Where the universe is heading - the arrow of time

Chapter 5
GRAVITATION AND THE GLOBAL STRUCTURE OF THE UNIVERSE:
RELATIVISTIC COSMOLOGY
5.1. Basic starting points and principles of cosmology
5.2. Einstein's and deSitter's universe. Cosmological constant.
5.3. Friedman'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. Dark matter. Dark energy.
5.7. Anthropic principle and existence of multiple universes
5.8. Cosmology and physics

5.6. The future of the universe. Time arrow. Dark matter. Dark energy.

An equally interesting and fundamental problem, such as the origin and early stages of the evolution of the universe, is the question of where the evolution of the universe is headed in the future? What happens to all the amazing structures and matter in space? Leaving aside unlikely scenarios (such as a stationary or oscillating universe), according to the standard cosmological model, the further fate of the universe depends on whether the average density of the cosmic mass r is less or greater than the critical density r_crit (5.26 ) :

• Closed universe
  At supercritical density, the universe is closed and will only expand to a certain limit, then gravity prevails, expansion stops and goes into shrinkage - the red shift changes to blue, the temperature of relic radiation rises slowly at first, but then grows indefinitely - until the final a very dense and hot end (theoretically a singularity), the gravitational collapse of the universe, sometimes referred to as a "big crunch" or a "big collapse". All structures, including the matter of which they are composed, will be destroyed.
     In a rough approximation, therefore, the final phases of a closed universe take place in reverse order to the formation and expansion of the early universe - with increasing relic radiation energy, the atoms of interstellar and stellar matter will be broken up again into elementary particles. In fact, in the final stage (unlike the early universe) will be a lot of compact objects - neutron stars and black holes, which due to accretion of particles and radiation fast grow and eventually merge.
     According to recent astronomical observations, this closed space scenario is unlikely.
• Open Universe
  If the density of cosmic matter is less than critical, the universe will expand constantly beyond all limits; according to the standard cosmological model, the expansion will slow down due to gravity, but it will never stop. There will be "enough time" to apply very time-consuming scenarios of astrophysical evolution of stars, galaxies and whole universe.
     After about 5-7 billion years, the Sun is slowly depleting its hydrogen reserves and, according to the astrophysical scenario of stellar evolution (§4.2, section "Late Stages of Stellar Evolution"), begins to transform into a red giant. Gradually, they will engulf the inner planets Mercury, Venus, and possibly Earth and Mars. After several million years, this red giant turns into a white dwarf. In the meantime, gravitational instabilities in the planets of the solar system will also be fully manifested, with some planets possibly leaving the system altogether.
     Over the next 10-30 billion years, gas and dust in galaxies will create several more generations of stars, which will enrich the cosmic matter with heavier elements by nucleosynthesis. However, the available reserves of hydrogen (which is the default "fuel" of stars) in galaxies are gradually depleting. In most galaxies, "stellar birthrate" are steadily declining. After 100 billion years, most galaxies will "burn out". Then there will no longer be material available for the formation of new stars, the universe will sink into an ever-increasing darkness, which will only occasionally be brightened for a moment by the supernova explosion - the final phase of some of the last massive stars. The last stars die out, eventually only the remaining compact bodies of the final stages of stellar evolution remain: white - then black dwarfs, neutron stars and black holes. Together with the remaining diluted gas, they will orbit the supermassive black holes in the center of the galaxies, and their substance will gradually cool, until they reach the temperature of the surrounding universe. This will take a very long time. A white dwarf will cool to a black dwarf state in about 10¹⁵ years.
     Minor episodes during this period will be fusions of neutron stars, which formed as part of binary (or multiple) systems. As they orbit each other, they will radiate the kinetic energy of the circulation through gravitational waves, gradually approaching them, until they finally merge. In this event, in addition to the flash of gravitational waves, a large amount of neutron material is ejected, which explosively nucleonizes to form a hot substance with a high content of heavy elements - it is described in §4.8, passage "Collisions and fusion of neutron stars ". These areas of hot matter will briefly illuminate the surrounding dark universe and dissolve with rapid expansion ...
     The further fate of these remaining structures depends on whether if the proton is a stable particle (as it seems to us from experience to date) or decays into leptons (as predicted by some grandunification theories, albeit with a very long half-life >10³³ years - in open universe, however, there is "enough time"!). That is not yet known... In the case of stable protons, these material structures in the open universe could perhaps remain unchanged forever.
     However, on such unimaginably long time scales, the quantum tunneling effect could possibly occur: light atomic nuclei could overcome the electric repulsive barrier between themselves and spontaneous fusion of light nuclei into heavier ones could occur - to "cold nuclear fusion". Under normal circumstances, cold nuclear fusion is impossible (cf. discussion in §2.3, passage "Alternative possibilities for nuclear fusion" - "(no)Possibility of cold nuclear fusion?"), the tunnel effect here has practically zero probability. However, in a time horizon of the order of >>10¹⁰⁰ years, even this minuscule probability could manifest..?.. According to this hypothetical idea of cold nuclear fusion, lighter atomic nuclei in compact cosmic objects, the remains of stars, could gradually merge into heavier ones up to iron ( this could take more than 10¹⁰⁰⁰ years to estimate). Only then could they perhaps collapse into neutron stars or black holes..?.. However, this mechanism will forever remain hypothetical, it will never be possible to verify it experimentally...
     In the second case, proton instability, there will be a gradual decay of protons in the nuclei of atoms in the gas and in the interior of compact bodies (except black holes). The energy released in this decay will maintain their slightly sub-zero temperature at a few tenths of a °K. The matter of black dwarfs, neutron stars, gases and the rest of the planets will slowly decompose into leptons and radiation, which will be scattered into the surrounding space.
     Meanwhile, most galaxies collapse into giant black holes - due to the emission of gravitational waves carrying away rotational energy. After about ~10³⁵ years, mostly only black holes remain in space, surrounded by sparse scattered radiation and light particles. Due to accretion, black holes will initially grow, but after a sufficient decrease in the temperature of relic radiation, their quantum evaporation predominates (see §4.7 "Quantum radiation and thermodynamics of black holes"). After a very long time (on the order of ~10⁶⁰ years), black holes evaporate by Hawking's quantum mechanism and the universe will be largely filled with very sparsely distributed particles and constantly diluting and cooling radiation.
     From the once richly structured magnificent universe, only a dull sparse mixture of subatomic particles - electrons, positrons, photons, neutrinos - will remain, flying in the endless darkness of the eternal freezing wasteland, without mutual interactions. Time seemed to stop, there will be no more phenomena and events, the universe will be practically empty and "dead". All usable energy will be depleted (degraded according to the laws of thermodynamics into waste heat - radiation), in such an environment there could not even be life and all chemical reactions would end. This endless freezing extinction of all structures and phenomena is referred to as the "thermal death" of the universe or the "great cold".
  Note:  The boundary case r = r_crit, when the universe will still expand so that at time t ®¥ the expansion stops to a limited extent, it does not have an independent importance for us here and from the point of view of the discussed issues we can incorporate it into the open universe.

