of motions :
1.Mutual distancing of galaxies according to Hubble's law due to general cosmological expansion.
2.Own, individual - peculiar - movements of galaxies, which are combine with the cosmological expansion. They are caused by gravitational interactions with large accumulations of matter in surrounding galaxies.
If cosmological expansion did not take place, the peculiar motion of galaxies induced by gravitational pull would cause all the galaxies in the cluster (or clusters of galaxies in the supercluster) to gradually cluster into a single gravitationally bound structure, a kind of giant "supergalaxy". In the current situation, however, galaxies perform mainly diverging cosmological motion, only slightly modified by mutual gravitational attraction. However, there are places where gravitational attraction has "won" the battle with cosmological expansion and galaxies are locally approaching each other (discussed in more detail above under "Gravitational interactions and galaxy collisions"). We observe this in our Local Group of Galaxies: for example, the neighboring galaxy in Andromeda, 2.5 million light-years away, is rushing towards our galaxy at a peculiar speed of 110 km/s. In about 4 billion years, they will "collide" - or rather penetrate - with our galaxy, and both galaxies will eventually transform into one large elliptical galaxy.
Note: Our solar system is unlikely to be directly affected by this collision. The distances between the stars are so vast that no two stars are likely to get close enough to each other when they collide with galaxies to collide, or be significantly more gravitationally affected. However, after the collision, our solar system will probably move further away from the center, or could be ejected from the emerging merged galaxy ...
In cosmologically+locally gravitationally curved spacetime, galaxies in clusters (and clusters of galaxies in superclusters) perform very complex movements, the details of which we do not yet know and whose mapping will be an important task for future large-scale exhibitions of the deep space sky. An analysis of the peculiar motions of galaxies and galactic clusters will not only show us our place in the vast universe, but would also help us map the distribution of dark matter in the universe.
In space, everything moves very fast !
The speeds at which macroscopic bodies and we humans move here on Earth are very small from a cosmic point of view. On the other hand, even though we sit still and "do nothing", we are only seemingly immobile. Together with our planet, we orbit the Sun at a speed of about 30 km/s, the Sun with our planetary system then orbits the galactic center at a speed of about 200 kilometers per second. And our Milky Way galaxy is (along with the entire Local Group of galaxies) rushes at a peculiar speed greater than 600 km/s towards a large concentration of matter (in the direction of the Centaur) within the supercluster of galaxies in Virgo. The mutual velocities of galaxies diverging due to cosmological expansion are often even significantly higher..!..
And similarly in the microworld, where the electrons in atoms orbit the nuclei speeds of tens to hundreds of thousands of kilometers per second... Only in our everyday macroscopic world, where "wild" atomic structures form crystalline solid or liquid structures, so macroscopic bodies structured in this way can occupy stationary rest positions relative to each other.

Density and distribution of matter in universe
All mass (matter, fields, particles, radiation) is distributed very inhomogeneously in the vast expanses of the present universe. From practically zero density in intergalactic space, through very thin gases in interstellar space including nebulae, considerable concentration in stars and planets, to huge densities inside white dwarfs and neutron stars. In the diagram below, various typical regions and objects in universe are marked, for which their average densities in mass units [kg/m³] and atomic-byryon density [number of atoms/m³] are tabulated :

Areas or objects	Mass density [kg/m³]	Mass density [atoms/m³]
Big voids	< 10^-³⁰ g/km³	< 10^-³ atoms/km³
Intergalactic space	~ 2x10^-²⁷ g/m³	~ 1 atom/m³
Interstellar space	10^-²³-10^-²⁴g/m³	20-50 atoms/cm³
Nebulae	10^-²⁵-10^-²³g/m³	10²-10⁴atoms/cm³
Main sequence stars	0,5 - 5 g/cm³	(2-20) x 10²⁶atoms/cm³
Central density of the stellar core	100-500 g/cm³	(5-25) x 10²⁸atoms/cm³
Planets - gas giants	0,1 - 20 g/cm³	(1-200) x 10²⁷atoms/cm³
Planets - terrestrial	3-6 g/cm³	(12-25) x 10²⁷ baryons/cm³
White dwarfs	10⁴-10⁷g/cm³	10³¹-10³⁴baryons/cm³
Neutron stars	10¹⁴ g/cm³	~ 5x10⁴⁰ neutrons/cm³
Black holes	? A - singularity ?	-
Average density of the entire universe	< 2x10^-²⁷ g/m³	< 1 atom/m³

The largest spaces in universe are occupied by the so-called large voids from which, already in the pre-galactic period, the gravitational contraction of matter "sucked" practically all matter into emerging galaxies and clusters of galaxies. Only tiny concentrations of hydrogen and helium atoms (nuclei) remained (originating from primordial nucleosynthesis after the big bang), probably less than about 1 atom in 1000 km³ of space.
In the resulting clusters of galaxies, there are also large distances between galaxies of the order of millions of light-years of intergalactic space. The density of gases here is also very low, approx. 1 atom per 1 m³. However, due to their huge volumes, these spaces contain more mass in total than the galaxies themselves, an estimated 50-80% of all mass. The matter between the galaxies is made up mostly of ionized hydrogen and helium, with a small admixture of heavier elements such as carbon, oxygen, nitrogen, silicon (they come from gas ejected by ancient stars in galaxies, especially at the end of their evolution). In the intergalactic space, lone stars ("stray, wandering") were also found, which were ejected from their "native" galaxies when moving under the gravitational influence between stars and during galaxy collisions.
Inside the galaxies, the stars are distant from each other on the order of units up to tens of light years (in our galaxy an average of 5 light years). In this interstellar space, the mass density is relatively higher, on average about 20-50 atoms/cm³. Matter in interstellar space has a significantly more diverse structure, density, and distribution than in the intergalactic environment. In addition to the diffuse diluted form, it also creates more concentrated clouds (10² -10⁴ atoms/cm³), which often condense into protostars, after which thermonuclear reactions are ignited and stars are formed (§4.1, section "Star Formation"), synthesizing heavier elements from hydrogen and helium. During their evolution, stars eject part of their material continuously through "stellar wind" or eruptions, and in the case of very massive stars, eventually through a catastrophic supernova explosion. The matter thus returns to the interstellar medium, where it mixes with matter that has not yet formed stars. This cycle of interstellar matter and stars enriches cosmic clouds with heavier elements. If clouds of interstellar matter are illuminated by stars from the surroundings or from within, they are astronomically observed as luminous nebulae (§4.1, passage "Nebulae"), or when they shadow stars or other luminous objects, they are observed as dark nebulae.
In addition to obligatory hydrogen and helium, the interstellar matter already has a higher representation of heavier elements - carbon, nitrogen, oxygen, sodium, calcium, silicon, as well as molecules of some compounds such as water, ammonia, formaldehyde, and some more complex ones.
Along with gas, the interstellar environment also contains dust in smaller quantities, the particles of which usually have a diameter considerably smaller than a micrometer. They are usually composed of silicates, carbon, ice, and iron compounds are also found. The dust content of the interstellar medium causes its partial opacity. If the dust is dense enough, it can almost completely absorb light, so we observe dark regions, dark nebulae. Due to the predominant sizes of dust particles, blue light is scattered more than red. When passing through the cloud, less blue light reaches us than red light - there is an interstellar reddening of the light compared to the situation without dust. Conversely, when viewed from the side, a cloud of dust illuminated by the surrounding stars appears blue.
Sufficiently dense clouds of gas and dust in the galaxy gradually condense, thicken and heat up due to gravity until thermonuclear fusion ignites, giving rise to stars. The average density of hydrogen and helium in the entire volume of a main sequence star is about 0.5 - 5 g/cm³ (the Sun has an average density of 1.4 g/cm³). Giant stars have a very low overall density of only about 10^-7 g/cm³ (this is due to the large expansion of the outer layers). However, the central density of the stellar core is quite high, about 100-500 g/cm³.
A star is formed only from the inner region of the protostar, a protoplanetary disk is formed in the outer region around it. In it, planets are gradually formed by gravitational contraction (§4.1, passage "Planets around stars"). The result is, on the one hand, large gaseous planets (in our solar system Jupiter, Saturn, Uranus, Neptune) with a total average density of approx. 0.2-20 g/cm³ and a central density of approx. 100 g/cm³. Then the smaller terrestrial planets (such as Earth, Mars, Venus, Mercury) with an average density of around 3-6 g/cm³ (Earth is 5.5 g/cm³) and a core density of about 10-20 g/cm³. The densities of stars and planets are already relatively high (they are close to the values we are used to in terrestrial conditions), many orders of magnitude higher than the gases in the surrounding universe.
Note:We have the best explored planets in our Solar system. Here, the large gas planets have an overall average density of about 0.5-3 g/cm³ and a central density of about 10 g/cm³. However, our 8 planets are statistically a very small sample for determining the general properties of the planets. However, in recent years, many planets have been discovered around other stars - exoplanets, for some of which, by analyzing the transit method, it was possible to determine their astronomical parameters, including size and mass, which makes it possible to determine their density as well. Exoplanets both larger and smaller than those in our system have been found, which has led to an expansion of the density range to 0.1-20 g/cm³.
In general, the density of gases and particles in interplanetary space around stars is somewhat higher than in outer interstellar space. In our Solar System, it is about 5-50 atoms/cm³ (about 5 atoms/cm³ around the Earth). It is largest near the central star, decreasing outwards with approximately the square of the distance. It is made up mainly of atoms and ions of hydrogen and helium and particles of the stellar wind (electrons, protons) constantly flying from the star's corona.
Extremely high concentrations of matter 10⁸ - 10¹⁴ g/cm³, compressed into a relatively very small volume, occur in compact gravitationally collapsed objects (§4.1, passage "Compact objects") - white dwarfs, neutron stars, black holes *). They most often arise from stars at the end of their evolution (§4.1, passage "Later stages of star evolution").
*)For black holes, however, this statement is misleading! A black hole is not a material object (essentially a vacuum), but a field - gravitational object, it is formed by extremely curved spacetime. Nowhere inside a black hole we would not find any substance in the usual sense. We could only hypothetically consider the mathematical singularity in the center of a black hole as a place with an infinite mass~energy density..?..
Quantifying the mass density of the entire universe is very problematic. We do not know enough about the structure of the entire universe. At most, we could only try to roughly estimate the average density for the region of the universe that has been observed astronomically so far. The opinions of experts differ, but due to the huge spatial distances in the universe, versus the number of observed objects, they are only very vaguely inclined to estimate only one atom per cubic meter (approx. 2x10^-²⁷g/m³)..?..
Astronomical measurements of fluctuations in the cosmic microwave background show that the universe is flat, not curved. Its density should therefore be close to the critical density needed for gravity to stop the expansion of the universe in the infinite time limit. At the current rate of expansion, this critical density should be about 10^-26 kg/m³, but this includes all the mass~energy. The agreement with the astronomical estimate from the observation is here with a question mark..?...
Apology:
Numerical values of mass densities in various regions and objects in space are only very approximate here, averaged from various sources, often subjectively selected. I would ask you to take them with a grain of salt, only relatively and as a framework..!.. With more perfect astronomical observations, they will certainly gradually become more precise.

