Cosmology - structure and development of the whole universe

AstroNuclPhysics ® Nuclear Physics - Astrophysics - Cosmology - Philosophy Gravity, black holes and physics

Chapter 5
5.1. Basic starting points and principles of cosmology
5.2. Einstein's and deSitter's universe. Cosmological constant.
5.3. Fridman's dynamic models of the universe
5.4. Standard cosmological model. Big Bang. Forming the structure of the universe.
5.5. Microphysics and cosmology. Inflationary universe.
5.6. The future of the universe. Time arrow. Dark matter. Dark energy
5.7. Anthropic principle and existence of multiple universes
5.8. Cosmology and physics

5.1. Basic starting points and principles of cosmology

Cosmology deals with the issue of the structure and development of the universe as a whole *) - a science standing on the border of astronomy, physics and philosophy. These are questions of the past of the Universe (or its origin), construction, development of the Universe and its future (duration or extinction). The dominant force in the universe is gravity. The physics of gravity and the structure of spacetime therefore play the most important role in cosmology and find significant application in it. In several paragraphs of this chapter, we will try to briefly analyze the basic principles and findings of relativistic cosmology, especially from this physical point of view (further details can be found mainly in [288], as wel as in [271], [200], [181], [215]).
*) The Greek word cosmos (cosmos) means world, universe (Latin synonym univesum); originally order, harmonic system (opposite of chaos), also ornament, beautiful jewel. The current usual meaning of Greek. cosmology (cosmology) = doctrine of the world, the universe. Related areas such as cosmogony (the science of the origin of celestial bodies, especially planets) or cosmography (the "topography" of celestial bodies) are based on the same ethymology. And also cosmetics in the sense of external beautification.

Mystical cosmology
From time immemorial, people have been interested not only in the problems of present life and local properties of nature, but also in eschatological issues and the
global structure of the world (universe) - how big the universe is and what its its shape, when and how did it originate and where does it go, what laws are governed, what is its essence. In antiquity and the Middle Ages, ideas about the structure and evolution of the universe stood on mystical foundations and had little to do with reality *).
*) The historical development of our knowledge of the universe, in the context of the development of the whole natural sciences, was discussed in more detail in §1.1 "Historical development of knowledge about nature, the universe, gravity". The questions of the construction and properties of the Universe and the position of man in it have been (and still are) reflected in various areas of human culture, philosophical and religious trends ("Anthropic principle or cosmic God").
Mystery: The Origin of the Universe ?
In these earlier times,
there was a particular emphasis on the origin of the universe. Different human cultures have created their own stories describing the origin of the world. Most of these creation myths (creation) of the world presupposes the existence of a supernatural divine or absolute force capable of creating the world. In others is the universe eternal, there is always the endless past and will exist forever. A common assumption was that the Universe arose - either spontaneously or by divine intervention - from the primordial nothingness or chaos, into which order was imprinted. From the point of view of the scientific cognitive method, according to which each effect arises from a cause, we can trace the chain of causes back in time until we reach the "original cause". But the question arises: what caused this root cause? Why does "something" exist at all, instead of nothing? A common simple superficial answer refers to God the Creator. The current best scientific answer is that our Universe (and perhaps other "universes") appeared spontaneously from random quantum fluctuations in the primordial vacuum manifold (discussed in more detail in §5.5, section "Chaotic Inflation", "The Origin of Multiple Universes").. However, this initial quantum vacuum is not some "nothingness" or emptiness, but in the spirit of quantum field theory it contains constantly fluctuating physical fields and their quantum - particles and antiparticles. From "quantum nothingness" - from "nothing" arose "everything"..?.. But they are all just hypotheses..!..

Scientific cosmology
It was not until Galileo's observations and Newton's law of universal gravitation erased the seeming abysmal difference between the laws of terrestrial nature and the "heavenly" laws of the universe. It has begun to show that the universe and earthly nature are governed by probably the same fundamental laws; we just observe them from a different "point of view". Since the days of Galileo and Newton, the knowledge of the universe has been based on rational natural (physical) laws, using calculations and predictions of the motion of celestial bodies, with an emphasis on ever-refining observations and confrontation with scientific experiments. Astronomy and cosmology have thus become a scientific discipline in which theoretical ideas and models are constantly corrected in order to gradually achieve the most accurate agreement with everything we observe in the universe. Even in the above-mentioned most difficult question of the origin of the universe ...
  Thus, the way to understand the universe is as follows: to extrapolate the physical laws resulting from experiments in our laboratories to the processes taking place in space, and to try to explain astronomically observed phenomena using these laws. In astronomy and astrophysics, this approach has led to impressive successes. Spectral analysis of radiation coming to us from evnen the remotest observed objects in the universe shows, that there to apply the same laws of classical and quantum mechanics, electrodynamics, atomistic, thermodynamic and gravity as here on Earth. Although this cannot be explicitly proven, it entitles us to believe that the laws of physics apply even where we have not yet "looked" - and perhaps even in places we will never be able to see..!..

However, cosmology seeks to extrapolate the laws of physics to the entire universe at any time in the past and future, and to explain its global structure and evolution. The question arises as to the legitimacy of such a bold and far-reaching extrapolation? *) - the universe as a whole would not have to have the same properties as the part we observed. But if we want to know megaworld, let's hope the material unity of the world governed by the universal laws of physics. Spectrometric analysis of radiation coming from even the farthest reaches of the universe shows, that the natural processes taking place here on Earth and in the whole observation of the available universe are governed by the same physical laws of mechanics, gravity, electrodynamics, atomistic, nuclear physics, thermodynamics, plasma physics, etc.
*) When building the current standard cosmological model (§5.4 "Standard cosmological model. Big Bang. Formation of the structure of the universe.") the Einstein's equations are used to the whole Universe. However, the general theory of relativity is reliably tested (experimentally or observationally) only on much smaller scales - here on Earth and in the solar system (bending of light rays in the gravitational field of the Sun, twisting of Mercury perihelion, Lense-Thirring effect of space-time entrainment rotating by Earth, gravitational frequency feed), or processes in small gravitationally collapsed compact objects; is summarized in §2.10 "Experimental verification of the theory of relativity and gravity"). However, galaxies are many billions of times larger and the observable universe is at least 1015 times larger. Admittedly, such far-reaching extrapolation is not really substantiated..!?.. Unfortunately, we can do nothing better. We have one option: to try such an extrapolation and to see to what extent the predictions from the resulting models correspond to the observed facts; if so, it justifies the extrapolation used and at the same time extends the validation of the given initial theory (here general theory of relativity) to a larger scale.

The uniqueness of the universe
In some important aspects, however, the universe (and thus the methods of its study) is still
different from other physical systems that we encounter in nature. Above all, it is the uniqueness of the universe: the universe exists only in "one edition", we can not do any experiments with it or observe and compare (perhaps statistically) different variants of the universe (we leave aside various speculations about the possibility of multiple universes, we will discuss below in §5.7 "Anthropic principle and existence of multiple universes"). Because there is only one universe and nothing outside of it, no system or observer can in any way break out or "emerge" from the universe, stand outside it, and examine it "from the outside" inward; everything is an integral part of the universe.
  When studying such a complex object as the whole universe, we have to make a number of simplifications and idealizations - we create so-called cosmological models (§5.2-5.5), which capture some basic global features of the whole universe, but abstract from the specific local structure of individual space objects (such as stars, galaxies, even clusters of galaxies...). 
Unimaginable size of the universe ! 
The dimensions of the universe are completely beyond human imagination, they cannot be compared to anything we are used to on a human scale. It is very difficult, or even impossible for us, to imagine the size of the universe. We have nothing to compare with ("uniqueness of the universe") and with such large distances and extensive spaces we have no personal experience ...