Fig.5.9. Schematic drawing of the most important stages of the evolution of the universe.    For an illustrative comparison of the closed and open space evolution scenario, see below Fig. 5.2.2´ a), b)

The evolution of the universe for both cases is schematically shown in Fig. 5.9, where the most important stages of evolution are also marked. If the actual density of matter does not differ enormously from the critical one, the evolution of the universe proceeds for a very long time roughly the same for the closed and open variant; only in the late stages does the dynamics of expansion and the course of astrophysical processes for both cases begin to differ significantly - upper part Fig.5.9 (clearly comparing scenarios of evolution of the closed and open space below to Fig.5.2' a), b) ).
   According to current astrophysical knowledge, the open universe variant probably corresponds to reality. This variant is summarized in the illustration ... from §5.4, which we will show here again for clarity :

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... However, we are mainly interested here in the late stages of the evolution of the universe.

The end of time ?
In §5.4, the passage "The beginning of time?", we discussed the issues of causal relationships at the beginning of the evolution of the universe according to the standard cosmological model. We have come to the conclusion that, from the point of view of the general theory of relativity, initial singularity was not only the beginning of the universe, but also the beginning of time. What about the passage of time and causal relationships in the final stages of the evolution of the universe? :
¨ In the case of a closed universe, the situation is to some extent inversely analogous to the beginning of the universe. All causal relationships end in the vicinity of the final singularity (they cannot be extended analytically beyond this world point) - the great collapse also represents the end of time.
¨In the case of the open universe, from a mathematical point of view, the coordinate time continues undisturbed to infinity. However, from the real point of view of the operationalist conception of time (see §1.1, passage "Space and time"), in the final stages of open space, where there will be no more phenomena and events ("thermal death"), we do not have time how and with what to measure (and in fact is not "what" to measure). In this sense, even in the open universe, the end of time effectively occurs.

The arrow of time
Before we continue to discuss the various variants of the future development of the universe, it will be useful to think about what actually distinguishes between the past and the future - what determines the direction of time, or as it is called "arrow of time" for short. This asymmetry of time - the "arrows" that point from the past to the future - plays a crucial role in our daily experience.
All basic laws of physics have the property of time reversibility : if these laws allow a certain causal sequence of events, then they also allow a sequence of time-reversed events. The laws of mechanics allow the reversal of every movement of a body. Similarly, the laws of electrodynamics do not distinguish between the future and the past (Maxwell's equations themselves are satisfied both by solutions in the form of usual retarded potentials and formally by "advanced" potentials - see §1.5). In short, the laws of physics are at their deepest level symmetric in time. If we remain purely at the level of mathematically formulated laws of physics, we will find no difference between the past and the future.
   Nevertheless, we observe a strong causal direction in all the actual events in nature - natural events always take place in one particular direction, while in the opposite direction never (at least never spontaneously: the glass bootle can roll spontaneously from the table and break, but the broken shards will never spontaneously combine in the original glass...). The observed mechanisms of this temporal direction of natural phenomena (in other words, specific "arrows of time") can be divided into four categories :

• The radiation arrow of time ,
  also called the electromagnetic arrow. It is given by the fact that the island system of accelerating moving charges emits electromagnetic waves, which carry energy from the source at the speed of light, while these waves will be manifest on distant bodies in the future (retarded) - §1.5, equation (1.47). The energy of the radiating system also decreases in the future.
  In addition to these "retarded" waves, the laws of electrodynamics formally allow for "advancing" waves - waves coming from infinity that the source absorbs; these waves can also be understood as waves radiated into the past. In fact, with each spontaneous emission of the source, we observe only the retarded emission of waves. The same applies to the emission of gravitational waves (§2.7).
• The thermodynamic arrow of time
  according to the 2nd law of thermodynamics, is determined by the monotonic increase of the entropy of an isolated system near thermodynamic equilibrium. Time flows in the direction in which things age, hot objects cool, systems decompose, their disorder increases spontaneously.
  From this regularity derives also the biological arrow of time, indicating the direction of biological evolution and the individual course of life of man and all living beings, accompanied by aging.
     The very laws of motion of individual parts of the system also allow for movements leading to a decrease in entropy, but their probability is significantly less than those which, according to statistical physics, lead to an increase in disorder (entropy). This is due to the fact that in practice the number of disordered states is incomparably greater than the number of ordered states. The second thermodynamic theorem is thus a statistical consequence of the fact that there are much more disordered states than ordered states *). And this situation is basically given by the initial conditions.
  *) Many different microstates correspond to one specific macrostate. Entropy (Greek entrope = change, transition ) is the number of different microstates (expressed by the logarithm of this number) that correspond to the same macrostate. The states with high entropy significantly exceed the states with low entropy. Therefore, almost every change in the system will most likely take place into a state with higher entropy. The time arrow of entropy growth is simply a statistical tendency of systems to evolve toward more common and frequent states.
  Although violation of the 2nd law of thermodynamics takes place locally, but only on small spatial and temporal scales. E.g. a molecule with a certain velocity (corresponding to the average thermal energy in a gas) with collisions with surrounding molecules can significantly accelerate (or slow down), but only for a very short time; then it returns to normal.
• The cosmological arrow of time
  is determined by the observation that as time grows, so does the expansion of the universe.
• The psychological arrow of time
  is based on the fact that our memory reflects the part of events which we call the past and which is clearly distinguished from the future in our psychic understanding. So we have a kind of "psychic feeling" for the passage of time - cf. analysis in §1.1, part "Space and time".