Phase transitions in universe
The process of evolution of the universe according to the standard cosmological model in the early stages was accompanied by phase transitions and gradual "separation" of individual types of radiation and some elementary particles from other matter :
First gravitational radiation separates from matter - probably in Planck's time ~10^-43sec. after leaving the singular state. Thus, if relict gravitational waves could be detected, we would gain valuable evidence of the nature of the Big Bang itself; however, there is no hope for this in the foreseeable future (for indirect detection, however, see §2.7, passage "Measuring the polarization of relic microwave radiation").
Neutrinos radiationis also soon effectively separated from the substance - in the lepton era about 0.2 sec. after big bang; there is some hope of successfully detecting relict neutrino radiation in the more distant future..?..
The energy of all other annihilations is transferred almost all to electromagnetic radiation. This was separated from the other substance after recombination of electrons with nuclei (hydrogen and helium) at a temperature of ~3.10³°K, which represented the phase transition from the plasma state to the gaseous state, already transparent for this electromagnetic radiation. At that time, electromagnetic radiation had an average wavelength of about 700 nm, which corresponds to the boundary of the visible and infrared optical range. Due to the expansion of space, the wavelength of this electromagnetic radiation has prolonged a thousandfold to about 1 millimeter (into the microwave region) and is now detected as relict radio radiation corresponding to a temperature of 2.7 °K.
Even before this recombination, inhomogeneities and turbulences causing pressure waves probably existed in the ionized matter of the universe resembling sound waves. This caused local compaction and, conversely, districts of lower density. After recombination and separation of photons from matter, these inhomogeneities "froze" and should be observable as subtle inhomogeneities of microwave radiation (of the order of only tens of microcelvines) against a globally homogeneous background of relic radiation. Relic radiation carries with it a kind of "imprint" of the universe, as it looked about 300,000 years after the Big Bang - it carries it in its inhomogeneities. Gradual refinement of the detection technique using satellite measurements gradually allows these subtle inhomogeneities to be accurately distinguished from the "foreground" of much stronger signals from the solar system and interstellar matter in the Galaxy (see "Relict Microwave Radiation" below).
Changes in the state of matter in the universe
Thus, in its evolution, matter in the universe has undergone phase transitions between several "states" of the substance. At the very beginning, it was a completely amorphous "state" of the unitary field, from which gravitational, strong, weak and electromagnetic interactions were gradually separated. There were probably no structures in the extremely "hot" and dense beginning of the universe. As the universe expanded and cooled, more and more complex structures formed in it. After separation of the strong interaction, quarks formed and the substance was probably in the "state" of the quark-gluon plasma (also called the "5th state of matter"), mentioned above in the section "Stages of the evolution of the universe". In time about 10 ms, due to a decrease in temperature ~ energy, the quarks due to strong interaction, mediated by gluons, bound into baryons (3 quarks) and mesons (quark-antiquark) - there was hadronization of quark-gluon plasma. Protons and neutrons were created in the universe, there was a phase transition to hadron plasma, the hadron era began. Here immediately followed the phase transition of annihilation of baryons and antibaryons. After a few tens of seconds (at the end of the Lepton era), the matter of the universe cooled so much that the protons and neutrons (remaining from baryon asymmetry) could combine into light atomic nuclei of deuterium, helium, lithium: the matter of the universe became an "ordinary" fully ionized plasma ("4th state" of matter) - a hot mixture of free negative electrons and positive ions of hydrogen and helium. The last phase transition in the early universe took place in about 380,000 years, when the matter-plasma cooled below about 3000 °K and the electrons began to bind permanently to protons and helium nuclei to form neutral hydrogen and helium atoms: there was a phase transition from the plasma to the gaseous state.
The substance of the universe then remained in this gaseous state for min. 100-200 million years, until the formation of the first stars, inside which there was again heating, ionization and the formation of the plasma state. In interstellar and intergalactic space, most matter remains in the gaseous state (free sparsely distributed atoms); however, due to ionizing radiation from stars, a small part of the surrounding gases in galaxies "reionizes" again - clouds of ionized hydrogen and helium are formed. Some of the gases then condense into a solid state of small particles of space dust. In the gas-dust disks around the forming stars, gravitational condensation creates planets on which all 3 common states occur - gaseous, solid and liquid.
Overall, however, only less than 10% of all atoms (atomic nuclei and electrons) in the universe are part of stars, planets and other cosmic bodies. The majority, more than 90%, remains sparsely dispersed in interstellar matter - gases, dust, nebulae.

How can we recognize the earliest stages of the evolution of the universe ?
The simplified laconic answer is: "no way!". The direct traces of the earliest stages are so "smoothed out" by further evolution of the universe *) that they are not directly observable. A relatively large number of different initial states are able to converge rapidly to the same equilibrium state, which then serves as a starting point for further evolution. These "space-forgotten" initial stages can be reconstructed perhaps only theoretically, with event. using the oldest trace, which is a microwave relic radiation (see the following section on microwave relic radiation).
*) This "smoothing out" refers mainly to the earliest stages around the Big Bang and the inflation phase. However, even in later stages, after the formation of galaxies, the first generation of large and luminous stars could strongly ionize the originally neutral intergalactic hydrogen (reionization), which would smooth out the finer spectral structures from the period immediately after recombination and separation of radiation from matter.
Thus, a certain way to obtain at least partial information about very early structures in space could be a detailed measurement of the properties of microwave relic radiation - its homogeneity, fluctuations (depending on angular distance and wavelength), polarization - see the passage below "Microwave relic radiation - a unique messenger of early space news". Already at the time of the separation of radiation from matter, there were germs of future structures in space, so these photons passed through places with different gravitational potentials, which led to small changes in their energy and wavelength - a slight "cooling" or "heating". These fluctuations should be visible even now, as slightly warmer and colder "spots" in the otherwise isotropic distribution of relic radiation - they represent a kind of "paleontological imprint" of the structures of the early universe. The temperature difference here is very small, on the order of 10^-5degrees, so the instrument technology of their detailed measurement is very complex.
Detailed examination of relic radiation made the COBE (Cosmic Background Explorer), WMAP (Wilkinson Microwave Anisotropy Probe) and PLANCK satellites. A brief description of the instrumentation and measurement results of these important experiments is provided below in the section "Relic Radiation Detection and Display".
In the early stages, the universe was very hot and dense - it was in a plasma state that did not transmit light or any other electromagnetic radiation. When observed in electromagnetic radiation, we can therefore only reach the end of the Big Bang - the end of the radiation era about 400,000 years after the beginning, to the sphere of the last scattering of electromagnetic radiation (microwave relic radiation). We do not see further into the past, because light and other electromagnetic radiation do not pass through the then hot and dense ionized environment. However, there are two entities - radiation modalities, which are able to pass through it and "bring out" some information about a very early universe :
- Neutrinos ,
which do not have an electric charge and do not have a strong interaction, only a weak (and gravitational) interaction. Thanks to this, they have extraordinary penetration even in very "exotic" environments (the origin and physical properties of neutrinos are described in more detail, for example, in §1.2. of the monograph "Nuclear physics and physics of ionizing radiation", part "Neutrinos - "ghosts" between particles"). The cosmological neutrinos originated mainly in the lepton period in the first second, so the relic neutrinos from that period could carry information about the early universe. Its initially high kinetic energy and density greatly decreased. So far, we cannot detect such low-energy neutrinos.
- Gravitational waves ,
which were generated during the turbulent processes of space formation, could in principle bring information about the earliest universe, from the inflation period of about 10^-35seconds. Although they weakened enormously during the expansion of the universe and extended their wavelength below a measurable level, at the end of the radiation era they could leave their "imprint" on relic radiation (§2.7, passage "Measuring the polarization of relic microwave radiation").