Determining the distances of space objects - a basic condition for cosmology
The cardinal problem of astronomy and astrophysics of outer space is the correct determination of distances stars, nebulae, star clusters, galaxies and other objects. Only in this way can we determine the radiant powers of these objects, which makes it possible to analyze the physical mechanisms that lead to such energy powers. And also the space-time structure of the universe. Distances in outer space are often determined by a relatively, careful comparison of the luminosities of stars of a certain type in our galaxy (the distance of which we more or less know) and similar stars in other galaxies. We then extrapolate this method to compare the brightness of closer and more distant galaxies. The results are often burdened with considerable inaccuracy. Contemporary astronomy has at its disposal four basic interconnected methods for measuring the distances of space objects: trigonometric method - luminosity method - cepheids - supernovae Ia - red spectral shift (it was discussed in more detail in §4.1, passage "
Determining the distances of space objects - a basic condition of astrophysics").

Cosmological principle
Most concepts of contemporary cosmology are based on the so-called
cosmological principle *), which is also sometimes referred to as Copernicus' principle. Copernicus' observation that the Earth was not the center of universe, gradually generalize so that even the solar system or galaxy, or the Local Group of galaxies, not only that they are not the center of the universe, but they do not have any significant position in the universe. The cosmological principle is then the hypothesis that all positions in the universe are essentially equivalent, no place in the universe is privileged. The cosmological principle can in principle also be verified in the laboratory - it is closely related to the reproducibility of laboratory physics experiments. If we do an experiment and then repeat it after a long time (in the same laboratory), we actually repeat it in another place in space and in a different time, because the Earth has already reached another place in space as part of its integration into several moving systems. Neverheless, accordind to experience, we get the same results within the limits of accuracy, which testifies in favor of the cosmological principle - physical equivalence of all places in the universe.
*) It is necessary to distinguish two levels of the cosmological principle :
1. Homogeneity and isotropy at the level of validity of physical laws, ie the assumption that physical laws apply equally everywhere throughout the universe;
2. Homogeneity and isotropy in terms of (average) mass distribution and other physical conditions in space.
  At one time, the third version was also discussed, the so-called perfect cosmological principle requiring that the mean density of matter be the same not only in different parts of the universe, but also in time. This incorrect version of the cosmological principle became the basis for a temporary erroneous hypothesis of a steady state of the universe (see below).
  The universe can be compared to a kind of "island empire" in which matter is very unevenly distributed: elementary particles form atoms, which cluster into stars and planets in which the density is many orders of magnitude higher than in the environment; stars are gravitationally grouped together with gas into huge stellar "islands" - galaxies, which cluster in gravitationally bound clusters and superclusters of galaxies. Neither these giant stellar "islands" or "archipelago" in the universe move randomly, but flows in a kind of "filaments", among which are almost empty huge "bubble". The Universe in these scales reminiscent of a kind of giant "cosmic spider web" (see §5.4, part "Formation of large-scale structure of the universe", Fig.5.5).
  However, in the cosmological study of the universe as a whole, it is necessary to disregard the "local" irregularities of the distribution of matter; these smaller structures are studied in classical astronomy and astrophysics. If we average the density of mass distribution in areas of large dimensions compared to the distance between galaxies and galaxy clusters (i.e. about 108 -1010 light-years), globally, this "blurred" mass will be distributed practically homogeneously and isotropically. This is required by the cosmological principle and confirmed by current astronomical observations *), including relict radiation. The universe is therefore "more or less" homogeneous and isotropic - on large dimensions it is the same in all places and looks the same in all directions. In §5.4 and 5.5 we will see that, according to the standard cosmological model, this is due to the emergence of the universe from the "big bang" and then the rapid "blow-out" during the inflation phase.
*) How perfect is the homogeneity of the universe ?
Of course, there are random differences in the distribution of galaxies and galaxy clusters, but on large scales they fit into an averagely homogeneous system. Astronomical observations made in the 20th century showed the upper limit of the size of any anomalous structure in the universe to be around 1÷1.2 billion light years. However, in 2022, a structure 3.3 billion light-years long (crescent-shaped, called the Giant Ark) was observed. And there are indications for perhaps even larger structures
(such as the Great Wall of Hercules manifesting in an increased density of GRB gamma-ray bursts) that can occupy up to 10% of the size of the observable universe.!... This suggests a greater heterogeneity of the universe than previously thought, so the traditional cosmological principle may need to be refined and it will perhaps even lead to a modification of the standard cosmological model..?..
Note: For some time, the Lambert-Charlier model of the hierarchical structure of the universe was discussed, which was to remove some cosmological paradoxes. According to him, the universe is formed by a sequence of hierarchically arranged cosmic systems: stars - galaxies - clusters of galaxies - ... etc., while the average density of matter decreases rapidly during the transition to a higher system. These structures, however, would be gravitationally unstable and would soon disintegrated. Now these concepts have lost their relevance and are not even in line with the new observational facts, which, on the contrary, confirm the legitimacy of the cosmological principle.
 The universe is almost absolute emptiness !
Due to the huge size of interstellar and intergalactic space, the current average density of matter in the observable part of the universe is only about 10-27 kg/m3, which corresponds to only 3 protons in 1 m3. It's an almost perfect vacuum that we can't even achieve under terrestrial laboratory conditions!
  The whole universe is just a huge emptiness, "polluted" by an almost negligible amount of matter. This somewhat paradoxical statement applies not only to vast cosmic scales, but also, in essence, to our terrestrial nature. Everything around us is made up of only a small amount of real - "solid", concentrated - matter. It starts with the atom, which is not some solid mass sphere, but consists of a very dense core measuring only 10
-13 cm and an almost empty electron shell. The nucleus, bearing more than 99.9% by weight of the atom, is about 100,000 smaller than the whole atom. Thus, an atom is actually an empty space, "polluted" by several protons, neutrons and electrons. About 99.98% of each atom is an empty vacuum. Even our body, which is built of these atoms, is mostly formed by emptiness: the whole "real" mass of our body could theoretically be compressed into a ball with a diameter of about 1 mm, the rest would be emptiness.
On the global scales of the universe, this "local" emptiness is exacerbated by the very sparse distribution of cosmic bodies and atoms of interstellar gases. It can be said that matter in the universe represents only insignificant "spots" in an otherwise completely empty and "clean" space. In addition to large areas of virtually absolute vacuum, however, there are unimaginably dense clusters of matter in space , resulting from gravity at the end of the life of very massive stars. They are neutron stars (discussed in §4.2, section "
Supernova explosion. Neutron star. Pulsars"). With even greater gravitational compression, black holes are formed, which, however, are again essentially "vacuum objects" (as discussed in §4.2, section "Complete gravitational collapse. Black hole.").