The question naturally arises as to whether all these manifestations of time are somehow connected to each other; or whether there is a "primary" or "universal" arrow of time, which is manifested by said "partial" arrows of time. So let's look at the possibilities of merging or reducing at least some of them.
   The psychological and thermodynamic arrows of time seem to be essentially the same : the psychological arrow of time is a consequence of the thermodynamic arrow, because mental processes share an arrow of time determined by thermodynamics. If we imagine (simply but concisely) the brain as a physico-chemical system of neurons performing logical operations and recording sensory sensations in memory, all these operations are irreversible for thermodynamic reasons. It is necessary to expend energy to arrange the memory elements in the brain into a certain state, while a part of it is always dissipated in the form of heat and thus increases the disorder of the whole system. According to the laws of thermodynamics, this increase in disorder is always higher than the increase in order in memory. The direction of time in which our memory records data thus agrees with the direction in which disorder grows - with the direction of entropy growth. It can even be said that the disorder (entropy) increases with time, actually because we conceive and measure time in the direction of increasing entropy..?..
   Finding a direct connection between the radiation (electrodynamic) and thermodynamic arrows of time is not easy. The electromagnetic arrow is in a way a manifestation of the principle (or requirement) of causality in the Minkowski spacetime of (locally) inertial systems, within which Maxwell's electrodynamics works (see §1.6 and 3.2). The thermodynamic (entropic) arrow of time is determined by the laws of statistical mechanics applied to a situation where the initial conditions imply a significantly larger number of disordered than ordered states. The laws of mechanics itself reflect, among other things, causal relationships. The idea that "field equations also determine the regularities of the motion of their resources" can also help to find connections (see §2.5); perhaps it will be ideologically possible to combine all of this comprehensively in future unitary field theory.
   As for the cosmological arrow of time, which points in the same direction as thermodynamics, it is probably just a coincidence: we live by coincidence in a stage of expanding space, so the arrow of time is now identical with the expansion of the universe. If the universe is closed and the expansion is replaced by contraction in the future, nothing will change on the arrow of time in locally inertial systems (as well as on local laws of physics in general), but agreement with the arrow of universe evolution will turn into contradiction *).
*) Some experts (including temporarily S.Hawking) once thought that the cosmological arrow of time is the primary and that as the evolution of the universe transitions from the stage of expansion to the state of contraction, the direction of the passage of time is also reversed. Now, however, they have mostly seen the erroneous of this view and accepted the position of Zeldovich and Novikov on the irrelevance of the cosmological arrow of time...

Inversion of the time arrow => Antiparticle, antimatter ? - No !
In the early days of quantum physics, antiparticles (such as the positron) were considered to be particles with "negative energy", or particles moving "backward in time" (formal coordinate transformations in the Dirac equation allow this). At one time, these concepts played an important heuristic role in the development of particle physics. Now these misleading notions are abandoned and both particles and antiparticles have an "equal" place in the standard model, in applications as well as in unitary schemes. They have nothing to do with the direction of time !

The arrow of time and the anthropic principle
The agreement of the thermodynamic, cosmological and psychological arrows of time can be put into a certain connection with the anthropic principle (its weak variant is enough) - cf. §5.7 and the work "Anthropic principle or cosmic God". We necessarily live in the "intermediate" stage of the expanding of space. In the late stages of the evolution of the universe, the conditions for the existence of life and intelligent information processing will not be suitable - there will be no one to study the connection between the expansion or contraction of the universe and the time direction in which entropy grows. In accordance with the concept of inflation expansion and the anthropic principle, the universe expands almost exactly at a critical speed, so that the shrinkage phase does not occur either at all or only after a very long time. In the meantime, all the stars will go out, the galaxies will collapse and no more free energy sources will be available. The universe will enter a state of almost maximum disorder, which will no longer increase locally - the thermodynamic arrow of time will actually disappear (cf. the above-mentioned passage "The end of time?"). Thus, life and all orderly processing of information will disappear....

We can therefore conclude that the common essence of all "partial" arrows of time is the principle of causality for each locally inertial frame of reference. In analyzing the various possibilities of the evolution of the universe, we are therefore entitled to proceed from the concept that there is a clear universal "arrow of time" determining the direction of evolution of physical systems in each locally inertial frame of reference. These local arrows of time are transmitted from one place to another by means of special- and general-relativistic transformational laws (§1.6 and 2.4) and create a branching causal structure in the spacetime of the entire universe.
Note: Some geometrical-topological aspects of the direction of the passage of time are also discussed in §3.3, passage "Closed worldlines and time travel" and in §4.4, the passage "Black holes - bridges to other universes? Time machines?".

The future development of the universe. Hidden-dark matter.
Let us now continue to discuss the individual eventualities of the future development of the universe. It is very difficult to decide which of the two basic branches of evolution according to Fig.5.9 is realized in the real universe. The accuracy of measuring the deceleration parameter q is still insufficient and when determining the average density r of matter in space, the problem of hidden matter (dark, non-radiant substances) is encountered. If we take only the "luminous" mass contained in galaxies and in clusters of galaxies, it leads to value r »10^-32 g/cm³, which is more than an order of magnitude smaller than r_crit (@ 5.10^-30 g/cm³ at H » 50 km/s.Mpc) and would indicate an open space. However, it turns out that this "luminous" substance is far from representing all the matter in the universe :
Hidden-dark matter in galaxies and clusters of galaxies
When monitoring the dynamics of the rotation of galaxies shows, that real (gravitational) mass of galaxies appear about one order larger than that from luminosity astronomically determined mass; according to today's observations, the galactic halo is much larger in size than previously thought and probably contains a larger portion of the total mass of galaxies. Even greater disproportion arises in galaxy clusters, where the relevant difference is almost two orders of magnitude - so that at the observed relative velocities of the individual galaxies, the system-cluster of galaxies can be stably gravitationally bound.
   This is evidenced by the analysis of the motion of glowing very sparse gas around galaxies. If the mass of the galaxy were concentrated only in the visible region, the orbital velocity of the surrounding glowing gas would be inversely proportional to the square root of the distance from the center of the galaxy (according to Kepler's law). In a simplified spherically symmetric model, at a distance r from the center of the galaxy, the orbital velocity of a substance will be given by the relation v² = G.M(r)/r, where M(r) is the mass contained in a sphere of radius r. For a constant density of matter r(r) = r then inside will be v²  = (4/3) pr G.r² (orbital velocity will increase in direct proportion to the distance r ), while outside the galaxy the dependence v² = G.M/r will apply, where M is the total mass of the galaxy. Outside the galaxy, according to Newton's laws, the orbital velocity of matter (gases) should decrease with the square root of the distance (dotted curve in Fig.5.10).

Fig.5.10. Typical rotation curve - dependence of the orbital velocity of matter on the distance from the center of the galaxy. Instead of the expected decreasing orbital velocity with distance in the halo galaxy, an almost constant rotational velocity is observed, indicative of a distributed gravitational hidden mass.