Microwave relic radiation - a unique messenger of early space informations
The concept of the hot and dense beginning of the universe - the Big Bang theory - thus shows that in the first 300,000 years after the Big Bang, matter was still so hot and dense that atoms could not exist, and the substance was in the state of fully ionized plasma in which photons, electrons, protons, and helium nuclei collided sharply. Collective interactions ("collisions") of electromagnetic photons with electrons most often occurred. The plasma state is opaque to electromagnetic waves. Each electromagnetic photon is absorbed by an electron within a few millimeters or centimeters after being emitted, after which it is re-emitted in a random direction with altered energy.
Compton and Thomson scattering
At the beginning of the radiation era, photons had high energy (of the order of MeV, corresponding to gamma radiation) and interacted with electrons by electron-positron pair formation and Compton scattering (see eg §1.6 "Ionizing radiation ", section "Interaction of gamma and X radiation" in the book "Nuclear physics and physics of ionizing radiation"). At the end of the radiation era, when the energy of photons was already much smaller than the rest energy of electrons (E_g = n.h << m_e.c²), it was then a Thomson scattering- elastic scattering of electromagnetic radiation on free electrons: the electric field of an incident wave accelerates a charged particle (here an electron), which causes this accelerating particle to in turn emit electromagnetic waves of the same frequency as the incident wave. The kinetic energy of particles and the frequency of photons will be the same before and after scattering, only the direction of their movement will change. The particle will move in the direction of an oscillating electric field, leading to electromagnetic dipole radiation (§1.5 "Electromagnetic field. Maxwell's equations."). The moving particle radiates most strongly in the direction perpendicular to its movement and the scattered radiation will be polarized along the direction of its movement. Thomson scattered radiation from a small volume element may therefore appear to be more or less polarized, depending on the angle from which it is observed. Overall, from a larger plasma volume, the polarization directions are chaotically variable and the radiation is non-polarized. Macroscopically, polarization can manifest during collective interactions of radiation with a large number of electrons. This occurs with Thomson scattering in the case of heterogeneous plasma, where certain "disturbances" (warmer or colder regions) can manifest themselves not only in different intensities, but also in changes in the polarization of the emitted radiation. And this could also be reflected in the radiation emitted from cosmic plasma at the end of the radiation era - in relict microwave radiation (as will be discussed below and also stated in §2.7, passage "Measurement of polarization of relic microwave radiation )
Relic radiation - origin and properties
Relic microwave radiation is an important consequence of the concept of a standard cosmological model with the beginning of the universe with a big bang. The early universe (in the era of radiation) was formed by a hot plasma of photons, electrons and baryons. The photons were in constant interaction with the electrons in the plasma through Thomson scattering. Cosmological expansion of the universe caused adiabatic cooling of the plasma.
In the form of plasma, the substance remained until about 400 thousand years after the Big Bang, when the universe cooled to 3000 °K, atomic nuclei (especially hydrogen and helium) could capture electrons more efficiently than they could eject by radiation - there was "recombination" occured, they formed neutral atoms. There was a phase transition of the substance from the plasma state to the neutral gas state. Very quickly, free electrons disappeared from matter, the universe became transparent to radiation (temperatures below 3000 °K), whose photons no longer formed or disappeared from this time of separation, traveled freely through space, increasing their wavelength due to the expansion of space (cosmological redshift) [67]. In 13 billion years of expansion, the wavelength of this "afterglow" of the Big Bang - relic radiation *) has increased a million times, to a few millimeters, and its temperature has dropped a thousand times to today's 2.7 °K. And this temperature will continue to drop as the universe continues to expand. Relic radiation is often abbreviated CMB (Cosmic Microwave Background). This CMB radiation fills all the observable space and contains most of the radiant energy of the universe.
*) This radiation is a remnant - a relic - a time near the beginning of the universe, from the end of the Big Bang - the era of radiation.
During numerous interactions in ionized plasma, where each particle was dispersed, absorbed and re-emitted many times, the substance reached a state of thermodynamic equilibrium *). Relic radiation comes from a plasma that has been essentially in a state of thermodynamic equilibrium and therefore has a virtually constant temperature - the same wavelength spectrum of an absolutely black body - regardless of the direction from which it comes (minor fluctuations are mentioned below).
*) The expansion of the universe, although much faster then than it is now, took a long time for individual particles compared to the time elapsed between individual collisions. Thus, each particle was able to transfer its kinetic energy to the other particles many times. However, this may not have been the case in the very early stages of rapid expansion; the problem of global homogeneity and isotropy arises, discussed below in the section "Difficulties and problems of the standard cosmological model", section "Problem of homogeneity and isotropy".
Astrophysical effects affecting microwave relic radiation
During their radiation and further propagation through space, microwave relic radiation is affected by some physical interactions with the material environment and gravitational gradients :
Influence of gravitational fluctuations of metrics in space on relic radiation - Sachs-Wolf effect
As analyzed in §2.4, passage "Gravitational electrodynamics and optics", electromag. waves when passing through a gravitationally curved spacetime are subjected to a frequency shift ("Gravitational frequency shift") and a curvature of the direction of propagation. This gravitational influence is naturally applied even to relic radiation coming from outer space. It basically takes place in two stages :
1.In the hot photon-electron-baryon plasma in the radiation era, there were undoubtedly inhomogeneities and fluctuations (discussed above in the passage "Fluctuation and acoustic oscillations in plasma substance"). On the surface of the final dispersion was thus found local areas of increased density that gave increased gravitational potential, causing higher gravitational red shift of the emitted radiation (which was based on a "deeper potential wells").
Even at its therefore, the radiation from the surface of the last scattering will be the wavelength ("temperature"DT) of the CMB affected by the local gravitational potentialj:DT/T =j/c² - this usual value of the frequency shift would apply in a static non-expanding universe. In reality, however, the universe expands with time t, a = a(t), which due to the effect of time dilation contributes the value DT/T = - Da/a, depending on the specific cosmological model. In the simplest case of the flat universe described by Fridman's model with the dominant substance at the time of recombination, the universe expands with 2/3 of the power of time: a(t) ~ t^2/3, thus canceling 2/3 of the normal red gravitational shift. The resulting effect of the observed change in the temperature of microwave relic radiation, caused by the gravitational potential on the surface of the last scattering, is thus DT/T = j/3c². It is 3 times smaller than would be expected under normal conditions without expansion.
This early effect of local changes in CMB temperature occurred at the time of the last scattering, thus reflecting the primary anisotropy caused by primordial inhomogeneities - it is discussed and shown below in the section "Spectrum and distribution of relic radiation".
2.Microwave relic radiation on its long journey through space will respond to fluctuations in metrics - gravitational potential. As they propagate through the vast spaces of space, relic waves - CMB photons - pass through places with large accumulations of matter in galaxy clusters, as well as vast "voids." In these places, CMB photons encounter significant fluctuations in the gravitational potential - potential "peaks" and "pits". During the arrival of relic radiation to the "l _in" places of increased mass accumulation, a blue gravitational shift occurs, and at emptier places, a red gravitational shift. When the output radiation from these locations, "l_out" is the opposite, blue and red shift takes a turn. It would be expected that the gravitational frequency shifts from the input and output would be canceled out ; so it would be in a static universe.
However, the universe expands, so that in the time interval between the entry of CMB photons into large gravitational anomalies and their exit into ordinary space (which can take billions of years!) , the space-time metric changes somewhat; the component g_oo of the metric tensor in the meantime weakens.... So the frequency shift at the output is slightly smaller than the original change in energy at the input - a small part of the frequency shift (temperature change DT) from the input to the transmitted radiation will remain permanently. This can be expressed by the integral relation DT/T = 2. _l_{_in}n^{^l}^out(j^·/c²)dl/c, where j^· is the rate of time evolution of the perturbed potential affected by gravitational fluctuation, dl is the element of length in the direction of photon motion. In summary, this can be expressed as DT/T » Dl . 2 Dj/c², where Dj is the magnitude of the change in gravitational potential due to the expansion of the universe over the length Dl = l_out -l_in the motion of the photon in the gravitational anomaly. Thus, such a modification of the DT/T radiation temperature occurs, when the passage of radiation through large areas of space with significantly increased or decreased mass distribution takes place a significant evolution of the gravitational potential between the entry into and exit of photons from the gravitational anomaly - potential "pit" or "hill".
As a result, relic radiation passing through the massive regions of galaxy clusters will appear slightly warmer, while radiation passing through large regions of emptiness will be slightly colder. In sensitive measurements of CMB inhomogeneities, it is necessary to distinguish between the actual primary fluctuations originating from the early periods of the elmag. radiation separation, from later secondary fluctuations caused by the passage of radiation through large gravitational anomalies in space..!..
The influence of fluctuations in metrics - gravitational potential - in space on the anisotropy of the relic microwave background is called the Sachs-Wolf effect, according to the authors who analyzed it in 1967. The process according to point 1 is sometimes referred to as the basic or early S-W effect. The process 2nd of the fluctuation of the metric as the CMB passes through large regions of galaxy clusters or voids such as the late integral Sachs-Wolfe effect, or the Rees-Sciama effect (1968).
Note: The integrated Sach-Wolf effect is not applied in the simplified Einstein-deSitter model, where the potentialj is constant. Occurs only in cosmological models with W_m ¹ 1 or W_L ¹ 1 (§5.3, passage "Relative W -parametrization of cosmological models").
Diffuse attenuation of inhomogeneities - Silk's effect
During the period of recombination (around 380,000 years), photons of emitted radiation from hot regions diffused and scattered to colder regions, thereby partially balancing the temperatures of these regions. The effect of diffusion damping caused the temperatures and densities of the hot and cold regions to partially adiabatically average, and the early universe became less anisotropic . ... .............. ................
The strength of this damping depends mainly on the distance at which the photons can move freely before scattering - length diffusion . .....
Due to the small length of diffusion in the substance of the time, diffusion damping is most pronounced in small angular dimensions ..... .... causes damping and smoothing of amplitudes .... in the angular spectrum CMB ....
Diffusion damping of this kind was first analyzed by J.Silk in 1968 in connection with the processes of galaxy formation.
Scattering of CMB radiation by ionized gas in galaxy clusters - Sunaev-Zeldovic effect
After the end of the radiation era, there was basically a neutral (non-ionized) gas in the universe - hydrogen and helium, through which relic radiation passes freely, without interactions. However, after the formation of galaxies and the formation of the first hot stars, their radiation began to ionize the surrounding gas again - reionization took place. In galaxies and galaxy clusters, therefore, there is also a hot ionized gas, in which the interaction of photons with charged particles can cause Compton scattering of CMB photons. This scattered radiation can cause small anisotropies in the observed CMB, which are caused by the kinematic effect of galaxy cluster motion relative to the CMB. They are observable as local slight changes in the thermal spectrum. Scattering also results in CMB polarization.
These secondary fluctuations must be distinguished from primary anisotropies, reflecting early cosmological inhomogeneities (perhaps dating back to the inflationary period) . However, they can provide information about the period of reionization and the formation of the first generations of stars. ..........
Polarization of relic radiation
Potentially interesting information about an even earlier universe could be encoded in the polarization of relic microwave radiation. The basic relic radiation, which arises during chaotic interactions of particles in hot plasma, is non-polarized (§1.1, part "Methods of exploring nature"). Polarization can be imprinted on him by two circumstances :
1. Dense or temperature changes in the hot plasma lead to slight polarization in the radial direction around the site of increased density. It is called the E-mode of polarization (the name is derived from the properties of the vector E of electric field intensity outgoing from the vicinity of the point charge), the plane of the electric field oscillates in two perpendicular directions. This polarization may suitably complement the measurement of relic radiation intensity fluctuations.
2. Gravitational waves of quadrupole character deform the plasma in diagonal directions and cause polarization of relic radiation in the so-called B-mode (resembling the vortices of the magnetic field described by the magnetic induction vector B ), where the field strength vector oscillates in directions of 45^o. These are assumed primordial gravitational waves, originating from the period of cosmological inflation (§5.5 "Microphysics and cosmology. Inflationary universe."). These massive gravitational waves deform the plasma in a specific way (quadrupole), the electrons of which can then polarize the waves during Thomson scattering of radiation (as mentioned above). Measuring the polarization of relic radiation could thus be an interesting information channel about the earliest universe, from which nothing but gravitational waves can get (we cannot directly detect primordial gravitational waves). It is discussed in more detail in §2.7, section "Measurement of polarization of relic microwave radiation".
Spectrum and distribution of relic radiation
Relic electromagnetic radiation was emitted from the last scattering of a hot plasma at a temperature of about 3000 degrees, so the energy-frequency distribution of photons, or equivalent wavelength - spectrum - at that time corresponded to Planck's radiation law of "absolutely black body" about this temperature :
I ( n ) = 4 p n ³ / (e ^-n^{/ T} - 1) ,
where I(n) is the radiation intensity of frequency n and T is the thermodynamic temperature of the radiating mass. At the initial temperature T ~ 3000 °K, it was visible light (with a maximum around ...-... A, which we would perceive as a blue-white color).
During the cosmological expansion of the universe, however, the wavelength of relic radiation also increased proportionally (proportionally to all wavelengths) and currently has moved to the area of radio waves with a maximum intensity around the wavelength of about 3-8 mm. The relic radiation now observed has a spectrum corresponding to the thermal radiation of a body with a very low temperature of 2.7 °K - Fig.5-CMB a).
However, this is only the average temperature of the relic radiation. When sensitively measuring the intensity and spectra of CMBs from different directions in space, small anisotropies are actually observed- slight differences in spectra and intensities (when displayed they are visible as a number of warmer and colder spots), corresponding to small differences dT in temperature T - Fig.5-CMB b). They reach values of at most milliKelvins and correspond to regions with a greater or lesser density of matter in the early universe. These fluctuations are in all directions in the sky spaced seemingly chaotic, but detailed analysis - angular spectrum as described below, shows some patterns which may have a profound relationship with the early establishment of the "germs" of the large-volume structure of the cosmos (cf. also above passage "Fluctuation and acoustic oscillations in plasma") :