Skeptical reflection :
The impossibility of physical travel to distant space - to other galaxies !
The gigantic vastness of the universe - the huge distances to other galaxies
(even to different parts of our Galaxy) makes it extremely difficult, if not impossible, to directly (physically) visit these places. There are two principle obstacles :
1. The slowness of space vehicles
Our space rockets are "snails" reaching a maximum speed of several tens of kilometers per second. At these speeds, it would take hundreds of millions of years to travel to objects in the distant universe. No hypothetical sci-fi possibilities like "warp drive" or travel through "wormholes" can be counted on; nothing like that works. The only future, in principle, realistic possibility is thermonuclear hydrogen fusion
(section "Fusion of atomic nuclei" in §1.3 of the book "Nuclear Physics and Ionizing Radiation"; it has an energy efficiency of about 0.7% m.c2), which would be possible to achieve a maximum speed of about 20-22% of the speed of light. And that's an optimistic estimate, assuming 100% lossless efficiency of all links in the fuel and rocket chain (we won't be able to do anything like that anytime soon!). Higher speeds could hypothetically be achieved using antimatter (see, however, the critical assessment in the section "Antiparticles - antiatoms - antimatter - antiworlds" in §1.5 of the mentioned monograph).
2. Erosion of the cosmic probe during movement through the interstellar medium
Even if we managed to reach speeds close to the speed of light, we would encounter a problem that is not usually analyzed : Interstellar and intergalactic space appears to us as a high vacuum, but it is not completely empty. Even though there are only a few hydrogen and helium atoms per 1m
3, at that high speed many millions of high-energy particles would strike the probe every second, destroying the probe's atoms and releasing high-energy radiation that would further damage the spacecraft and its electronic systems (and possibly the crew in the case of a manned mission).
  Even more dangerous damage would occur upon collision with particles of cosmic dust. Not only would there be a small hole that could be sealed, but there would be a high-energy explosion that would melt and vaporize the wall of the probe, accompanied by strong radiation. Also, when passing through a planetary system with a higher density of interplanetary gas, erosion could burn up the space probe in a short time...
Conclusion : No macroscopic material object - no cosmic probe - realistically, it is not able to fly to the intergalactic distance! There is no way to fly through space faster than about 20% the speed of light. And at this high speed, the probe material will be eroded by the constant collision of hydrogen and helium atoms in the interstellar medium (as well as more severe damage from collisions with cosmic dust grains). The lifetime of the probe will only be on the order of tens to hundreds of years, which is far from enough to reach intergalactic distances. Even the hypothetical achievement of higher speeds would not eliminate or reduce this erosion - the flight time would be shortened, but the intensity of the erosion would increase...
  Any space probe, traveling at speeds close to the speed of light, would be vaporized by collisions with cosmic matter particles, before reaching galactic distances...
  When exploring the distant universe, we will probably be forever dependent on the passive detection and analysis of particles and radiation of various kinds, emitted from these distant places
(electromagnetic radiation, cosmic ray particles, neutrinos, gravitational waves, ...). However, thanks to constantly improving technologies for accurate "passive" analysis of radiation from the most distant and hidden regions of space, we learn much more about them than if we were "physically there"...
And there is no question of "settlement" the distant universe ! Similarly, a physical visit to each other by possible extraterrestrial civilizations located at great galactic distances will never be possible
(see also the discussion "The search for extraterrestrial life" in the treatise "Anthropic Principle or Cosmic God"); a biological visit is of course completely excluded, but a robotic one will not be possible either..!..
Quantum teleportation ?
The only, but for now completely sci-fi possibility, how we could reach large interstellar distances in a certain sense could perhaps be (quantum) teleportation :
1. Break down our body into atoms or subatomic particles, with a detailed record of all their physical and chemical bonds. 2. Send these particles at near-light speed, including the structure information, to another target part of the universe. 3. At the destination, assemble these particles into atoms, molecules, tissues and biological structures, according to the sent plan.
  The problem with this straightforward approach is how much of the sent particles would actually make it to the distant destination? - many of them would probably be destroyed by collisions with cosmic rays and particles of interstellar matter. Therefore, it would be more appropriate not to send actual particles, but to send only quantum information about them, using laser-encoded electromagnetic radiation; and assemble an organism at the target location using particles and atoms that are normally found there - information teleportation.
  However, we will not be able to attempt anything like that in the foreseeable future...

Our modest place in the universe
In people's daily lives, we observe that lack of knowledge leads to arrogance and pride, better knowledge awakens modesty and humility. So it is also in science. Every newfound knowledge of the universe, space, and time pushes us away from that privileged place in the center of the universe, that we once proudly claimed. We now know that we are just insignificant organisms living on a tiny grain of powder in a vast cosmos. This should lead us to modesty, rejection of religious and other false superstitions, to ennobling our relationships with each other and with living and non-living nature..!..

Newtonian cosmology. Static universe.
In the 18th and 19th centuries, classical mechanics, together with Newton's law of gravitation, celebrated great success
es in explaining all mechanical and gravitational phenomena not only on Earth, but also made it possible to explain the structure and dynamics of our cosmic environment - the solar system. Therefore, it was offered to try to understand the structure of the universe as a whole on the same basis: In the cosmic space there are stars spread, which exert Newtonian gravitational forces on each other. These gravitational forces, according to the laws of mechanics, then determine the movements of the stars (or, in equilibrium, their immobility).
Back then, galaxies (except our Milky Way), interstellar matter, or exoplanets around stars were not yet known...

   The basic premise, seemingly resulting from astronomical observations, was the static nature of the universe, according to which the universe is filled with "perennials" that are at rest (today we know that this assumption does not correspond to reality at all). If the universe were then a finite material system, due to gravity, all matter should cluster into one large compact body. However, even the conception of the universe, which represents an infinite Euclidean space on average uniformly and statically filled with stars acting on each other according to Newton's law of gravitation, encountered insurmountable difficulties :
 Photometric Paradox of the Night "Dark Sky"
The most famous is the so-called Olbers photometric paradox formulated in 1826 - the "dark sky" paradox - "why is it dark at night?". If the stars are uniformly and statically distributed in the infinite universe, the sky would have to shine day and night from horizon to horizon as dazzlingly bright as the surface of the Sun *): for in every spatial viewing angle, each surface element contains, on average, a number of stars proportional to the square of the distance from us, while the intensity of light from there is also inversely proportional to the square of the distance. It can be imagined even more vividly by looking at the sky in any direction, some stars always stick to the surface
(just like in a vast pine forest, we see only trees in every direction). There should be a star shining in every direction - the stars should cover the entire observed "firmament". We cannot see individual distant stars, but the sum of their light should be seen as a continuous glow. There would be neither day nor night, but still only a blinding conflagration!
*) Most of the stars, about 70%, are red dwarfs, so the night sky should be intensely yellow-red..?..
The assumption of light absorption by an interstellar substance will not help here, because it would heat up with the absorbed energy in the final time and from
  it would radiate in thermodynamic equilibrium with radiation from stars.
  The explanation of the photometric paradox from the point of view of today's knowledge of astrophysics and cosmology consists in three circumstances :
1. The photometric paradox arises only on the assumption that the stars shine for an infinitely long time, as was thought at the time. Considering that stars actually shine only for a finite time (~106 -1010 years), the photometric paradox does not arise even in an infinite homogeneous universe. Considering the actual astronomically observed average density of stars in the universe, the stars do not have enough energy to fill the entire space with light and turn the dark sky into a bright one.
2. Even the age of the universe is finite. The greatest distance from which light can reach us is approximately 13.8 billion light years. Anything beyond that distance is too far. There hasn't been enough time in space yet for the light from these distant objects to reach us. So the sky is dark also because the light from the most distant stars has not yet reached Earth...
3. We live in an expanding universe. So with respect to very distant objects (stars, galaxies, early hot universe) we are moving away at a high speed (or they are moving away from us quickly). As a result, any light emitted by distant objects exhibits a spectral red shift - a decrease in frequency. Visible light becomes infrared, later radio waves. We cannot see this radiation with our eyes. However, sensitive detectors installed on satellites can detect this radiation, measure its frequency spectrum and angular distribution in the sky (see §5.4. passage "Microwave relic radiation - a unique messenger of news about the early universe"), showing even small inhomogeneities, from which later they developed the large-scale structures of the universe. In these images (which are an example of a master detection technique!) we can see how our sky is "illuminated" from all directions by weak cosmic microwave radiation. This radiation was originally emitted as visible light by a hot gas at about 3000 °K at the beginning of the era of matter, but it comes from so far away in the expanding universe that its frequency has dropped about 1100-times to the microwave radio region.
  So, generally speaking, our night sky is not completely dark, but is permanently irradiated by weak microwave radiation, corpuscular cosmic radiation ("Cosmic Rays"), radiation from stars, and temporarily also by solar radiation reflected from the Moon and from the planets (mainly Venus, Mars, Jupiter, Saturn).
 The Gravitational Paradox; cosmological weakening of gravity ?
Furthermore, the gravitational paradox is manifested here, consisting in the fact that
that in the model of the universe as an infinite Euclidean space evenly filled with matter (stars), the gravitational potential would become infinitely large. Due to symmetry, the homogeneously distributed mass to the infinity should be in equilibrium, because gravitational forces act on the same effect on any material element in the same way and their effect is canceled. For a truly infinite case, however, these forces from each of the direction of the infinite; the overall strength, field strength, and integration potential diverge. If the mass is to be in static equilibrium, the intensity of the gravitational field E must be zero everywhere, so according to Newton's law of gravity expressed in form