In reality, however, it is observed that up to a distance of several radii of the visible part of the galaxy, the gas orbital velocity remains roughly constant (solid curve in Fig.5.10, which is "flat"), so that in this non-radiative region the mass density appears to be approximately the same as in the luminous areas of the galaxy. It can be said that stars in galaxies and galaxies in galaxy clusters orbit and overall they move so fast, that centrifugal force and inertia would have long ago had to scatter them into space, if they had not held by the gravity of some unknown hidden mass. This fact was pointed out in 1934 by F.Zwicky, who at the observatories in Mt. Wilson and Mt. Palomar observed faster movement by spectrometry galaxies at the edge of a cluster of galaxies and stars in the peripheral parts of galaxies, than would correspond to the law of gravity at astronomically determined masses of "luminous" matter.
Because this problem is closely related to the virial theorem (§1.2, passage "Distribution of kinetic and potential energy. Virial theorem") known from classical mechanics (according to which the sum of potential energy and twice the kinetic energy of a stationary system of bodies is zero), it is said sometimes also about the "virial paradox".
   In order to explain this paradox, it is necessary to assume that in galaxies a much stronger gravitational field acts than corresponds to the classical mass of electrons, nucleons, atoms, ions that form stars (with planets) and interstellar gas. There must be a large amount of some hidden and non-radiant dark matter that has gravitational effects. The measured rotational curves of ordinary galaxies show a content of at least 70 % of dark matter (up to 90% in dwarf galaxies). Measurements of motions in large systems of galaxy clusters show that hidden matter is not only contained in galaxies, but is distributed throughout the universe (with different local densities).
  This hidden mass should be composed of particles that are affected only by gravitational and possibly weak interaction (the effect of weak interaction would be negligible due to the low effective cross section and short-range), but they are not affected by strong and electromagnetic interactions (or electromagnetic interaction does not manifest observationally). Hidden matter would be affected - and would affect the surrounding universe - only gravitationally (see below).
   In short, galaxies rotate too fast to be held together by the gravity of the visible matter in stars and interstellar gas. So there should be a kind of hidden gravitational "glue" that holds galaxies and clusters of galaxies together, so that the stars do not fly away from the rotating galaxies into the surrounding universe. Without this hidden matter, galaxies and galaxy systems would be unstable and would not hold together.

Dark matter is therefore a hypothetical form of matter that is spread over very large regions of the universe. It holds together the galaxies that orbit faster in the peripheral regions, than would correspond to the gravity of visible matter; the same is true in galaxy clusters. It is called "dark" because it does not emit, absorb or reflect any electromagnetic radiation, making it invisible to telescopes. However, its existence (and some basic properties, especially its distribution) can be derived from its gravitational effects on visible matter, radiation and on the large-scale structure of the universe. Below we briefly discuss these effects and try to find possibilities for revealing the nature and composition of dark matter.
   In addition to observing the motion of stars and gas in galaxies and the motion of galaxies in galactic clusters, there are others indications of the presence of dark matter :
¨ In addition to stars and cold interstellar gas, there are also very hot gas in galaxies, which is ionized and shines mainly in the X-ray field. Due to the high temperature of the gas, the speed of chaotic movement of electrons and atoms-ions of hydrogen and helium is quite high, exceeding the escape velocity (about 500 km/s) needed to leave the gravitational influence of the galaxy. Such hot gas would dissipate in a short time and escape from the galaxy. The presence of this hot gas in galaxies indicates a much stronger gravitational field than corresponds to the classical mass of stars and interstellar gas.
¨ The gravitational field of galaxies and clusters of galaxies curves the light that passes around them - leading to an effect gravitational lenses (§4.3, section "Gravitational lenses"). From how the gravitational field of a galaxy or cluster of galaxies affects the light from more distant galaxies beyond it by the effect of a gravitational lens, the mass of that galaxy or cluster of galaxies can be determined. The masses here also come out much larger than the classical luminous mass and interstellar gas.
¨ Cosmological evolution of the early universe according to the standard model (§5.4, part "Standard cosmological model ") :
> The course of primordial nucleosynthesis in the first about 3 minutes depended on the proportion of baryon and non-baryon matter (§5.4, part "Initial nucleosynthesis") - with a larger proportion of nonbaryonic substance, it is sufficient to produce less helium. The observed amounts of primordial helium ⁴He (25%), deuterium and ³He suggests significant presence nonbaryonic substances (cf also below note on the primary nucleosynthesis in the passage "From what is dark matter?"); otherwise helium would be more ...
> The formation of galaxies and galaxy clusters
in the era of matter was significantly influenced by the composition of matter in the universe (§5.4, part "Forming the large-scale structure of the universe", section "Structure and evolution of galaxies "). If this substance were composed only of protons, electrons and atoms of hydrogen and helium, intense radiation (from the not too long time of the radiation era) would hindered and prevent the formation of galactic structures for a long time - the universe would remain homogeneous, smooth, without large-scale structures. The presence of dark matter, which does not directly interact with radiation, soon allowed gravitational contractions to "win" over the destructive effects of radiation. The observed faster (earlier) formation of galactic structures requires for its explanation additional (only gravitationally interacting) matter - dark matter than would correspond to the dynamics of known matter during the expansion of the universe. This is perhaps the most important cosmological indicia for hidden matter - it enabled, among other things, the formation of our Galaxy, in which the solar system, planet Earth, the evolution of life and our existence..?..
Note: Some doubts about the concept of dark matter and alternative explanations are discussed. below in the passage "Doubts of Nonbaryonic Dark Matter - an Alternative Explanation? ".

Transparency, structurelessness and large-scale dominance of dark matter
Dark matter should be about 10 times more in galaxies and galaxy clusters than luminous (or radiation-absorbing) matter - it is dominant on a large spatial scale. The name "dark matter" could lead to the misconception that this substance will absorb light much like the dark clouds of interstellar dust. Nothing like this is observed, "dark" or rather "hidden" matter is perfectly transparent to light and other electromagnetic radiation. It does not emit, absorb or reflect electromagnetic radiation, it shows only a universal gravitational interaction and probably also a weak interaction (see below). If this is the case, dark matter is not able to dissipate its internal energy, it cannot "settle" in large quanties near the stars, its accretion is negligible *). It can collect and gravitate only in huge formations of matter such as galaxies and clusters of galaxies. It can be said that dark matter can be a kind of "backbone" or "skeleton" on which ordinary luminous matter is "packed".
*) A massive star, if it is inside a cloud of dark matter, can in principle absorb a small amount of dark matter by spherical accretion (radiation and stellar wind do not prevent this). A gravitationally bound disk of rotating dark matter can form around massive compact objects such as black holes, but with virtually no accretion. Due to the absence of friction, the orbiting dark matter cannot get rid of excess angular momentum in any way and therefore cannot descend to progressively lower orbits to finally be absorbed by a black hole (cf. "Accretion disks around black holes" in §4.8); will continuously orbit around. This phenomenon can be expected especially for supermassive black holes in the center of galaxies, where a greater concentration of dark matter is assumed and the dark-matter rotating disk can be very massive. Although it does not directly contribute to accretion, it can greatly influence the structure and dynamics of the normal-mass accretion disk.
   In addition to its gravitational influence on the motion of glowing astronomical objects (stars, galaxies), dark matter manifests itself in an attractive gravitational influence on the propagation of light - the effects of a gravitational lens (§4.3, section "Gravitational lenses"). For the curvature of electromagnetic rays, it does not matter whether the gravitational substance is glowing or dark. In this way of "gravitational lensing", it would be possible to detect the distribution of dark matter even without a direct link to luminous matter (even hypothetical "dark galaxies"..?..).