Fig.5-CMB. Properties of microwave relic radiation CMB.
a) The basic spectrum of relic radiation corresponds to the thermal radiation of an absolutely black body with a temperature of 2.7 °K.
b) Detailed map of small anisotropies of relic radiation scanned from various parts of the sky. It is shown in a cartographic pseudocylindric projection (Mollweid-Babinet projection), which is often used to display a global map - an atlas - of the entire globe, or an atlas of the stars of the entire night sky.
c) Angular spectrum of temperature fluctuations - dependence of amplitude dT of temperature-power fluctuations of relic radiation on their angular magnitudes df in the sky.

Angular spectrum of temperature fluctuations
The detailed map of relic radiation ( Fig.5-CMB b)) shows a large number of warmer and colder spots, which have different angular sizes and temperature differences. It is interesting to analyze their spectral representation statistically - how many spots of different sizes and temperature differences are in the sky. Fig.5.-CMB c) shows the angular spectrum of thermal anisotropies CMB, also called angular power spectrum. It arises from a basic detailed map of the distribution of small CMB anisotropies in the sky (b) by means of angular amplitude analysis: the angular range df in the sky *) is plotted on the horizontal axis, for which they are plotted on the vertical axis the average amplitudes of the temperature differences dT measured from the energy-wave spectrum of the CMB from the whole map in this angular range.
*) On the angular scale, it is customary to plot the values of the angles df in the reverse order, from large angles of 90° towards small angles of the unit and tenths of a degree. For detailed analysis of CMB angular spectra (instead of angular scale - angular degrees °), quantification using multipole moments l = 180/df (upper horizontal scale in Fig.5-CMB c) is often used, for which spherical harmonic analysis is performed. The sphere of the last scattering corresponds to an angle of about 1.5 °, or l ~ 110.
For large angles in the sky of the order of tens of degrees, there is only a small variability of amplitude fluctuations (at the beginning of the graph in Fig.5.-CMB c) this little interesting area is not drawn ), caused by the passage of CMB radiation in places with larger and smaller mass accumulation and gravitational potential in galaxies and galaxy clusters (late Sachs-Wolf effect). For smaller angular sizes of unit and tenths of a degree, significant peaks of increased anisotropies dT of temperature CMB are seen in the angular spectrum for certain specific small angular ranges that correspond to plasma acoustic oscillations at the end of the radiation era (their origin was discussed in the section "Fluctuations and acoustic oscillations"). in plasma substance"). For very small angular ranges below approx. 0.2 °, diffusion damping of fluctuations is significantly manifested, the peaks are still lower until they disappear. In very small angular ranges below approx. 0.05 ° (l> 2000), there are no longer any minor fluctuations in relic radiation...
Detection and display of relic radiation
Microwave relic radiation permeates the entire universe and is found all around us, but we cannot perceive it with our senses, the eye is insensitive to microwaves. Only highly sensitive electronic devices of high-frequency technology in the field of very short waves can register it. In the specially shaped wires - antennas - of these devices, microwave radiation induces weak electrical signals: alternating electrical voltage at high frequencies (tens to hundreds of GHz), which is amplified many thousands of times in electronic circuits and then its amplitude and frequency are evaluated.
The first detection of microwave relic radiation
In 1965, A.Penzias and R.Wilson discovered a cosmic radiation background while analyzing the noise of a radio telescopic receiving antenna - weak microwave electromagnetic radiation, which comes isotropically from all directions of the sky, is non-polarized, long-term constant (independent of the season). Further measurements showed that its spectrum corresponded to the radiation of an absolutely black body at a temperature of about 2.7 °K. It is a relic radiation, a "cooled" remnant of the radiation era after the Big Bang, the "thermal afterglow" of the Big Bang.
Two types of detectors are used to measure weak microwave relic radiation :
1.Direct radio detection of electromagnetic waves
The weak AC electrical signal from the receiving antenna is transmitted by a line to a low-noise preamplifier (using, for example, single-electron transistors and HEMP heterostructure transistors with high electron mobility). Then it is amplified as standard and electronically evaluated by high-frequency electronics methods. The advantage of radio detection is good frequency - spectral - resolution, insensitivity to cosmic radiation, lower demands on cryogenic cooling. For direct radio detection of the highest frequencies >100 GHz of CMB submillimeter waves, today's low-current electronics do not yet have fast enough electronic components.
2.Thermoelectric - bolometric - photon detection
Therefore, thermoelectronic techniques are used for the very high-frequency regions of hundreds of GHz, already approaching the thermal infrared range. It is not the electronic amplification of the signal from the incident wave, but this electromag. wave (stream of photons) is absorbed and converted into heat, increasing the temperature of a small plate, which is sensed by a highly sensitive termistor - called bolometers (its function is described in detail e.g. in §2.5, "Semiconductor detectors", section "Microcalorimeter detectors", Fig.2.5.2 in book "Nuclear physics and physics of ionizing radiation"). The detection element consists of an absorbent material (a thin layer of metal) with a small heat capacity, in which the absorption of radiation causes an increase in temperature. This temperature increase is measured by a thermoresistor with a high temperature coefficient. The detection element itself is cooled to an average temperature significantly lower than the temperature of the incident radiation (to about 0.1 °K) . Particularly sensitive is the use of the sharp onset of superconductivity of some materials in the temperature range of tenths of °K - TES (Transition Edge Sensor).
For sufficiently sensitive measurement of slight temperature differences of relic radiation (expected at the levels of microkelvins) it is necessary the input preamplifiers and bolometric detectors to reduce noise cooled using liquid helium to temperatures close to absolute zero (for superconducting bolometers, this is of course a basic condition for their operation...).
The display of relic radiation consists in measuring the relic radiation (its intensity, wavelength, or polarization) from many different directions and in drawing an astronomical map of the sky in these quantities - Fig.5-CMB b). The primary display element of a relic microwave radiation detector is a telescopic lens - a spherical or parabolic mirror, or a refractive lens, which creates an optical image of microwave radiation into the focal plane. A microwave radiation detector - antenna - is placed in this focus. Either it is a single detector and the image is achieved by rotating the lens to different angles. For more complex systems, the whole field - a matrix of detectors ("antennas") is used, which captures the CMB image at once in the entire field of view of the lens.
The basic measurement consists in detecting the intensity of the CMB in several frequency bands, which in the imaging mode will provide a map of the isotropy of relic radiation in terms of intensity and spectrum. Against the background of the global isotropy of relic microwave radiation (with sufficient sensitivity of the apparatus) areas of slight fluctuations are displayed - small anisotropy of CMB in the places of galaxy germs - Fig.5-CMB b).
Differential microwave radiometer
To display the spatial distribution of intensity and small fluctuations of microwave radiation, it is appropriate, instead of independent measurement of beams from individual directions, to use simultaneous measurement of two beams from different angles using a pair of identical radiometers suitably electronically connected to generate the signal difference - so-called differential microwave radiometer. .................
The measurement of the polarization of microwave radiation is performed by means of a suitable design of the antennas, in which the signal after passing through the antenna is divided into responses from two perpendicular directions. It can be a warp of wires stretched in two mutually perpendicular directions, or a warp of perpendicular bolometric strips, or the received signal can be split and guided for detection by two waveguides perpendicular to each other. Such antennas show maximum sensitivity to radiation polarized parallel to their direction, so that by electronically evaluating the response from both parts, the direction of polarization of incident radiation can be determined (differences in relic radiation polarization are expected very small; however, most of the polarization of the observed microwave radiation originates from the magnetized interstellar dust in the Galaxy...).
Millimeter electromagnetic waves are strongly absorbed in water, so they are partially absorbed even in atmospheric humidity in the atmosphere. Therefore, areas with a minimum of water vapor are suitable places for the detection of microwave relic radiation :
1. High mountain areas. 2. Desert regions - dry air. 3. Polar regions where water vapor in the atmosphere "freezes" at low temperatures.
In these places, the construction of complex devices for the detection and analysis of relic microwave radiation is being installed or planned.
However, the most suitable place for CMB detection is, of course, the universe - space probes. They were in orbit with an interval of 6-10 years four space probes measuring microwave radiation from space have been launched :
Relikt (.........)
was the first spacecraft to (in addition to another research program) to detect and image microwave radiation from space. It was launched in 1983 as part of the USSR space program - Prognoz 9 satellite. It orbited on a very eccentric orbit (1000 km perigeum, 750,000 km apogeum) with an orbital period of 26 days. Its differential microwave modulating radiometer operated in the frequency band 37.5 GHz with an angular resolution of 5.8° and a differential sensitivity of approximately 25 mK. In addition to finding some weak diffuse radio sources, only the dipole anisotropy of microwave radiation of kinematic origin, caused by the motion of the satellite reference system with respect to the reference system of relic radiation, was measured. However, the sensitivity of the device was not enough to detect primary CMB anisotropy ...
COBE (Cosmic Background Explorer)
was the first spacecraft to sensitively detect and image microwave radiation from space. It was launched in USA - NASA in 1989 on a polar geocentric orbit and worked for 4 years. A spectrophotometer for measuring the spectrum of relic radiation, a differential microwave radiometer and a broadband infrared detector were installed on board the satellite. In addition to the detection of several galaxies in the region of long-wave infrared radiation (infrared detector), the spectrum of relic radiation was accurately measured, which corresponded to the radiation of an absolutely black body with a temperature of 2.7 °K. During a measuring period of 4 years, a differential microwave radiometer created a map of the microwave radiation of the entire sky, on which (after filtering out other radiation sources) the anisotropy of microwave relic radiation was first displayed. Relic radiation fluctuations were measured with an angular resolution of 7° and a differential sensitivity of about 0.4 mK.
WMAP (Wilkinson Microwave Anisotropy Probe)
was designed for sensitive measurement of relic radiation fluctuations. It was launched by NASA in 2001 and introduced into the L2 Lagrange point (of Earth-Sun system, at a distance of about 1.5 million km from the Earth), the measurements took place until 2010. A differential microwave radiometers are located in the focal plane of two mirror telescopes (primary mirrors 1.4x1.6 m, secondary mirrors 0.9x1.0 m), which sense radiation from two opposite directions. Measurements are performed at various frequencies in 5 radio frequency bands, from 23 GHz to 94 GHz. The WMAP probe was a significantly improved continuation of the COBE probe - fluctuations of relict radiation were measured with an angular resolution of 0.35° and a differential sensitivity of about 20 mK (ie with more than 30-times better parameters than COBE). After filtering out other radiation sources, this created a detailed picture capturing the own - primary - anisotropy of relic radiation, originating from the sphere of the last scattering at the end of the photon era. In this picture, in addition to the visual evaluation, it is already possible to quantitatively analyze the regularities in the angular spectrum of temperature fluctuations CMB (according to Fig.5-CMB b, c).
Planck (the name is based on the physics of M. Planck, who based on the analysis of the radiation spectrum of a black body founded the concept of energy quantization in physics)
was launched by the European Space Agency in 2009 and also placed close to the L2 Lagrange point, it was operated until 2013. To focus microwave radiation, the Planck probe uses one mirror telescope (primary mirror 1.56x1.1 m, secondary mirror 1.05x1.1 m), in the focal plane of which sensitive detectors of two different technologies are located: "Low-frequency" radio detection system operating in range 28.5-70.3 GHz divided into 3 bands, and a high-frequency detection system consisting of bolometric detectors (cooled to 0.1°K), operating between 100-857 GHz, divided into 6 bands. The Planck probe was an improved continuation of WMAP - it measured in a very wide frequency range of 9 frequency bands from 28.5 to 857 GHz and had a significantly higher temperature sensitivity of 2 mK and a better angular resolution of 0.06° (especially in the high frequency range).
Various components in microwave radiation
In the area of centimeter and millimeter waves, radiation of various origins, not only relicts, comes from space. And this radiation is further affected by some astrophysical circumstances. There are several steps to extract the actual (primary) relic radiation :