div E   = - 4 p G r   , or   Dj   = 4 p G r   ,      

the density of mass r must also be zero everywhere. Under Newton's law, therefore, only empty space could be a static "universe". Seeliger tried to modify Newton's law of universal gravitation by adding into Poisson's equation another "cosmological" member -L.j, causing "weakening" of gravity at great distances :

Dj - L . j  =  4 p G r   .     (5.1)

This equation has as a solution the potential (1.19) (now referred to as the Yukawa type) , which decreases to infinity so fast that the expressions for the potential and intensity of the gravitational field excited by a homogeneously distributed mass converge. The given equation is satisfied by a constant potential, which gives zero intensity of the gravitational field. In order for this modification of Newton's law not to affect the agreement with experimental data which exist within the solar system, must be "cosmological constant" L sufficiently small ( L <~10-45 m-2). In light of the findings later, Seeliger's attempt to overcome the gravitational paradox was unsuccessful. Instead of modifying Newton's law, the second basis of Newton's cosmology was to be modified - give up the assumption of the static nature of the universe; but something like that could hardly have occurred to anyone at the time. Until the 1920s, it was thought that the universe was immutable and eternal, consisting of one galaxy, the Milky Way, surrounded by infinite empty and dark space.

Relativistic cosmology
Since the interaction of cosmic objects located at great distances from each other takes place mainly through
gravity, it is not surprising that research in the field of gravity helps to solve basic cosmological problems. The creation of Einstein's general theory of relativity - the modern physics of gravity - set completely new horizons in cosmology, for which he laid a solid scientific basis. All cosmic bodies distributed in the universe create gravitational fields - they curve spacetime according to Einstein's GTR equations, and this curved spacetime according to the gik metric tensor in turn determines the movements of matter in the universe (it is discussed in more detail below in the passage "Relativistic cosmological model").
   A.Einstein was well aware of this, and so in 1917 he tried to apply his gravitational equations to the universe as a whole and thus create a relativistic model of the universe. He proceeded from the assumption of homogeneity and isotropy of the distribution of matter in space. Moreover, he believed, in accordance with the firm beliefs of physics and philosophy of the time, that the universe was static. When used for static cosmology, the original Einstein equation (2.50) behaved similarly disadvantageously as the older Poisson equation - the only homogeneous static solution here is the Minkowski spacetime corresponding to empty flat space *).
*) Today we know that the main source of difficulties in both Newton's and the original Einstein's cosmological model is common: it is a presumption of static (time invariability) of the universe. However, this assumption seemed completely natural to all naturalists, including Einstein, until the 1920s, and there was no doubt about its legitimacy.
  It is worth noting that many basic findings of relativistic cosmology regarding the dynamics of space expansion, critical density, etc., can be obtained even in Newtonian cosmology, if we do not consider a homogeneous and isotropic distribution of matter in space as static, but as expanding (a kind of "vertical upward throw" from each point according to Hubble 's law, given in the initial conditions). However, these contexts became clearer only later, when the results of relativistic theory were already known.  

Static Einstein's universe
Therefore, since Einstein did not find any solution compatible with the static spherical universe, he decided to modify his original gravitational equations R
ik- (1/2) R.gik = 8p Tik by introducing the so-called cosmological member L.gik , which could "stabilize" the universe. This cosmologic member which here plays a similar role as a member L.j in equation (5.1) of Newton-Seeliger cosmology; but here it does not have to introduce "from the outside" (ad hoc), but arises already when deriving Einstein's equations of the gravitational field - see §2.5. Based on such supplemented gravitational equations Rik- (1/2) R.gik - L.gik = 8p Tik , Einstein's cosmological model of the static universe was created, discussed in more detail in §5.2 "Einstein's and deSitter's universe. Cosmological constant.". Although this model has not proven to be realistic, it is often used to compare the parameters of newer cosmological models (see eg §5.3, section "Relative W-parameterization of cosmological models").
  Later, when Hubble's observations revealed that the static universe thezis was wrong, Einstein called the cosmological contant as the "biggest mistake of his life" **), which prevented him from theoretically predicting the cosmological redshift caused by the expansion of the universe.
Much later, however, some experts welcomed the cosmological term and used it in theories attempting to explain some of the problems of the original standard cosmology. In §5.5 "Microphysics and Cosmology. Inflation Universe." it will be shown what role the cosmological member can play in the so-called inflationary expansion of the very early universe. And in §5.6 "Future of the Universe. Arrow of Time. Hidden Matter.", section "Accelerated Expansion of the Universe? Dark Energy?" we will see that the cosmological constant can explain the accelerated expansion of the universe in its late evolution.

Dynamic expanding universe
In 1924-29, E.Hubble, while systematically observing extragalactic "nebulae" with a telescope on Mount Wilson
(mirror diameter 2.5 meters), discovered that they were in fact foreign galaxies, whose distance he determined using the Cepheids contained in them (§4.1, passage "Variable Stars"). Hubble found that the radiation spectra of distant galaxies show a systematic shift toward the red region, the magnitude of this redshift not depending on the direction in which the galaxy lies, but is approximately proportional to the distance l of the galaxy :

z  =def.   Dl / l   =  H . l   ,   (5.2)

where l is the wavelength of light and the coefficient of proportionality H between the galaxy's velocity and its distance is is now called the Hubble parameter or the Hubble speed. The name Hubble constant *) is also used for it, but this can be somewhat misleading :
*) It is a constant only in the sense that it does not depend on the distance l . However, in the context of the global evolution of the universe, its value of H(t) depends on the time t .