What is dark matter made of ?
The question naturally arises, what is this hidden dark matter made of? In particular, they could be the usual forms of matter such as ionized intergalactic gas, molecular clouds, "infrared" or "brown" dwarfs similar to Jupiter (stars so light that they did not ignite thermonuclear reactions), burnt-out stars of the 1st generation, after which left black dwarfs, neutron stars and the like. They could also be numerous smaller black holes of stellar origin (most of the degenerate matter hidden in these black holes has a baryon origin). This component is called baryon dark matter and is not fundamentally very different from the commonly known substance composed of atoms (more than 99.9% by weight here is made up of baryons - protons and neutrons in the nuclei of atoms).
   However, most astrophysicists are inclined to believe that most of the (hidden) matter in the universe is contained in so-called "nonbaryonic" matter *) such as neutrinos or some "exotic" structures formed from quarks, hypothetical gravitins, axions, s-neutrinos (also called neutralin), and the like. These exotic particles of non-baryon nature are collectively named WIMP (Weakly Interacting Massive Particles) - see §1.5 "Elementary particles", passage "Hypothetical and Model particles" in the book "Nuclear Physics, ionizing radiation".
*) One of the clues for this view is based on a detailed analysis of the cosmological theory of primary nucleosynthesis, according to which the density of baryons in nucleosynthesis had to be about one order of magnitude lower than critica,l in order to explain the observed relative abundance of light elements (especially helium and deuterium). The observed representation of ⁴He and D (²H) indicates the amount of baryon mass W_b » 0.05 - compare with the footnote in §5.4, passage"Lepton era - Initial nucleosynthesis ". Therefore, all known atoms together (especially their nuclei composed of baryons) are not enough to explain the hidden substance, its gravitational action. If all non-luminous matter were baryon, there would be much more helium in the universe.
 Neutrinos ?
First candidates for the composition of dark matter is naturally offered neutrino. If neutrinos had a non-zero rest mass greater than about 5 eV/c², their total gravity could even lead to a closed universe. The rest mass of neutrinos was first measured in 1982, but then very inaccurately. Newer measurements of the mass of neutrinos (mentioned, for example, in the section "Neutrinos - ghosts between particles" of the monograph "Nuclear physics and physics of ionizing radiation") indicate the rest mass of neutrinos m_on <~ 2 eV. This question remains open, astrophysicists mostly doubt the substantial presence of neutrinos in the hidden matter of the universe, estimating it at a maximum of only about 1-2%. Although neutrinos are abundant in the universe (along with photons, they are the most abundant particles), their rest mass is too small to explain the observed large amount of gravitational dark matter. In addition, due to the low rest mass, the neutrinos move at high speeds: such a mass of light fast particles would be too "hot" *), so it could not form the observed gravitationally bound structures and would not explain the observed hierarchy of galaxies - the cluster of galaxies. Even the current galaxies do not have such a strong gravitational field that they are able to hold "clouds" of neutrinos forming dark matter. The speed of their chaotic motion is higher than the escape velocities from the galaxies - the neutrino would soon disperse and escape from the galaxy. So dark matter should be made up of heavier, slower-moving particles.
*) According to the speed of motion of the particles that make up dark matter, it can be divided into two types :
¨ Hot dark matter is made up of light particles moving at high speeds, comparable to the speed of light (such particles during the existence of the universe could therefore fly through a substantial part of the observable universe). Such particles leave the places of gravitational fluctuations very quickly. Thus, hot dark matter could not stimulate the formation of structures in the universe from originally small fluctuations to large units (the rapid motion of particles would rather eliminate these fluctuations). Only large structures could form - first superclusters of galaxies, of which clusters of galaxies, then galaxies. Particles of "hot" dark matter cannot be kept in gravity fields of galaxies, their speed is many times higher than that escape velocity from galaxies - they cannot create hidden matter in a galactic halo.
¨ Cold (cryogenic) dark matter is formed by heavy particles moving at low speeds compared to the speed of light. Such slow particles of cold dark matter could be gravitationally attracted by small fluctuations in density distribution in the early universe and further increase these fluctuations. Thus, cold dark matter can stimulate the formation of large-scale structures in the universe "bottom-up": from galaxies, through clusters of galaxies, to superclusters of galaxies. It can explain the observed rotational curves of galaxies.
   Dark matter in the universe probably consists of both of these species, but most of it is its cold component. Astronomical observations (fluctuations of relic radiation, distribution of galaxies and clusters of galaxies, computer simulations) indicate the formation of a large-scale structure of the universe in a "bottom-up" direction.   
 W I M P  ?
Neutrinos are therefore probably only a minor component of dark matter. Unfortunately, the main "candidates" for hidden matter in space remain hypothetical hitherto undiscovered particles from the WIMP group (Weak Interactic Massive Particles). According to the unitary theory of sypersymmetry, there should be a "superpartner" for each particle, differing, among other things, in spin (for particles with half-number spin, the superpartner should have an integer spin and vice versa). It is believed that a large number of these superparticles formed in the early universe. Most of them disintegrated later, but due to the disruption of left-right symmetry, (left-handed) relict superparticles could remain here - WIMP, interacting with matter only by weak and gravitational interaction. The WIMP particles do not disintegrate spontaneously, but in collisions they are transformed ("annihilated") into a pair of X particles and its antiparticles. It could be, for example, neutraline (see the section "Hypothetical and model particles" in §1.5 of the above-mentioned monograph in electronic version). Neutralins (supersymmetric particles to neutrinos) have a relatively large rest mass, estimated at about 50-200 proton masses. If there are heavy WIMPs, their relatively small numerical representation (units of % with respect to the number of baryons) would suffice to explain the gravitational effect of dark matter *); they would form the desired "cold" component of dark matter.
*) This small number also contributes to the difficult detectability of heavy WIMP particles of hidden matter. While neutrinos are abundant, so some of those trillions of neutrinos can sometimes be detected (Neutrine Detection), the frequency of WIMP interactions with particles of our ordinary substance, or with each other, is so low that it is below current detectability. However, with the progress of electronics and detection technology, it is to be hoped that in the end it will succeed ...
   But it should be noted that we are capable only detect high-energy neutrinos, originating from nuclear reactions in stars (from the Sun), from a supernova explosion, or from cosmic ray interactions. However, cosmological significance may be rather low-energy neutrinos (of relict, primordial origin), which we are unable to detect.
  Other particles that are sometimes considered in connection with dark matter are axions - hypothetical particles introduced in quantum chromodynamics as a quantum of fields compensating for the strong interaction of CP-symmetry breaking. Axions do not have an electric charge and interact very little with matter through weak and strong interactions. They have very little mass (comparable to or less than neutrinos), so there would have to be a huge number of them in space to explain hidden matter; they could perhaps come from the processes of symmetry breaking and separation of interactions at the earliest stage of the universe. Axions could form a "hot" component of dark matter, along with neutrinos.
   The last candidate for dark matter could be the so-called mirror matter, hypothetically postulated in connection with parity symmetry and its disruption in weak particle interactions (it is also described in the section "Hypothetical and model particles", passage "Shadow or mirror matter - Catoptrons?", in §1.5 of the monograph "Nuclear physics and physics of ionizing radiation").
   In connection with the geometric theories of superstrings (§B.6. "Unification of fundamental interactions. Supergravity. Superstrings.") there have been some sci-fi speculations, that dark matter particles do not occur in our 3-dimensional space, but in another extra- dimension, that interacts with our universe only gravitationally; therefore they cannot be discovered by any particle experiments or detection ..?..
 Black holes ?
Black holes of small and medium masses could generally be ideal candidates for dark matter, as they do not emit light and, due to their very small dimensions, practically do not absorb light from an astronomical point of view. Stellar black holes of mass >~3M_¤ (formed by the collapse of massive stars at the end of their evolution - §4.2, passage "Complete gravitational collapse. Black hole.") are too few. An interesting hypothesis, however, is the black holes of primordial origin (§4.8, passage "Primordial Black Holes"), which could have formed in large numbers from the hot, extremely dense plasma that filled the universe immediately after the Big Bang. Microscopic quantum fluctuations they increase to a macroscopic scale during inflationary expansion - regions with significantly lower and higher densities of matter and energy have emerged, from which all structures in the universe later created. In the very early stages of the universe, soon after the inflation period, a large amount of significant condensation could be present, which could quickly collapse into black holes. This would create a large number of primordial black holes of various weights, especially low ones. These primordial black holes can be considered of non- baronic origin, they formed before nucleosynthesis. Their detection is very difficult, it could perhaps be possible through gravitational microlenses :
  If some compact object (with a mass of at least 10^-9 M_¤) were to pass through the line of sight from a more distant star towards us during its movement, it could cause a transient achromatic brightening of the star. The mass of this transiting compact object could be estimated from the degree of this brightening . Such gravitational microlenses are very rarely observed; those few cases are not distinguishable from free moving errant planets..?..
  If the hypothesis of primordial black holes were to be confirmed, it would be a very plausible origin of dark matter, as there would be no need to look for any unknown particles outside the standard model... Alternatively, primordial black holes could form at least part of the dark matter..?..