The basic image of microwave radiation from space at lower resolution shows a homogeneous distribution from all directions of the sky. Cosmic microwave radiation appeared so isotropic to the first pioneers A.Penzias and R.Wilson in the 1960s, as well as in further measurements until the late 1970s. It is not marked here artificial light bar in the middle, coming from the belt of our Galaxy.
A more sensitive measurement shows a dipole anisotropy of kinematic origin, caused by the movement of the observer - our solar system - against the cosmic background of the CMB. We are traveling at a speed about 370 km/s relative to the cosmological reference frame. This movement results in a "dipole" anisotropy (amplitude of about 3 mK) of the measured radiation, which appears slightly warmer in the direction of movement than in the opposite direction. These are the Doppler velocity red and blue frequency shift.
After correction for kinematic anisotropy, measurements with higher resolution show local fluctuations, which are dominated by the belt of our galaxy (Milky Way). Microwave radiation is generated there by electron-ion scattering, synchrotron radiation of fast charged particles in a galactic magnetic field, and thermal radiation of dust.
After subtracting the galactic foreground and further increasing the sensitivity and resolution, a detailed image is created capturing the self - primary - anisotropy of relic radiation, originating from the sphere of the last scattering at the end of the photon era. In this picture, in addition to the visual evaluation, it is already possible to quantitatively analyze the regularities in the angular spectrum of temperature fluctuations of the CMB according to Fig.5-CMB b, c.

Anomalies in the distribution of background radiation
On the detailed map of small anisotropies of relic radiation sensed from various places in the sky in Fig.5-CMB b) are, in addition to the random statistical alternation of small warmer and colder districts, to see even some anomalies - larger areas mainly of reduced temperature of registered microwave radiation, a kind of "cold spots". The deepest cold spot (-70 mK) is located on the southern edge of the CMB map, the other two larger ones (but less deep, about -30 mK) are almost in the middle and on the right edge.
An unambiguous explanation for these anomalies is still lacking. A promising explanation could be based on the existence of large "voids" (see Fig.5.5) between us and the cold place shown. The integrated Sach-Wolf effect would then reduce the energy of the transmitted CMB photons. There have also been "exotic" speculations that it could be a place of collision of our universe with another universe within the concept of multiversa..?..
A masterpiece measuring astrophysics techniques
Accurate detection, spectrometry and imaging of relic microwave radiation from space is a very difficult task requiring state-of-the-art technology at the very limits of possibilities. Metaphorically, it can be said that a detailed map of small anisotropies of relic radiation displayed from various places in the universe (Fig. 5-CMB b) and other details) is "masterpiece of art" of measuring astrophysical techniques..!..
Informations carried by relic radiation
Liberated photons of relic radiation have properties formed during the last few interactions with the original plasma and thus carry information about conditions about 380,000 years after the origin of the universe - from the realm of last scattering. Information about earlier events in the universe is not directly contained in them, but we can try to reconstruct them theoretically, by comparing model predictions of the then behavior of the universe and their reflection on the distribution of matter at the time of recombination with the measured data on microwave radiation.
So what can we find out from relic radiation? First of all, by measuring the spectrum, ie the dependence of the radiation intensity on the wavelength, we find that the relic radiation is really the radiation of an absolutely black body with a Planck spectrum at a temperature of 2.73 °K. This shape of the spectrum could only have arisen due to the thermal equilibrium between photons, electrons and baryons in the early universe, at the time of CMB creation - its emission. It is convincing proof of the concept of the hot early universe, the idea of the Big Bang. Its practically isotropic distribution proves the legitimacy of the basic cosmological assumption that the universe is truly homogeneous and isotropic on a large scale (and can be modeled as Fridman's universe).
Accurate measurement of the spectrum - wavelength, temperature - relic radiation allows (in co - production with the measurement of cosmological redshifts of spectra) to specify the age of the universe. On larger scales, this radiation is isotropic *) with the indicated temperature, but at smaller angular dimensions there are small fluctuations (at the level of only tens of microkelvins) initiated by the expected inhomogeneities of the substance during recombination (discussed above in the section "Phase Transitions in Space"). These micro-kelvin fluctuations in relic intensity are measured by high-resolution satellite instruments. This creates a detailed microwave map of the large-scale structure of the universe - Fig.G5-CMB b), which captures the germs from which galaxy clusters and galaxies probably later formed. It turns out that there is a correlation between the thermal anisotropies of relic radiation and the large-scale structure of the universe.
*) Global isotropy applies to an observer who is at rest due to the cosmological expansion of the universe. However, as our Earth orbits the Sun (average speed 30 km/s) and our solar system orbits the center of the Galaxy (at a speed of about 220 km/s), a slight anisotropy of relic radiation is observed . However, this anisotropy is of purely kinematic origin and has nothing to do with the actual astrophysical properties of relic radiation. Another minor distorting component is microwave radiation from the Galaxy. For accurate measurements of CMB properties, these kinematic and galactic effects must be subtracted from the native measured data and the remaining small but true astrophysical anisotropy of relic radiation must be analyzed (discussed above in the section "Various Microwave Components").
Acquisition - specification, verification - of cosmological parameters from relic radiation
The properties of detected relic radiation are naturally dependent on physical processes in the early and later universe and on the dynamics of cosmological evolution. This is described by cosmological models, so, conversely, from the properties of relic radiation, it is possible to determine which values of cosmological parameters best correspond to the measured spectra and angular distributions of the CMB. The current standard cosmological model LCDM has 6 main parameters; CMB properties also have something to say about some of them. For this purpose, the curve of the angular distribution spectrum of the relic radiation fluctuations in Fig.G5-CMB c) is particularly suitable. Using computer modeling, we change the selected investigated parameter in LCDM and observe "what it will do" with the angular spectrum of CMB fluctuations; we try to find such a value of the given parameter for which the best agreement with the measured curve is achieved (using the least squares method or statistical Bayes analysis) :
- Baryon density
As shown in the section "Fluctuations and acoustic oscillations in plasma", the rate of propagation of density oscillations in plasma (speed of "sound") v_s is a function of baryon density - by the higher the density of baryons, the lower the speed of "sound". Since the pressure in acoustic oscillations is given by the speed of sound, at lower value of sound speed, ie higher density of baryons, higher amplitudes of the main acoustic peaks in the angular spectrum of CMB fluctuations should occur (other peaks for smaller angles are reduced due to diffusion damping of inhomogeneities). The best agreement with the measured spectrum is achieved for W_B » 0.05, ie for the representation of baryon mass about 5% in the total critical mass-energy density of Fridman's cosmological model.
- Mass density
The main share of fluctuations in the spectrum of angular anisotropy of CMB energy comes from the period of transition of the era with radiation dominance to the dominance of matter, near the recombination period. The gravitational potential decreases here, temperature fluctuations increase and the timely Sachs-Wolf effect makes a significant contribution to the angular power spectrum. Since this transition period depended on the mass density ~ W_M .H², the effect of increasing the amplitudes by fluctuations is more pronounced on larger angular scales (smaller l ) for smaller values of mass density. Amplitude fluctuations in the angular spectrum of energy is therefore at an angle range of about 1° -2° (Multipole l ~ 110 - the last scattering sphere) increases, including the acoustic amplitude of the first peak, with decreasing mass density W_M. The fit shows the best agreement with the measured angular spectrum according to Fig.G5-CMB c) for W _M » 0.2 .
- Spatial curvature
The angular spectrum of power fluctuations CMB also depends on the spatial curvature of the universe, which modifies the observed (apparent) angular magnitude of distant objects. Compared to the basic case of flat space, the observed apparent magnitude of the same fluctuations in the last scattering sphere increases or decreases for a positively or negatively curved outer space. As a result, the acoustic peaks and the decrease by diffusion damping in the angular spectrum generally shift towards larger or smaller angles df (or vice versa to smaller or larger multipolarities l ). The fit in the cosmological LCDM model gives the best agreement with the measured angular CMB spectrum for the value W_K » 0, ie for the spatially planar universe.
- Character of primordial inhomogeneities - adiabatic versus entropic
Primordial perturbations, probably originating from the inflationary period (discussed in §5.5 "Microphysics and cosmology. Inflationary universe."), can be basically of two types: adiabatic and entropic (isocurvaturic) - were described above in the section "Fluctuations and acoustic oscillations in plasma matter".". Did these primordial "seeds" arise for the formation of cosmic structures only as changes in the representation of various types of particles and radiation, or were they also local compaction of matter-energy? For adiabatic and entropic modes of acoustic oscillations, the difference p/2 is in the oscillation phase, so that on the angular spectrum of CMB fluctuations the positions of the peaks for the entropic character correspond to the valleys for the adiabatic regime and vice versa. Accurate measurements of the CMB angular distribution indicate the adiabatic nature of primordial inhomogeneities.
- Reionization - optical depth CMB
Intergalactic gas, which by the process of recombination (approximately 380,000 years after the beginning of the universe) became neutral and transparent to radiation, was later partially re-ionized by UV radiation from the first stars and active galactic nuclei. From astronomical surveys of distant objects, it is estimated that this reionization process was completed at z ~ 0.5-0.6. Free electrons in this ionized gas then scatter photons of CMB relic radiation, cause partial opacity of the space environment - Sunaev-Zeldovich effect. This effect causes attenuation in the CMB angular power spectrum. The magnitude of this attenuation is exponential and is expressed as exp(- t), where t is the so-called optical depth of Thomson scattering. In the angular power spectrum, the optical depth is manifested in such a way that for larger t (approx. 0.5) the overall amplitude of the peaks of acoustic oscillations decreases, while in the region of larger angles (small l) the amplitude remains roughly the same; this relative compensatory increase in anisotropy for larger angles is due to the Doppler effect in peculiar motions of large areas with more ionized gas. The measured spectrum best corresponds to the value of the optical depth t ~ 0.09, indicating a relatively small effect of reionization on the propagation of relic microwave radiation.
" Window " to the early universe
Overall, relict microwave radiation, as the oldest "light" or electromagnetic wave (originally a light), is currently the most important source of information about the early universe, bringing unique information from a time when there were no stars or galaxies, not even atoms and molecules, there was no substance similar to the one we know and from which we and everything around us are composed. It brings information from the time when the conditions for the formation of the currently observed structures in the universe were just being established, and indirectly it may also bring information from the events of the very origin of the universe. The astronomy of microwave radiation is such a unique "observation window" into a very early universe, which will undoubtedly open more and more with the advancement of detection technologies...
From a cosmological point of view, it is particularly interesting to compare - to correlate distribution of small structures-inhomogeneities at the time of recombination, observed by CMB fluctuations, with astronomical observations of the current large-scale clustering of galaxies (extensive sky surveys with statistical evaluation). It helps to better analyze the dynamics of the expansion of the universe during the entire long period of its existence ...