  Determining the exact actual value of the Hubble coefficient H (t) is not very easy. In our immediate vicinity, cosmological expansion has little effect and the measurement results are distorted by local galaxy motions. When measuring in outer space, we look back to the past and it can be difficult to reliably extrapolate the current value of H(t) if we do not know in advance the dynamics of the expansion of the universe.
  As the Hubble constant H
0, it is more adequate to take the value of the Hubble parameter H(t) at the current time of evolution of the universe t~14×109 years, i.e. at redshift z=0. Based on measurements of a larger number of galaxies, the current value of the Hubble constant H0 ~ 70 km/s/Mpc (megaparsec 1Mpc = 3.26 million light-years).
  The measurement of the Hubble constant and some differences in the values are discussed in §5.4, the passage "How fast is the universe expanding? - precise measurement of the Hubble constant".
  In addition, Hubble's observations showed an approximately homogeneous and isotropic average mass distribution in the visible part of space with a density of about 10-31 -10-29 g/cm3. The Hubble redshift, which is the same for all spectral lines and wavelengths, is most naturally interpreted as a Doppler effect *) caused by rapid distancing of far galaxies from us. The farther apart the galaxies are, the faster they move away each other. The inverse value of the Hubble constant 1/H0 represents the so-called Hubble time - the age of the universe derived from the instantaneous rate of expansion, without taking into account the effect of gravity on the dynamics of expansion; is about 14 billion years.
*) The Doppler effect is a kinematic effect arising from the relative movement of a wave source and an observer (wave detector). It generally applies to all types of waves. If the wave source with a certain constant frequency fo moves towards the observer (receiver), this observer registers a higher frequency f than what source it actually radiated. Conversely, when the source moves away from the observer, the registered frequency is lower than the actual one. The relative difference between the actual fo and the observed f frequency (Doppler frequency shift) increases in proportion to the velocity V of the source relative to the observer: f = [1 + (V/v)] fo , where v is the propagation velocity of the given wave; Df/fo = (f-fo)/f = V/v. The same applies to the wavelength l = v/f. By measuring the difference between the frequencies or wavelengths of the primary radiated wave and the received wave, we can determine the mutual speed movement of the source and the observer. For electromagnetic waves, of course, v = c.
Note: This rule also applies when the source of the received wave is the reflection of the wave from a certain moving object (including a flowing gas or liquid). It is used in radar technology and ultrasonic sonography.
 Global receding <-versus-> peculiar motions of galaxies
From a global point of view, galaxies primarily perform a diverging cosmological motion. However, individual galaxies are also influenced by the gravitational action of other, surrounding galaxies. This can cause local deviations in their movement - so-called peculiar movements
(lat. peculiaris = special, individual, strange). Although the universe is expanding overall, from a local point of view not completely uniform, some galaxies can move faster or slower, depending on their masses and distances from other nearby galaxies. The local gravitational attraction can sometimes even overcome the global cosmological expansion and some galaxies can move towards each other.
  An example is our Milky Way galaxy and the neighboring galaxy in Andromeda, about 2.5 million light-years away, which are approaching each other at about 110 km/s. In about 4 billion years, they will "collide", or rather "penetrate", and both galaxies will form one large elliptical or irregular galaxy. There are many such groups of galaxies that are bound by their own gravity and moving through space. Galaxy "collisions" are discussed in §5.5, the passage "
Gravitational interactions and galaxy collisions" and "Galaxy clusters".

Age and size of the universe
 The age of the universe
For many centuries, the universe seemed to be like a philosopher and a natural scientist as permanent and unchanging, the age of the universe considered infinite
(if we ignore some of the illusory value of about a thousand years, derived from unsubstantiated religious legends of the divine "creation of the world", which, moreover, they were in ancient times invented from anthropocentric backgrounds, without relation to the universe - the construction of which people at the time had no idea). This view changed dramatically after Hubble's discovery of the expansion of the universe. If we project the observed moving away of all galaxies from each other into the past, against the flow of time, we inevitably come to the moment when all these galaxies had to be close together (figuratively "at one point") --> the universe cannot be infinitely old, the age of the universe is finite. The event when the universe "freed" itself from highly compresed condition and began its expansion evolution is now called "big bang" - is discussed in detail in §5.4 "Standard cosmological model. Big Bang. Formation of the structure of the universe.".
  The total age of the universe - the time elapsed since its creation - is determined or estimated by basically two approaches :
1. Analysis of the dynamics of the expansion of the universe 
in principle, it makes it possible to determine retrospectively the time "t = 0" from which the evolution of the universe began. The basic way here is to use the inverse value of the Hubble constant : 1 / H represents the so-called Hubble time - the age of the universe derived from the instantaneous rate of expansion, without taking into account the effect of gravity on the dynamics of expansion; is about 14 billion years
(which surprisingly agrees quite well with more complex methods) . .... Within the standard cosmological model, the exact determination of the age of the universe lies in the problem of determining the values of cosmological parameters (§5.3, passage "Relative Omega-parameterization of cosmological models") - this allows in this model the idea of "running the cosmological clock back in time" up to the moment t = 0 (t0). This extrapolation can be performed exactly on the basis of Fridman's equation (5.23). This can be illustrated by the above Hubble time 1/H :
            t 0 = ( 1 / H ) . F (Omega) ,
multiplied by the correction factor F(Omega), which is a function of the "Omega" cosmological parameters dependent on the specific density and composition of matter in space. Relict microwave radiation measurements are now used to accurately determine the age of the universe (coefficient F)
(§5.4, passage "Microwave relic radiation - messenger of early space news"). Minor fluctuations in the cosmic microwave background make it possible to fine-tune the values of the "Omega" cosmological parameters. According to new measurements, the original range of 13-15 billion years has been specified to 13.8 billion years.
2. The age of objects in the universe
The universe must be at least as old as the oldest objects in it
... If we can determine or estimate the age of such objects, it sets a limit for the minimum age of the universe. To determine the true age of the universe, we must add the time of origin to this value of this analyzed object from the big bang, if we are able to reliably estimate it. The search for the oldest stars is important for this analysis. These occur mainly in globular clusters, where they formed at about the same time, soon after the beginning of the universe (they can therefore serve as "cosmic clocks"). The oldest globular clusters contain active stars only less than 0.7 times the mass of the Sun
(the more massive ones have long since burned out), whose age is estimated at 11-18 billion years (considerable uncertainty in this estimate is due to inaccuracy of the distances of the star clusters and ignorance of some details of dynamics stellar evolution).
   Another alternative method turns to the chemical evolution of the universe - nucleosynthesis. Uses radioactive dating using radionuclides with extremely long half-lives
(from a general point of view of nuclear physics, the principle of this method is discussed in §1.4 " Radionuclides ", part "Radioisotope (radiometric) dating" in monograph "Nuclear physics and ionizing radiation physics"). For dating minerals on Earth and in meteorites, the isotope rubidium Rb-87 is most often used, which with a half-life of 47 billion years is converted to strontium Sr-87, whose representation is compared to Sr-86. For meteorites, this is 4.56 billion years old, which is considered the age of the solar system. For interstellar gas and old stars, the isotope pair with Re-187 was used, which with a half-life of 40 billion years is transformed into Os-187, then the pair U-235 and U-236, or the ratio of Uranium-238 to Thorium-232.
 The size of the universe
Determining the "size of the universe" is also a difficult and debatable task. The area astronomically observable from us from Earth - the observable universe - is constantly increasing with the improvement of observation technology. The most distant objects are observed at a distance of almost 13 billion light-years. By analyzing the redshift of relic radiation and the rate of expansion, it is estimated that with the inclusion of the cosmological expansion of the universe, the observable universe is a sphere with a radius of about 45 billion light-years. This expansion made it possible for us to observe light from a galaxy now even 40 billion light-years away
(with a correspondingly large spectral redshift), while this light traveled to us in only about 13 billion years. Including the dynamics of space expansion (hypothesis of accelerated expansion - §5.6, section "Accelerated expansion of space? Dark energy?"), the diameter of the universe could be even about 100 billion years! This would be the size of the space that matter reached during expansion from the beginning of the universe; if the universe is open, it has no boundaries...
    This distance value corresponds to the event horizon - an interface beyond which we can no longer be seen in principle. If an object were at a greater distance than the light could have covered during the existence of the universe, then such light has not yet reached us - and due to the expansion of the universe, it will not even reach it! Such extremely distant objects lie forever outside our observable universe. 
    Moreover, if the conclusions of
inflationary cosmology leading to the multiverse - the existence of more universes (§5.5, part "Chaotic inflation", passage "The emergence of more universes") were valid, the question of "the size of the whole universe" would be unsolvable and irrelevant ..!..
   It is estimated that there are about 10
21-1023 stars in the observable universe, in more than 1012 galaxies.