Unstructuredness and spreading-out of dark matter
Another question is, what distribution and what structures can dark matter form? Interstellar gas composed of ordinary matter (such as hydrogen and helium) can condense by gravity to form globules, protostars, and stars (§4.1, "Star Formation" section). At first glance, dark matter could do the same. However, contraction and collapse require the way in which the particles lose the kinetic energy generated by the adiabatic compression and slow down so that gravity prevails and the contraction can continue. In ordinary matter, this occurs loss of kinetic energy through electromagnetic interactions, radiation of electromagnetic waves. However, dark matter particles (such as putative WIMPs) do not have an electromagnetic interaction and have no way to lose energy. From this point of view, dark matter probably cannot form more complex gravitationally compressed star-sized structures.
   For similar reasons, dark matter cannot contribute significantly to accretion on compact objects. Ordinary matter trapped in the accretion disk loses kinetic energy and angular momentum due to friction (caused by electromagnetic interactions), thus moving in a spiral until it is absorbed (§4.8, section "Accretion disks around black holes"). Dark matter probably does not show friction, its particles would orbit the compact object constantly in the disk. Only particles coming with a very small impact parameter can be captured - in the case of dark matter, only spherical accretion can occur, which is generally inefficient.
  According to current knowledge (these are rather hypotheses...), dark matter does not create local structures, it is spread out in clouds comparable to galactic dimensions. This is probably the case in the current cold rarefied universe.
The role of dark matter in the early universe ?
However, it could be different in the early dense universe, in the period of the formation of the first stars and galaxies. Dark matter, in close contact with atomic-baryonic matter, could significantly participate in the gravitational contractions of dense, extensive clouds of this mixture. Clusters of dark matter could have initiated the formation of galaxies (it is briefly discussed in §5.4, section "Formation of the structure of the universe", passage "The role of dark matter"). Also, the early massive stars of the 1st generation could contain, in addition to the usual atomic-baryonic matter, a certain amount of dark matter, which collapsed in the protostar phase together with molecular clouds of hydrogen and helium (§4.1, passage "Formation of stars"). Dark matter could also be involved in the early formation of giant black holes, present at the center of most galaxies (§4.8, section "Mechanism of quasars and active galactic nuclei", passage "How did supermassive black holes originate?").

Doubts about non-baryonic dark matter - an alternative explanation ?
The concept of dark matter outlined above is now almost universally accepted in the astronomical and astrophysical community. However, there are some problems and controversial issues :
¨ Nonbaryonic particles designed as dark matter components are purely hypothetical , not part of a standard particle model, have not been demonstrated in laboratory experiments at large accelerators, nor have they been detected in radiation coming from space. This circumstance diminishes the credibility of the nebaryonic dark matter.
¨ The question of accuracy and interpretation of measured data - the correct determination of the amount of classical baryon mass and its distribution in galaxies and surrounding space.
¨ Application of Newton's laws over vast distances in curved spacetime. We would see the observed effects (even without the assumption of unknown dark matter) if the gravitational force on large galactic scales decreased with distance more slowly than Newton's law assumes (as well as the general theory of relativity). In this context, an alternative eventuality of the modification of Newton's law of gravitation is sometimes considered ("MOND - modified Newtonian dynamics", §1.2, part "Galactic modification of Newton's law of gravitation - MOND"). The observed astronomical measurements of the dynamics of the motion of stars in galaxies and galaxies in galaxy clusters, which are generally attributed to the gravitational effect of dark matter, could thus be explained by another form of gravitational law. By appropriate modeling of MOND parameters, anomalous rotational curves of galaxies can be explained quite satisfactorily (but not anomalies in galaxy clusters and galactic collisions). These efforts do not yet seem very justified and promising (Milgrom's MOND, with its accelerating dependence, is an artificial and not very convincing ad hoc theory ); dark matter is likely to be explained in simpler physical ways. Or even discrepancies can only be caused by an incorrect model of the distribution of baryonic matter in galaxies and galaxy clusters ..?..