Cosmological parameters
We describe the structure and evolution of the universe using a number of so-called cosmological parameters - global astrophysical quantities quantifying the most important properties of the universe. These are mainly: the speed of expansion of the universe and its dynamics (deceleration or acceleration); composition of the universe (representation of baryonic and dark matter, dark energy, radiation, neutrinos); significant critical values determining the basic behavior of the universe; degree of inhomogeneities (fluctuations) of mass and spatial curvature; the time of separation of radiation from the substance; the rate and time period of intergalactic gas reionization.
Cosmological parameters are then part of a certaincosmological model, here the standard cosmological model LCDM.
The most accurate values of the cosmological parameters determining the structure and evolution of the universe are now obtained by co-producion of two or three different areas of astronomical measurements :
- Extensive astronomical observations of galaxy distribution and cluster, their photometry and spectrometry, including cepheids and supernovae Ia.
- Sensitive measurements of microwave relic radiation, especially spectra of angular distribution of CMB anisotropies.
- Recently, the detection of gravitational waves has begun to contribute to this.
Using computer modeling of the results of all these measurements, detailed values of important cosmological parameters were obtained (from the point of view of the current universe) :

Parameter	Value	Variance
Hubble constant (current value)	H ₀ = 70.4 km s ^-1 Mpc ^-1	± 2%
The age of the universe	t ₀ = 13.8 . 10 ⁹ years	± 0.015%
Density of baryons	W _b = 0.0456	± 3.51%
Density of dark matter	W _dm = 0.227	± 6.1%
Density of gravitational matter	W _m = 0.31	± 0.0062
Critical density of gravitational matter	r _crit = 8.62. 10 ^-27 kg / m ³	± 1.4%
Dark energy density	W _L = 0.728	± 2.2%
Proportion - density - radiation	W _rad = 0.005
Neutrine density (at neutrino mass)	W _n <0.0012 ( S m _n <0.6 eV)
Spectral index of mass fluctuations	n _s = 0.96	± 0.4%
Mean quadratic mass fluctuation (in the sphere 8 h ^-1 Mpc)	s ₈ = 0.81	± 10%
Amplitude of space curvature fluctuation (k ₀ = 0.002 Mpc ^-1 )	D _R² = 2.44 . 10 ^-9	± 3.6%
Redshift in separation time	z _rec = 1090	± 0.2%
The age of the universe in the time of separation	t _rec = 377700 years	± 0.8%
Optical depth of reionization	t _reion = 0.087	± 16%
Red shift of reionization	z _reion = 8.5	± 12%

Reconciling all the results of astronomical measurements and determining the most probable values of cosmological parameters from them is a demanding computer task. It uses a Bayesian statistical analysis and multiparametric Fisher matrix.
The specific values of cosmological parameters (and their selection and modification) differ somewhat in the literature; based on the results of increasingly sensitive astronomical measurements, they are continuously updated.
Astrophysical significance of cosmological parameters
Briefly - in terms of words - here we summarize what the individual cosmological parameters describe and what is their significance for the structure and evolution of the universe :
- > Hubble's constant H , resp. its current value of H₀, is the coefficient of proportionality between the distance of an astronomical object and the expansion rate of its receding. It is the most basic parameter of the expansion of the universe, used from the very beginning of building relativistic cosmology (§5.1 "Basic starting points and principles of cosmology", relation (5.2), and §5.3 "Fridman's dynamic models of the universe", relation (5.24)). Sometimes it is also used the so called called reduced dimensionless Hubble constant H = H₀/100 km s^-1/Mpc.
-> Age of the universe t₀ derived from the dynamics of the expansion factor a(t) - from the origin of the universe (big-bang t = 0) to the present (t = t₀). Ways to determine the age of the universe are discussed in §5.1, section "Size and age of the universe".
-> The density of baryons expressed by the parameter W_b , which determines the course of the initial nucleosynthesis (described above in the section "Primary cosmological nucleosynthesis"), leading to the basic composition of the universe.
-> The density of dark matter described by the parameter W_dm , which in the sum with the baryon mass W_b gives the total density of the gravitational mass W_m, determining according to Fridman's equations the dynamics of global expansion of the universe. And then also the dynamics of galaxy formation, their motion and evolution (dark matter is discussed in §5.6, section "Hidden-dark matter").
-> Critical density of gravitational mass r_crit (5.26), for which the universe would be spatially planar, expanding exactly at the escape velocity.
-> The density of the dark energy , described generally by the parameters W_de, in the LCDM model then the parameter W_L - dark energy is modeled by cosmological constant L.
Note: The omega-parameters of the relative density of baryon and dark matter are sometimes multiplied by the reduced Hubble constant h, and the resulting parameters W_b .h² and W_dm .h² are called the "physical" density of baryon and dark matter.
-> Density - representation of radiation W_rad was dominant in the early universe, especially in the radiation era. Since during the expansion of the universe the radiation decreased faster (r_rad ~ a^-4) compared to the density of other matter (r_m ~ a^-3), the proportion of radiation decreased to the current only 0.05 %.
-> The density of neutrinos W_n is not yet exactly known, they are only estimates of the upper limit. Besides estimating the number depends on the neutrino rest mass neutrinos, which is very small, was measured only an upper limit of about 0.2 eV (neutrinos is discussed in detail in "The neutrinos - "ghosts" inter particles" §1.2 monograph "Nuclear Physics, ionizing radiation").
The above parameters of density - the relative representation of different types of matter in the universe - changed significantly during evolution (current values are given in the table above). They resulted in the representation of matter according to the illustrative diagram in §5.6, passage "What is the basic composition of universe?".
-> Scalar spectral fluctuation index of material of n_s describing the relative representation - the spectrum - inhomogeneities of different sized mass-energy density. These inhomogeneities primordial possess approximately scale-invariant spectrum, n_s ~ 1.
-> Mean square fluctuation of the mass parameters described above s₈ - the mean square fluctuation of the mass in the sphere having a radius of 8h^-1 Mpc (chosen because it roughly corresponds to the typical scale massive cluster galaxies). The value of s₈ is around 0.8 .
-> The amplitude of space curvature fluctuations D_R² expresses the magnitude of changes in space curvature induced by mass-energy density fluctuations. Similar to inhomogeneities in mass density (spectral fluctuation index and mean square mass fluctuation) is quantified by Fourier analysis. The scale of the wave coefficient k is normalized here to k₀ = 0.002 Mpc^-1 (corresponds roughly to a multipole value of l ~ 30 in the angular spectrum of temperature fluctuations CMB in Fig.5-CMB c)).
Note: Mass-energy fluctuations, their influence on the formation of structures in space and parameters for their quantification were discussed above in the passage "Fluctuations and perturbations in cosmic matter".
-> Red shift in the time of radiation separation from matter , or recombination, z_rec , which corresponds to the age of the universe at the time of separation t_rec.
-> Optical depth of reionization of space gas t_reionby ionizing radiation of stars, supernovae and quasar associated with the formation of galaxies and stars in the universe. It is the mean free path traveled by the photons in the universe than they are scattered (the first scatter is taken) for electrons (re) ionized intergalactic gas - "optical thickness" of the cosmic environment.
-> Red shift of reionization z_reion indicating the time period when this reionization occurred.
Some cosmological parameters are interdependent, derived. In the current categorization, the standard cosmological model LCDM is described by 6 basic parameters (the choice of some of these parameters as basic, among several other alternative global space parameters, is sometimes debatable...): baryon density, dark matter density, age of space, scalar spectral fluctuation index and optical depth of reionization. In principle, other parameters can be calculated from these 6 parameters (it can be model dependent ...). E.g. from the parameters of the density of baryons W_b and the density of dark matter W_dmby substituting into Fridman's equation (5.38) we can get the value of Hubble's constant H...
In the above table we have arranged the cosmological parameters according to the immediate astrophysical influence on the evolution of the universe and the gradual formation of structures, not according to the formal "basicity" ...