Cosmological expansion of univese
The kinematic explanation of the cosmological spectral shift using the Doppler effect of rapidly receding galaxies is adequate from the local point of view of classical physics or special theory of relativity. Hubble's rule that the farther galaxies are, the faster they move away from us (and from each other) suggests that this is not the movement of galaxies through space in the classical (mechanical) sense. Rather, they appear to be carried away by the ever-expanding geometric "fabric" of space itself.
    From the point of view of the globally curved space-time, which the universe is according to the general theory of relativity, the expansion of space as such, which carries the distant galaxies to even greater distances, and these galaxies themselves do not move relative to this space (the galaxies' own motions are small at relatively relativistic speeds and are irrelevant here - due to the Doppler effect, they cause very little additional - positive or negative - spectral shift to cosmological redshift). Both of these explanations are equivalent only when observing not too distant galaxies.
The superluminal rate of expansion of space ?
.According to current relativistic cosmology, a short period of so-called inflationary expansion of the universe took place at the beginning of the evolution of the universe (§5.5 "
Microphysics and cosmology. Inflationary universe. "), when the germinal universe swelled exponentially. It expanded much faster than the speed of light. It would seem to be in conflict with the special theory of relativity, but this is not the case here: nothing moved at super-light speeds through space - the space itself expanded very rapidly and carried a physical field with it. What drove him to this rapid spontaneous expansion is not completely known, it is assumed that it was the so-called dark energy (§5.6 "The future of the universe. Time arrow. Dark matter. Dark energy. "), thanks to which it is observed even in the late phase (here slow - gradual) so-called accelerated expansion of the universe.

An alternative explanation for the redshift; aging light ?
alternative explanations for the redshift have also emerged , trying to find another mechanism for losing the energy of light quanta from distant cosmic objects. The simplest explanation would be the loss of energy by the interaction of photons with intergalactic matter. However, such collisions of photons with other particles would also lead to a change in their momentum, ie to their scattering and thus to the blurring of the image of the source, which is not observed - the images of even the most distant objects are sharp. The most common hypothesis was the "aging" or "fatigue" of photons from distant galaxies during their long journey through space - photon could spontaneously emit some particles carrying away part of its energy (eg a neutrino-antineutrino pair). However, no such process has ever been observed in the laboratory, and in addition, the probability of spontaneous photon decay would have to be energy dependent (inversely proportional to the photon energy), so the redshift would be different in different parts of the spectrum. Nothing like this, however, not observed, red shift for all wavelengths equally (exact measurements showed that the red shift of radio waves, l = 21 cm in distant galaxies is the same as the shift in the optical field). In addition, the emission of photon particles would lead to a change in their momentum and thus in the direction of photon motion, which would cause blur images of distant sources, similar to intergalactic absorption. Also, the assumption that the redshift has a locally gravitational origin does not hold up to a more detailed analysis - light would have to be emitted from areas near the horizon of a compact formation that would certainly collapse soon at such a mass (as a galaxy). All these alternative explanations turned out to be ad hoc hypotheses, explaining only some aspects of the phenomenon; they do not correspond to current knowledge and are now abandoned. Only the mechanism of the Doppler effect, or global expansion of space, faithfully explains all the basic properties of the phenomenon - the same relative shift value for light of all colors and electromagnetic waves of all frequencies and the absence of blurring of observed distant objects or blurring of their spectral lines.

According to the cosmological principle of homogeneity and isotropy, ie the equality of all observers, every observer everywhere must see that distant galaxies diverge from him - in other words, the universe as a whole expands *). Hubble's discovery thus showed that there was no need to look for static solutions for the distribution of matter and fields in space; on the contrary, dynamic solutions will better reflect reality. These findings proved to be in full agreement with the earlier (1922) found Fridman solution of Einstein's equations by which the solution of gravitational equations even without a cosmological term is also three-dimensional homogeneous and isotropic space that is not static, but its radius of curvature changes with time.
*) No specific place is the center of expansion of the universe, respectively each location is this center of expansion. On a cosmological scale, everything starts from everything ...

From a local and kinematic point of view, we can imagine the redshift as a Doppler effect. From the global point of view of relativistic cosmology, an alternative but essentially equivalent explanation emerges: the cosmological redshift can be attributed to the "expansion" of space during the time that light from its source propagates through this space. The wavelength of light increases as it moves through space - at different times and at different speeds depending on how fast the space was expanding. The magnitude of the redness, ie, the extension of the wavelengths, is proportional to how much the universe has expanded during the time that light traveled to us. The resulting red shift from thus, it depends on the distance of the observed object and on the dynamics (history) of the expansion of space. The measurement of the spectral shift in galaxies and quasars lying at different distances thus in principle provides information on the temporal dynamics of the expansion of space - information on the history of the expansion of the universe; however, the objective and accurate determination of these large distances is a difficult astronomical problem.
    The most distant galaxies and quasars observed so far reach redshift values around 5. The largest possible redshift can be observed in relic radiation: z
relict » 1100 - this value results from the ratio of the temperatures of end of radiation era of 3000 ° (when the radiation separated from matter) and the current temperature relic radiation 2.7 °: 3000/2.7 » 1100; these temperatures are inversely proportional to the mean wavelength of the respective radiation.

Energy and the Law of Conservation of Energy in an expanding universe
In classical physics and in everyday life, energy is a cardinal quantity that we can measure, transform it between different types, use it, but we cannot create or destroy it - the law of conservation of energy applies. Energy is neither created nor destroyed, it is only redistributed. The global energy of the entire universe is a complex and debatable issue. What could she relate to? The prevailing opinion is that the amount of energy in the universe is constant and comes from a mysterious process of the creation of the universe - the big bang. In §5.4 "
The Standard Cosmological Model. The Big Bang. Formation of the Structure of the Universe." and 5.5 ("Microphysics and cosmology. Inflationary universe.") we will see, that in the very first moments of the creation of the universe, processes were probably taking place during which the law of conservation of energy could not be spoken of. Energy is a quantity that does not exist by itself, but is always relative to other objects, particles, systems. And in these first stages of "chaos" there were no such objects yet. Only after the end of the inflationary phase and the onset of the hadron era, the (local) law of conservation of energy probably becomes applicable.
  Even though the universe is probably infinite, that doesn't mean it has infinite energy. Energy is not evenly distributed in the universe, there are areas where it is more or less. Although the total amount of energy in the universe does not change, its density decreases during the expansion. And eventually it will be so low that it will be almost zero everywhere and the universe will reach a state of maximum entropy. Then nothing will happen anymore, no stars and planets will be formed, no life
-> "heat death" of the universe (§5.6 "The future of the universe. The arrow of time. Hidden matter. Dark energy.").
  As the universe expands, the light
(and electromagnetic radiation in general) that passes through, it also expands - spectral redshift. This means it loses energy because longer wavelengths have lower energy. When the spectrum of electromagnetic radiation is redshifted during its journey through expanding space, its energy decreases due to the increase in wavelength. The question arises, where did this part of the lost energy "go"? Is she lost forever? - is energy escaping from space? Isn't this a violation of the law of conservation of energy? Such a contradiction would arise from the point of view of classical physics or STR. In the general theory of relativity, however, the concept of energy is more complex (see §2.8 "Specific properties of gravitational energy"). In locally inertial frames of reference, the law of conservation of (non-gravitational) energy continues to apply. However, in curved spacetime, what we call energy may not itself be conserved in general. And so it is also in "time-curved" space-time, in which the expansion of space takes place. Here, the "geometric" (gravitational), electromagnetic and kinematic contribution to the quantity that we are used to using in classical physics as "energy", is combined.
  The all-pervading medium in space is the gravitational field. As the universe expands, so does gravity. The energy that light loses as it travels through expanding space is balanced by the energy that gravity gains as the universe expands. The total energy of the system remains the same, only its distribution and form changes.