The more complex dynamics of the expansion of the universe ?
Some new aspects in the issue of the distant future of the universe, in relation to the mean density of matter in the observed part of the universe, are now brought about by the presumed inflationary expansion of the early universe (§5.5, section "Inflationary expansion of the universe"). As a result of this inflationary stage, the radius of the universe would probably be many times (by many orders of magnitude) larger than the horizon, ie than the observable region of the universe. The "local" density in the observed part of the universe may then differ somewhat from the global mean. That means that even very accurate determination of the average density of matter in the observed universe it cannot decide on its own between a closed and an open universe, especially if this measured density wil be near to the critical density. After a sufficiently long time, the density of matter in the now observed part of the universe, "mixes" with the density of matter in other parts of the universe and the total density can move to the "opposite side" of the r = r_crit limit than now. Let us recall that according to the current quantum cosmology of the inflation model, a closed universe is probably expected, albeit very near to the planar one, as mentioned in the previous paragraph (approximate flatness also indirectly follows from the anthropic principle, §5.7).
   However, see below the new findings - "Accelerated Expansion of the Universe? Dark Energy?" :

Cosmological Surprise :
Accelerated Expansion of the Universe? Dark energy?
According to the standard cosmological model (§5.4), the expansion of the universe is hampered by the attractive gravitational effects of matter and must therefore slow down - both in the closed universe (where it would eventually contract) and in the open universe (where the expansion will slow down, but it never stops completely). After all, to quantify the deceleration of the expansion of the universe, we introduced the so-called decellation parameter q in §5.3. We now know that the gravity of dark matter in particular should make a decisive contribution to slowing down the expansion of the universe. The cosmological constant in Einstein's gravitational equations, according to previous ideas, perhaps may have played a decisive role in the inflationary expansion of the universe at the very begining (as discussed in more detail in §5.5 "Microphysics and Cosmology. Inflationary Universe."), but did not need to be considered for further evolution of the universe.
   As discussed in §5.1 and 5.3, the dynamics of expansion (or contraction) of the universe, ie the time course of the scale factor or expansion function a(t) - the expansion history of the universe, can be find out by determining the relationship between the cosmological redshift Z in the spectrum of distant objects and their distances. These distances are derived from the ratio of the actual and observed (apparent) luminosity of suitable "standard candles" (§4.1, passage "Determining the distances of space objects - a basic condition of astrophysics"). For large cosmological distances, type Ia supernovae are suitable "standard beacons" (SN Ia; they are described in more detail in §4.2, section "Supernova explosion. Neutron stars.", passage "Supernova types and their astronomical classification"), which astronomers are currently able to observe with the help of large telescopes up to distances of more than 6 billion light-years. Supernova Ia can be identified by the shape of the spectrum, their brightness is determined from the course of the light curve - the increase, peak and decrease of the brightness of the supernova. Photometric measurements of such different distant supernovae (with different Z 's) make it possible to determine how the universe expanded at different time periods. By performing multiple measurements at multiple distances, we can create a graph mapping the expansion of the universe as a function of its age.
   In 1998-99, two groups of American astronomers undertook the astronomical "mapping" of the dynamics of space expansion by photometric measurement of a large number of type Ia supernovae. The first was led by A.Reiss and B.Schmidt (Space Telescope, Baltimore) within the project "High-Z Supernova Search" - to search for supernovae with a large redshift Z. The second group ("Supernova Cosmology Project") was led by S.Permutter (Lawrence Berkeley Laboratory). The original goal of these observations was to find out, how big the slowdown in the expansion of the universe is.
  This accurate photometric measurements of distances supernovae type Ia (discussed below) hawe shown, that very distant supernovae type Ia (high value Z) are less bright than would correspond to their cosmological red shift Z in universe, the expansion of which slows down due to the gravitational effects of the mass (the dynamics expansion of the universe see §5.3). For closer supernovae with a smaller Z, the relationship between distance and redshift corresponded to the standard scenario. However, the most distant galaxies seem to have driven "something" further than the usual Fridman expansion of the universe. Respectively (which is the same thing), these very distant galaxies, corresponding to the earlier periods of the universe, are moving away at a slower speed than would correspond to Fridman's dependence.
  From such a measured relationship between the cosmological redshift and the distance of supernovae, it was surprisingly observed that the expansion of the universe is probably not slowing down at the moment, but is accelerating on the contrary! The expansion of the universe has normally slowed down only to about half the current age of the universe, to about 6-7 billion years, but then began to accelerate, which still continues.
Photometric measurements of supernovae Ia
A supernova of type Ia arises in a close binary star consisting of a giant star and a white dwarf, where matter is transferred from the giant to a white dwarf, whose mass gradually increases. It then crosses the Chandrasekhar limit (1.4 M_¤) and the white dwarf explodes thermonuclearly, which manifests itself as a type Ia supernova explosion - see §4.2, section "Supernova explosion. Neutron stars.". All type Ia supernovae explode according to the same mechanism and with the same initial mass *) and therefore the amount of energy released is practically the same every time.
*) It's only approximative, more detailed measurements show that the initial white dwarfs have somewhat different mass before the Ia supernova explosion. However, by analyzing their light curves and spectra, Ia supernovae can be normalized as "standard candles" (§4.2, passage "Astronomical classification of supernovae"), with an accuracy of about 10%.
  Thus, from the relative observed brightness, the distance of such a type Ia supernova can be determined, independently of the spectrometrically measured cosmological redshift z = (l - l_o)/l_o of radiation from the supernova (l_o is the wavelength of a certain spectral line at time t_o of transmission beam, l is the wavelength of the same line at time t of beam capture). In §5.3, a scale (expansion) function was introduced to describe the evolution of the universe a(t) indicating how distances in the expanding universe change with time t . For two time instants t_o and t, there is a simple relation z = (a - a_o)/a_o between the values of the scale function a and the cosmological redshift z , where a_o characterizes the dimensions of the universe at time t_o sending a ray and a the dimensions of the universe in time t of its capture. Of which a = (1 + z) .a_o , so from the measured cosmological redshift we can determine how the dimensions of the universe have changed since the light beam captured today was emitted. Careful analysis of the radiation from a number of differently distant supernovae can reveal the relationship between the cosmological redshift and the distance of the supernovae, from which it is possible to "trace" how the universe expands. And it is these measurements that show the time dependence a(t) similar to the curve L> L_E in Fig.5.3c in §5.3, according to which the rate of expansion of the universe slowed down in the early stages, but is currently increasing, in Fig. 5.3'c :

Figure 5.3 is presented here again for clarity (with a red marking of the important curve for this issue) :

Figure 5.3´. Evolution of cosmological models - time course of radius a (scale factor) of the universe, depending on the value of cosmological constant L and mass distribution density r (r_crit is the value of critical mass density, a_E and L_E denote values of space radius and cosmological constant corresponding to Einstein's cosmological model).
For our purpose, the graph L> L_E in Fig. c) on the right is important here, which expresses the newly observed dynamics of the evolution of the universe, with late accelerated expansion.