How fast is the universe expanding? - accurate measurement of the Hubble constant
The basic cosmological phenomenon of the expansion of the universe is expressed using the Fridman equations (5.23a,b), which determine the time evolution of the expansion factor a(t) of the spacetime geometry. This evolution of the universe can also be equivalently expressed using the Hubble velocity parameter H (as it was derived in §5.3, the passage "Fridman's equation of the evolution of the universe") - the coefficient of proportionality between the distance of the object (galaxy) and its receding speed. It is the speed at which any distant object is swept away from the observer by the expansion of intergalactic space itself.
The Hubble expansion parameter is generally a function of time H(t), but equivalently it can also be expressed as a function of redshift H(z). Within the framework of the current most complex cosmological model LCDM (discussed above in the passage "Stages of the evolution of the universe") and its Omega-parametrization (§5.3, passage "OmegaParametrization"), this functional dependence H(z) of the Hubble expansion parameter on redshift z :
H(z) = H₀ × sqrt[O_rad(1+z)⁴ + O_m(1+z)³ + O_k(1+z)² + O_L] ,
containing omega-parameters representing various components of matter~energy contained in the universe and contributing to the dynamics of expansion (W_rad is the contribution from radiation and relativistic particles, O_m expresses the density of non-relativistic matter, O_k the contribution of the geometric curvature of space, O_L the representation of dark energy induced by the cosmological constant L).
The current value of the expansion (at z=0) is called the Hubble constant H₀ - it indicates the current rate of expansion of the universe. The Hubble constant is constant only in a given time, its value changes during the evolution of the universe. Accurate measurement of this parameter H₀ is important for the analysis of the evolution of the universe. With the gradual improvement of the astronomical measuring technique, the value of the Hubble constant H₀ was constantly refined, it settled at a value of around 70 km s^-1Mpc^-1.
Currently, three diametrically different methods are available to determine the exact value of the Hubble constant :
-> The classical method of "standard candles" - study of the radiation of suitable bright stars (pulsating Cepheids, type Ia supernovae) in distant galaxies, for which their distance can be determined (see "Ladder of cosmic distances" in §4.1) and at the same time using the red shift in the spectrum their electromagnetic radiation and the speed of their receding. This is the basic straightforward method of investigating the expansion of the universe, its results are the most plausible, model-independent of the cosmological model.
-> Analysis of relict microwave radiation - slight differences in the temperature map of relict radiation (it was discussed in detail above in the section "Relict microwave radiation - a unique messenger of messages about the early universe"). Clustering due to baryon "acoustic" oscillations, which are later reflected in the distribution of galaxies - the probability of finding them at a certain distance from other galaxies - is analyzed. As the universe expands, this characteristic distance widens, making it possible to measure the Hubble constant (as well as the density of dark matter). It is an indirect and strongly model-dependent measurement of the Hubble constant. However, detailed analysis of relict microwave radiation is generally very beneficial for understanding the large-scale structure and evolution of the universe.
-> Simultaneous detection of gravitational waves + electromagnetic radiation from the fusion of very massive bodies, during which both intense gravitational waves and the emission of electromagnetic radiation arise. They cannot be two black holes (where only gravitational waves are produced, but no electromagnetic ones), but two neutron stars (discussed in §4.8, passage "Neutron Star Fusion"). The analysis of the incoming gravitational waves will make it possible to reveal the gravitational details of the collision - the mass of the bodies, the released energy of the waves, the distance of this collision can be deduced from the intensity of the detected gravitational waves. From the measurement of electromagnetic radiation, its red spectral shift can then be determined. The Hubble constant is then determined from the receding speed and distance determined in this way. This method of combining gravity and electromagnetic waves is sometimes called a "standard siren". It is an objective model-independent method of measuring the expansion of the universe. These multimodality observations are few so far, they led to a preliminary value of about 70 km s^-1Mpc^-1, but with a large statistical uncertainty... Future multimodality detection of gravitational waves from neutron star mergers will surely refine these values.
It would be optimal if all three methods lead to approximately the same value of the Hubble constant. However, current measurements using "standard candles", Cepheids and supernovae, give a Hubble proportionality coefficient of 73 km s^-1Mpc^-1, while measurements of the cosmic microwave background (by the Planck Space Observatory) give a slightly lower value of 67 km s^-1Mpc^-1. A few years ago these differences would have been considered negligible. However, with the current improved measurement methods, these differences significantly exceed the declared measurement errors (which are estimated at about 1%). This discrepancy is now widely discussed, it is often called Hubble tension.
If this is not a measurement error, it could indicate that we are missing something in the standard LCDM cosmological model, some mysterious circumstance of how our universe expanded during its existence. Cepheid and supernova data suggest somewhat faster expansion (73 km s^-1Mpc^-1) of the relatively closer universe than cosmic microwave radiation analyzes for the outermost regions of the cosmos (a somewhat slower expansion of 67 km s^-1Mpc^-1) indicate. Why is the universe in our relative proximity (up to a distance of about 3 billion light years) expanding somewhat faster than the rest of the distant universe ?
One of the possible explanations could lie in a special astronomical configuration of anomalous irregularities in the mass distribution: that we are with our Galaxy in a region of space where there is relatively somewhat less matter - in a kind of local hypodensity "bubble". The density of matter around this bubble is higher, so this surrounding matter gravitationally pulls the galaxies in the bubble towards the edges of the bubble. Therefore, they are moving away from us faster than the average cosmological expansion would correspond. There is also speculation about an unknown form of dark energy that could have been at work in the beginnings of the universe or even about a revision of the theory of gravity (such as MOND - critical discussion in §1.2, passage "Galactic modification of Newton's law of gravity - MOND" - probably not!)..?.. It is not yet known...

Difficulties and problems of the standard cosmological model (non-inflationary)
Although the standard cosmological model describes the evolution of the universe very convincingly and is now almost universally accepted, there are some controversial issues and problems in its original (non-inflationary) version . This is their "key word" list :
- Problem initial singularity
- Problem spatial flatness of the universe
- Problem of horizon - global homogeneity and isotropy of the universe
- Problem baryon asymmetry of matter in the universe
- Problem absence relict magnetic monopoles and other exotic particles
- Problem initial inhomogeneities necessary to later formation of galaxies and large-scale structures of the universe
- The problem of large numbers and Planck scales
We will mention here some of them, as well as attempts to solve them first in conventional cosmology, then in the next §5.5, based on the model of inflationary expansion of the very early universe .

Problem initial singularity
The most fundamental problem, both physically and from a philosophical point of view, is the problem of singularity at the begining of the universe and the related finiteness of the universe in time. If we go back in time, at the beginning of the universe the temperature and density of matter will increase enormously, as well as the curvature of spacetime, beyond all limits, everything will diverge to infinity, a singularity arises. According to Fridman's cosmological models, the universe had its singular beginning in each case (and if r > r_crit, it will have its singular end), while the laws of conservation of electric, baryon, and lepton charges, as well as some philosophical arguments, speak in favor of the eternal existence of the universe.
Therefore, attempts were made to "save the eternal universe" and thus avoid the problem of emergence, ie the question "what was when there was nothing yet?". One such attempt is a model of the so-called oscillating universe taking a literal solution (5.33), geometrically represented by cycloids and interpreted as meaning that in a closed universe the big bang is not the beginning of evolution and the "big crash" the end of evolution, but the universe undergoes an infinite sequence of cycles expansion and shrinkage (Fig.5.6a). However, this idea has two shortcomings in principle :
The first is geometric-topological: if GTR applies, the universe must undergo a singularity during shrinkage (as follows from Hawking's and Penrose's theorems, especially from Theorem 3.6, see §3.8), for which the solution can no longer be analytically extended. There is no known any mechanism, by which the universe would begin to expand again after reaching singularity (at least not as "the same universe").
The second problem stems from thermodynamics: if the 2nd law of thermodynamics is fulfilled, the entropy of matter in the universe increases monotonically during both expansion and contraction (a particularly significant increase in entropy occurs during star formation, nuclear reactions and gravitational collapse). Leaving aside the speculation about the "delivery of negative entropy" by the singularity, the entropy from one cycle to another increases by a finite non-zero value. Therefore, successive cycles cannot be the same. In each subsequent cycle, the energy per baryon is greater than in the previous cycle, so the size of the maximum radius is also larger. Due to the growth of entropy, the evolution of the oscillating universe would look as shown in Fig. 5.6b - the amplitude and period of individual cycles is constantly increasing. Since in the present universe matter has finite entropy, the universe could only go through finite number of such cycles.
Thus, the model of the oscillating universe is not able to express the eternal existence of the universe from t = -¥; the problem of the origin of the universe only pushes further into the past. According to the findings of contemporary astrophysics, it seems that if the universe is closed, it is single-cycle *).
*) Current note: However, some new alternative hypotheses to the process of origin and evolution of the earliest phases of the universe introduce new research in superstring theory - see the passage "Astrophysical and cosmological consequences of superstring theory" § B.6 "Unification of fundamental interactions. Supergravity. Superstrings.".

Fig.5.6. Time dependence of the radius of a closed universe (r > r_crit) according to an oscillating model.
a ) The simplest idea of an infinite sequence of identical cycles of expansion and contraction of the universe.
b ) Due to the growth of entropy, the period and amplitude of the oscillations would constantly increase.