Hot early universe , "big bang", background radiation
From the properties of Friedman solution came G.Gamov, which between 1946-1956 expressed and developed the hypothesis of the "hot universe", according to which the temperature in the universe in the early stages after the "big bang" (Big bang - the singular origin of the universe corresponding to time t=0 in Fridman's model - see §3.3) reached billions of degrees, and during this hot stage all chemical elements from hydrogen to uranium were formed by nuclear synthesis reactions; today we know that nucleosynthesis was more complicated - see §5.4, section "Primordial nucleosynthesis" and §4.1, section "Thermonuclear reactions in stars".
  The hot early universe was filled with high-energy quantum, but as a result of the expansion of the universe, the energy of each photon was constantly decreasing; now the spectral energy distribution of these "relict" photons (left over from the hot early stage) should correspond to blackbody radiation heated to several °K, which corresponds to radio waves of the centimeter band. This hypothesis not initially given greater attention until 1965, when A.Penzias and R.Wilson in the analyzing noise of the radio telescopic receiving antenna discovered cosmic background radiation - weak microwave electromagnetic radiation, which comes isotropically from all directions of the sky, is non-polarized, time constant (independent of the year 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. This confirmed the concept of an expanding universe with a very hot early period. Relativistic cosmology has thus irrevocably shown a that the universe is a dynamic object, evolving not only in this parts (evolution of stars and galaxies), but also as a whole.

Steady-state theory of the universe
The idea of an expanding and generally evolving universe was initially met with distrust and resistance from astronomers. As an alternative to the theory of expanding universe and the Big Bang in 1948 F.Hoyle, H.Bondi and T.Gold proposed theory steady state of space (TSS Theory steady-state universe), called theory of stationar universe or solid state of the universe. It is based on the so-called perfect cosmological principle, requiring that (on a large scale) the mean density of matter be the same not only in different parts of the universe, but be the same over time. Steady state theory does not deny the spatial evolution (expansion) of the universe, but seeks to preserve a static (time-invariant) solution of cosmological equations - to preserve the universe eternal in time, not changing its appearance, without the temporal beginnings of the universe
(the objection was accentuated: if the universe had its time beginning, what was before him?). The universe is expanding, but the density of matter does not change in it, because in the "gaps" of the growing space, new matter "from nothing" is constantly being created (a hypothetical "C-field" has been introduced). To maintain a steady state (against the existing expansion), the formation of a new mass at the rate of 1 hydrogen atom per 1 m3 would 5 billion years (such a small increase cannot be confirmed or refuted). The erroneous of the steady state theory of the universe became apparent in the 1960s, when observations of quasars and radio galaxies showed that they were only at great distances and therefore existed in the distant past, while according to the steady state theory they should occur evenly everywhere. The definitive refutation of the stationary universe theory came with the discovery of relict microwave radiation, which unequivocally supported the theory of the hot beginning of the universe and the "dilution" of matter and radiation as it expanded.

When astronomers aim powerful telescopes at distant objects, they can observe the evolution of the universe in a way. This is due to the finite, constant and fixed speed of light. Distant galaxies whose light came to us billions of years ago look different from similar galaxies relatively close to us. By observing ever greater distances, we also penetrate the ever greater "depths of time". And we observe that the universe previously looked different then now...

Further significant development of cosmology was stimulated by the application of knowledge of nuclear physics and elementary particle physics to processes in space, especially to the hot early universe. Nuclear astrophysics has emerged that can convincingly explain the entire "chemical evolution" of the universe, ie both the nuclear reactions in the stars and the initial nucleosynthesis in the early hot universe. Fridman's solution, supplemented by a detailed theory of physical processes in the early hot universe, gave rise to the standard cosmological model (§5.4 "Standard cosmological model. Big Bang. Forming the structure of the universe."), which broadly explains the observed structure and evolution of the universe. In recent years, the efforts of cosmologists have focused mainly on the study of the earliest stages of the evolution of the universe just after the Big Bang - quantum cosmology and the hypothesis of inflationary expansion of the very early universe have emerged to solve some problems of the standard model (§5.5 "Microphysics and cosmology. Inflationary universe.").

Relativistic cosmological model
The process of constructing a relativistic cosmological model consists of the following main stages :

If space-time can be found that is an exact solution of Einstein's equations for the real distribution of matter and well describes the global properties of the universe (agrees with the findings of the visible part of the universe obtained by observation), such a solution can be considered an adequate cosmological model.

Matter in the universe
First we notice stage c). Cosmology deals with the properties of the universe on large cosmological scales, larger than about 109 light-years. From the point of view of these scales, the dimensions of astronomical objects (observed in the sky) are quite insignificant (galaxies with typical dimensions of 100,000 light-years are ten thousand times smaller than this basic scale, galaxy clusters a thousand times smaller). From this large-scale point of view, galaxies and their clusters are only a kind of tiny "dust particles", whose internal structure does not play a proper role from the point of view of the whole. From a cosmological point of view, then, we can imagine the present universe as a space filled with sparsely distributed "dust" *).
*) This "sparse spreading" is valid at the present stage, in the beginning of the evolution of the universe it was a "dense spreading" of high-energy particles and radiation!
    In cosmology, therefore, it is abstracted from specific local structures, as matter is usually considered "dust" or "gas" (ideal liquid) - it can be both an intergalactic gas in the usual sense, and a relativistic "gas" of photons, or a gas whose "molecules" are stars, galaxies or clusters of galaxies. The uniform distribution of the averaged mass in space (cosmological principle) is similar to the homogeneity of a gas (or liquid), which is very inhomogeneous at molecular scales, but from a macroscopic point of view it appears perfectly homogeneous.  In the cosmological approximation, therefore, we can consider the whole universe to be filled with an ideal "gas", whose molecules are galaxies or rather clusters of galaxies, photons of radiation, intergalactic gas. The energy-momentum tensor of such a cosmologically distributed mass in space is therefore expressed in the form corresponding to an ideal fluid (derived in §1.6, passage "Energy-momentum tensor")

T ik   =   (p + r ) u i u k - p. g ik   . (5.3)

When modeling the mass filling the universe in the form of an ideal fluid, it is necessary to know the dependence of the density r on the pressure p, ie the equation of state, for solving the equations of space-time evolution of the universe. However, to analyze the basic issues of global evolution, it is sufficient to limit ourselves to two extreme cases :

Analysis of the evolution of the universe for this basic substance will be in terms of relativistic cosmology, the structure of spacetime performed primarily in §5.3 "Fridman dynamic models of the universe", from the perspective of a particular physical cosmology then §5.4 "Standard cosmological model. Big Bang. Formation of the structure of the universe.", §5.5 "Microphysics and Cosmology. Inflationary Universe" and §5.6 "Future of the Universe. Arrow of Time. Dark Matter. Dark Energy".

Geometry of the universe
In models based on the cosmological principle, three-dimensional space must be
homogeneous and isotropic, ie all points and all directions are equal here, they are no different. In differential geometry, it is shown [214], [155] that such three-dimensional space (except planar Euclidean space) is a space with constant curvature R, independent of spatial coordinates or a direction, that is spherically symmetric with respect to the each point; therefore, any point can be chosen as the origin r = 0 of the spatial coordinates.
    This basic geometric aspect can be illustrated for clarity on a 2D analogy with  two-dimensional area. Homogeneous and isotropic 2D surfaces can be of three types :
-->   2D Euclidean space is flat (non-curved), it is the simplest special case of the more general Riemann space, it has zero curvature everywhere. In Cartesian coordinates (x, z), the length element according to the Pythagorean theorem is simply dl 2 = dx2 + dy2. In the polar coordinates (r, J) given by the transformations x = r.cos J , y = r.sin J, the length element is
          dl 2 = dr 2 + r 2 d J 2 .
-->   2D sphere - the surface of a sphere of radius R , the spherical surface is a Riemannian space with positive constant curvature, in which the length element in polar coordinates has the form
          dl 2 = [dr2/(1-r2/R2)] + r2dJ2 .
--> 2D " saddle " surface is a Riemannian space with negative constant curvature, in which the length element in polar coordinates has the form
          dl 2 = [dr2/(1+r2/R2)] + r2dJ2 .
  The length element in a two-dimensional homogeneous isotropic space with constant curvature can therefore be written in polar coordinates in the general form
            dl 2 = [ dr 2 / (1 - k.r 2 / R 2 ) ] + r 2 d J 2 ,
where the curvature parameter k
= + 1, 0, -1 is introduced.
    Analogously, the length element dl in three-dimensional space with constant curvature, it can generally be expressed in spherical coordinates in the form


where the quantity R -> a (with a dimension of length) indicates the radius of curvature of the space (the radius of curvature of space is customary to denote R ; however, this would be confused with scalar curvature R , so in cosmology it is customary to denote curvature space of space a ). The parameter k = 1, 0, -1 characterizes the global type of space curvature :

k = + 1 ® space with positive constant curvature;
k =    0 ®  Euclidean flat space;
k = -
1 ® space with constant negative curvature .           

A more detailed analysis of the space-time geometry of the universe using this metric, but the time variable a = a(t), in Einstein's gravitational equations will be performed in §5.3 "Fridman's dynamic models of the universe".

Topology of the universe
The local geometry of space-time is determined by the distribution of matter in the universe - matter~energy curves space-time, in which bodies and particles then move along geotedics, representing the straightest possible trajectories. The curvature of spacetime is described by Einstein's equations, the application of which to the universe under appropriate simplifying assumptions leads to Fridman's equations (5.23) describing a universe whose space can have positive, negative or zero curvature, as mentioned above; see §5.3.
  However, this local geometry generally says nothing about the global shape, ie the overall topology of space. In standard relativistic cosmology, a simply continuous universe (with a sphere topology) is considered, on which Einstein's, DeSitter's or Fridman's cosmological models work. Theoretically, however, the universe could have a more complex, multi-conected topology, with different topological tunnels or identifications of different parts, as has already been discussed in §3.3, the passage "
Time Travel"; such a universe could even look like an "emmental"...
  The complex multiple conected topological structure of the space of the finite universe would have interesting implications for what the observer sees in such a universe: in principle, he could see multiple images of galaxies, stars, and himself, as in a mirror maze. And in time at different stages of development. It could not be ruled out that when we observe a distant galaxy, it could be our own Galaxy a long time ago billions of years ago! However, it would be very difficult to astronomically recognize that the two galaxies observed are one and the same galaxy, represented by the passage of light through the complex topological structure of the universe *), if not hopeless! We would see them from different angles and especially, due to the spatial scales of many billions of light years, in completely different time stages of development, changed beyond recognition ...
*) Incomparably more difficult than it is with multiple imaging due to gravitational lensing
(§4.3 , passage "Gravitational lenses. Optics of black holes.") .
  A certain way to obtain at least partial indications for certain topological structures of the universe could be a detailed measurement of the properties of microwave relic radiation - its homogeneity, fluctuations (depending on the angular distance and wavelength), polarization. Already at the time of the separation of radiation from matter, there were nuclei of future structures in the universe, 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 is very small, of the order of 10-5 degrees, so the relevant projects of their data measurement are still being prepared *) - see §5.4, passage "Microwave relic radiation - a unique messenger of early space informations".
For a detailed study of relic radiation, a satellite was launched in 1989 COBE (Cosmic Background Explorer) and in 2001 the WMAP satellite (Wilkinson Microwave Anisotropy Probe); even more accurate PLANCK probe in 2007.
  All these theoretical speculations about a more complex topology have no justification in astronomical observations, so we will stick to the interpretation of relativistic cosmology the simplest and, from the current point of view, the natural assumption of a simply continuous topological structure of the universe.
A certain exception will perhaps only be discussions about the possibility of the existence of multiple universes (§5.5 "Microphysics and cosmology. Inflationary universe." and §5.7 "Anthropic principle and the existence of multiple universes"); however, this will not be the introduction of some a priori complex topology, but of hypothetical topological properties "induced" by turbulent quantum-gravitational processes at the beginning of the universe.

Correct and erroneous cosmological ideas about the universe ?
The development of cosmology was accompanied by many mistakes. During our knowledge of nature and the universe, there were a number of ideas and concepts, most of which were partially or completely erroneously. In the beginning, it was a misconception of the Earth as a flat plate: the view of a man standing in a free landscape really suggested a flat area, possibly wrinkled by mountains. Later, the idea of the globe standing as the center of the universe, around which everything revolves: we live on a cosmic "carousel" of rotating Earth, which suggests the orbit of cosmic bodies around us - was refuted by the Copernican heliocentric system. The idea of the central position of the solar system in space still persisted. The Milky Way astronomically appeared to be a whole universe that was considered static. Stars used to be considered unchanging "perennials" - all stars and planets are in a state of infinite unchangingness and cyclical motion, from the infinite past to the "ages of ages"..!.. Even A.Einstein initially believed in the global static of the universe (see above the passage "Einstein's static universe" and §5.2 "Einstein's and deSitter's universe. Cosmological constant. "). Only E.Hubble's observations of 1924-29 showed the existence of many galaxies moving away from each other - a vast dynamic expanding universe.
  The current Standard Cosmological Model (§5.4 "Standard Cosmological Model. The Big Bang. Shaping the Structure of the Universe.") is very well astronomically and physically based, convincingly explaining everything we observe in the universe. However, even here there are some unresolved issues, such as the question of the origin of the universe, or the mystery of dark matter and even more mysterious dark energy (§5.6 "The future of the universe. The arrow of time. Dark matter. Dark energy."). Only the more distant future will show how these issues can be solved, or what we were wrong about again, and what new phenomena and concepts will appear ..?..

4.9. Gravitational collapse -
- The biggest disaster in nature
  5.2. Einstein's and deSitter's universe. Cosmological constant.

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

Vojtech Ullmann