Contemporary cosmology is still very far from solving the problem of singularity and the creation of the universe, which is almost metaphysical in classical theory, although some hypotheses of "quantum cosmology" have already been stated (see the next §5.5 "Microphysics and Cosmology. Inflationary Universe."). It should be noted that in the standard cosmological model, the singularity arises from the strict "straightforward" extrapolation of the current behavior of the universe (Hubble's expansion) to the initial time t = 0 using the classical general theory of relativity. The resulting singularity is only a mathematical abstraction. In fact, in the early phases of the dense and hot universe, the quantum laws of gravity and other interactions played an important role (discussed above in the passage "Very Early Universe"). The inclusion of these quantum interactions in the cosmological model can remove the initial singularity - the universe did not have to be singular at first, although it could have a very high but final density and temperature (cf. also the discussion "Physical unreality of singularities" at the beginning of §3.7 "Spacetime singularities").

The problem of homogeneity and isotropy
Another problem of cosmology is the problem of global homogeneity and isotropy of the universe. In the light of the standard scenario of the origin and evolution of the universe, a non-trivial question arises: why is the universe so homogeneous and isotropic from a global perspective? There are basically two extreme options :

The first option would not be a reasonable explanation in principle, because it only shifts the cause of homogeneity and isotropy to a fundamentally unknowable initial singularity. Quantum effects also lead to the assumption that fluctuations causing inhomogeneities and anisotropy must have occurred in the initial phases. Therefore, in cosmology, a lot of effort was devoted to the research of models more general than Friedman's, ie anisotropic and possibly and inhomogeneous cosmological models, in an effort to find effective mechanisms for their "isotropization" during the expansion and transition to Friedman's already at early stage. In this way, perhaps it might be possible to explain the high homogeneity and isotropy of the universe that we observe.
The simplest anisotropic cosmological modelis an anisotropic homogeneous spacetime (universe) with Euclidean three-dimensional space, in which expansion in different directions can proceed at different speeds. The metric of such a model has a shape

where the difference of functions a, b, c, depending only on time, expresses the anisotropy of expansion. Einstein's equations for this metric (dots above a, b, c again mean time derivatives)

contain only relative velocities ^.a/a and the relative acceleration ä/a (similarly b and c ) of expansion in individual directions. Vacuum solutions of these equations (without the right-hand side) were found by Kasner in the 1920s [149]:

In this Kasner solution, only one of the three parameters p₁, p₂, p₃ remains independent. If we choose p₁ < 0, will be -1/3 L p₁ L 0 , 0 L p₂ L 2/3 , 2/3 L p₃ L 1- the expansion takes place in two directions Y and Z, while in the third direction X contraction occurs. Kasner's solution is applicable when the left side of Einstein's equations is substantially larger than the right-hand side; this is fulfilled especially at the very beginning of evolution around the singularity (dynamics here do not depend on the presence of matter - it is a "vacuum phase"). Further generalization to anisotropic inhomogeneous mode can be achieved by the features a, b, c in (5.50), respectively the parameters p₁, p₂, p₃ in (5.52) will vary from place to place. However, the results of the analysis of such models are quite ambiguous for a large number of variables.
The physical mechanisms of isotropization of the anisotropic early stage of the universe during further evolution can be classical or quantum. From the classical point of view, it can be shown that in the "hydrodynamic" equation of state of matter, a substance filling a universep = k.r (and therefore especially the hot space p = r/3) very soon prevail terms on the right side of the equations of which leads to a rapid transition Kasner anisotropic solutions in to Friedman isotropic solutions. From a quantum point of view, it is clear that in the vicinity of the singularity during anisotropic deformation of space, there must be a very intense formation of particles from a polarized vacuum. This spontaneous quantum production of particles near the singularity will affect the dynamics of evolution and can lead to a very efficient dissipation of anisotropy (there is a kind of quantum "vacuum viscosity").

Horizon problem
All these mechanisms can lead to local isotropization of the universe. However, in clarifying the global homogeneity and isotropy of the universe, we encounter another fundamental problem. A necessary condition for any physical processes in the early stages of cosmological expansion to ensure overall homogeneity and isotropy of the universe, is that all parts of the region in which homogeneity is to occur are causally connected during the operation of the balancing processes. Only then can inhomogeneities be compensated by proper "mixing" of the individual parts. According to the theory of relativity, only those areas that can be connected a light signal, can interact with each other. However, it exists in Friedman's cosmological model an optical horizon (having a radius of about c.t, where t is the time since the beginning of the universe), which is relatively small in the early period, so that areas that could interact with each other since the beginning of expansion were too small to ensure global homogeneity and isotropy of the universe *). However, relic radiation shows that already in the period t £ 10⁵ years from the beginning of expansion (and probably much earlier - at t £ 10³s, as the analysis of initial nucleosynthesis shows) the universe was highly homogeneous and isotropic on scales of many orders of magnitude larger than the c.t horizon in the standard model. That is the problem of the horizon or causality **).
*) As mentioned at the beginning of this §5.4, the earlier is the moment during the Friedman expansion according to the standard model, the smaller part of the existing universe is contained within the horizon. For example, areas of space just a few degrees apart in the present sky were not yet in causal contact at the end of the radiation era (when recombination and permanent separation of radiation from matter). In the Planckian period t » 10^-43s, when according to the expansion law of the standard model, today's observable universe was ~10^-3cm in size and the causal horizon was ~10^-33cm, the universe even consisted of ~10⁹⁰ causally separated parts!
**) Distant ("opposite") regions of the universe will fly from each other too fast, than to "have time to agree" that they should be arranged so that the universe will later show such perfect homogeneity and isotropy.

The problem of flatness - the precise tuning of the universe
Another global problem of the standard cosmological model is the mystery of global flatness, or the precise tuning of the early universe. We observe the universe as a whole on large scales as almost perfectly straight (only on local scales it is curved by the gravitational action of individual cosmic bodies). Size |r - r_crit|/r_crit , characterizing the degree of difference between the universe from the plane space, changes according to the law during expansion

as follows from equations (5.23) - (5.26). Although the current value of the average density of matter in the universe r is not yet known very accurately (0.05 r_crit < r < ~ 2. r_crit), the current value |r - r_crit|/r_crit cannot be too large, as follows moreover also from the anthropic principle (§5.6). In the early stages of the evolution of the universe, when, according to (5.31) it was ^.a^-2 ~ t, however, the quantity r - r_crit|/r_crit had to be very small; to the current radius of the universe a was greater than about 10²⁶ m, in the lepton era (t » 1 s) in quantity r - r_crit|/r_crit should not be greater than about 10^-8, and in Planck's time t » 10^-43s the universe had to be set to a critical density even with incredible accuracy greater than 10^-59 (!), if the expansion took place according to the standard cosmological model. Otherwise, the universe would either collapse long ago or, on the contrary, dissipate rapidly without the formation of galaxies.
Within the framework of the standard model does not explain why the universe in its earliest stages, had the density of matter with such extremely high accuracy equal to the critical density, or why the initial rate of expansion was so precisely "tuned" to the escape velocity..?..

The problem of seed inhomogeneities
From a global perspective, the universe is homogeneous, but in smaller scales, there are significant inhomogeneous structures - galaxies, clusters of galaxies, stars etc. In order for the observed galaxies and clusters of galaxies could by gravitational contraction arise, had in the earliest stages of evolution of the universe be some "germinal" inhomogeneities or density fluctuations must have existed, with a well - defined "spectrum" (in which the amplitude of the inhomogeneities is almost independent of their spatial magnitude). The standard model is also unable to explain the origin of these inhomogeneities.

The problem of baryon asymmetry
Outside from the possibilities of the standard cosmological model, there is also the problem of baryon asymmetry of the universe, ie the question of why there was already a small surplus of baryons over antibaryons in the hadron era, leading to the universe being filled only with matter - and antimatter almost non-existent; however, there should be the same number, all experiments in nuclear physics show that particle interactions always a combined production of particles and antiparticles, in a ratio of 1:1 (discussed above in the section "Stages of the evolution of the universe", passage "Very early universe" and "Standard Cosmological Model", which will be further mentioned in the following §5.5 "Microphysics and Cosmology", passage "Baryon asymmetry of space").

The problem of the absence of relict exotic particles
In the earliest stormy phases of the universe, according to unitary field theories, a large number of "exotic" particles should be formed (from our current point of view), such as magnetic monopolies , gravitin, ... Some of these particles are sufficiently stable and could would, as a relic, persist into later periods of the universe, even to the present. Why don't we observe them, nor their influence on the evolution of the universe?

The standard cosmological model is able to answer these problems (apart from the completely unsolvable problem of initial singularity *) only by the excuse that "the initial conditions were (by chance or by God's cause?) just such that the universe now has the structure as we observe". At other times, the "justification" of the initial conditions is given on the basis of the so-called anthropic principle discussed in §5.7 "Anthropic principle and the existence of multiple universes". The emergence of the universe of given properties from the singularity is, within the standard model, a phenomenon without any physical cause, which cannot be rationally explained in any way. It is therefore not surprising that the questions of the cause of the universe and the origin of its properties were often referenced to in the field of metaphysics, and even theology. The real physical solution of these questions will be discussed in the following §5.5 "Microphysics and cosmology. Inflationary universe.".
*) Again, it should be noted that the mathematical abstraction of the singularity is the result of extrapolation using the classical general theory of relativity, while at the inclusion of quantum laws of gravity and other interactions may not arise!

Examples of typical galaxy shapes :		Source : Hubble Space Telescope

Spiral galaxy	Elliptical galaxy	Irregular galaxy

Gravity, black holes and space-time physics :
Gravity in physics	General theory of relativity	Geometry and topology
Black holes	Relativistic cosmology	Unitary field theory
Anthropic principle or cosmic God
Nuclear physics and physics of ionizing radiation
AstroNuclPhysics ® Nuclear Physics - Astrophysics - Cosmology - Philosophy

Different stages of mutual interaction, collision and merger of two galaxies

Neighboring galaxies Tidal action Beginning of collision Slow merging stage After high-speed collision

Various regions and objects in universe :

Average density of matter in various regions and objects in universe :


5.3. Fridman's dynamic models of the universe		5.5. Microphysics and cosmology. Inflationary universe.

Physical cosmology - the origin and evolution of the universe