Regression analysis of the Hubble diagram of the measured dependence of the relative magnitude of type Ia supernovae on the cosmological redshift best corresponded to the curve of the cosmological model with parameters W_M = 0.29 and W_L = 0.71 (W parameters were introduced in §5.3, passage "Relative W - parameterization cosmological models"). The analysis according to Fridman's cosmological model (equation (5.23a) in §5.3) led to the value of the cosmological constant L » 1.2x10^-52 m^-2.
Accelerated expansion of universe - versus its revision ?
In this part of our treatise on the evolution of the universe, we will discuss the analysis and implications of the hypothesis of accelerated expansion of the universe and dark energy, which is widely accepted in contemporary cosmology. At the end of this section, however, we will briefly discuss more recent measurements and analyzes of the frequency shift of a larger number of supernovae, "A revision of the accelerated expansion of the universe?", which probably show a smaller rate of accelerated expansion, or perhaps even the abandonment of the concept of accelerated expansion and dark energy..?..
Dark energy
It has been hypothesized that this accelerating expansion is caused by a kind of pervasive vacuum so-called "dark energy" DE (Dark Energy) with a negative energy density so high, that its repulsive effects overcomes the gravitational action of all matter in the universe. In the simplest case, it is assumed that dark energy and emerging repulsive action are distributed approximately homogenous in space.
   This mysterious hidden or dark energy is sometimes referred to as the "fifth state" or "quintessence" (see below). As shown in §5.2, part "Cosmological constant", further in §5.3 and §5.5, such vacuum dark energy would equivalently generate a cosmological constant L> 0 (case w = -1 in table (5.61) below) in Einstein's equations (5.7) of the general theory of relativity, leading to a negative pressure that would induce "antigravity" repulsion at cosmological distances , acting opposite to the gravitational attraction of ordinary matter. That would be the simplest explanation of dark energy (various hypothetical possibilities to explain the origin of dark energy are briefly discussed below in the passage "The nature of dark energy?").
   So if dark energy is the energy of (empty) space itself, then as the universe expands, more dark energy comes into the universe, which causes the expansion to accelerate, it is still faster. According to current cosmology, the primary cause of the universe's expansion is the energy-momentum left over from the Big Bang. And the repulsive force of dark energy, when it prevails over the attractive cosmic gravity, will further accelerate this expansion permanently. According to current knowledge, it seems that the universe will not only expand forever, but its expansion will continue to accelerate more and more...
 Dark energy equation of state
Equation of state of dark energy can be modeled in a simple general form as an "ideal liquid"

where p_de is the pressure, r_de is the dark energy density and w is the state constant.
   If the universe were filled only with the dark energy "de", the acceleration ä of the scale function a(t) with time is given by substituting p_de and r_de into 2. Fridman's equation (5.23b), in a simplified form: ä/a = -(4pG/3).(r+3p/3). If the value of the state constant w < -1/3, this leads to a positive value of ä, ie to a cosmic acceleration of the expansion. And as shown in (5.28) - (5.29), from the 1st Fridman equation (5.23a) the expansion law follows for the equation of state of type (5.59) a(t) = a₀ .t ^{2 / [3 (w + 1)]} .
   In connection with the concept of dark energy, it is therefore useful in Fridman's equation (5.40) to replace the cosmological term L and W_L - to generalize (this generalization is evident from the table (5.61)) with dark energy density r_de and its relative density W_de = r_de/r_de-crtit - by the contribution of dark energy :

(5.60)

The "functioning" of this contribution of dark energy in the dynamics of the expansion of the universe depends on the value of the coefficient w in the equation of state p_de = w.c².r_de of dark energy :

These options (except for the uninteresting case a)) will be discussed below.
   If the dark energy density is constant over time or decreases more slowly than the density of ordinary matter (ie slower than 1/a³ for matter, or 1/a⁴ for radiation), the scenario of the evolution of the universe would correspond to the curve L> L_E in Fig.5.3.´c): after the end of the initial inflation expansion and the onset of the Fridman expansion, a period of deceleration would take a long time, when the gravitational effects of total matter (shining + hidden) prevail over the repulsive forces of dark energy and the expansion slows down. After a proper reduction in the density of the mass, a reversal would occur. For a short time, the two forces would be balanced ("indecisive universe"), then dark energy would prevail and cosmic expansion would eventually go from the deceleration stage to  acceleration - the constant acceleration of expansion, towards the "thermal death" of the universe ...

Unless a convincing alternative astrophysical explanation of the observed data *) for distant supernovae is found (eg light absorption mechanisms from supernovae in the dust component of an intergalactic substance, different evolutionary properties of early stars formed from a substance with less heavier elements, or inadequate use of existing physical models to extremely long time and space intervals, ...), the accelerated expansion of the universe and the existence of dark energy must be taken very seriously. It would be one of the most surprising and mysterious discoveries in the history of astronomy!
*) The processing of some newer and larger sets of several hundred distant type Ia supernovae somewhat reduces the statistical significance of the data from the first observation (and perhaps does not even rule out a constant rate of expansion ..? ..), further measurements will specify ....
Three indications for dark energy
We now have three independent indications for the accelerated expansion of the universe :
× The measurement of supernovae Ia
is the most important, it is a direct indication - it has been discussed above. In addition, there are two other indirect, looser and model-dependent indications:
× Inhomogeneities of relic radiation in correlation with the large-scale structure of the universe 
The small anisotropies of relic radiation reflect inhomogeneities in the distribution of matter just after the end of the radiation era. One of the possible origins of these inhomogeneities may be the so-called acoustic horizon of density waves-oscillations in the hot plasma of the lepton and radiation era (it is discussed in §5.4, passage "Baryon acoustic fluctuations"). It is believed that galaxies later formed from these initial inhomogeneities, stretched by the expansion of space over long distances of hundreds of millions of light-years. Their current distribution - clustering - depends on the dynamics of the expansion of the universe.
Detailed analysis of relict radiation inhomogeneities (performed by COBE and WMAT satellites, even more sensitive analysis of relic radiation is performed by PLANCK satellite) and its correlations with astronomical mapping of the large-scale distribution of galaxies suggest that the observed clustering structure corresponds to the accelerated dynamics of space expansion.
After all, even the comparisons of the density of galaxy clusters with low and high redshifts give a slight indication for accelerated expansion ...
× Measurement of the dynamics of the expansion of universe using quasars 
In addition to supernovae Ia, the dynamics of the expansion of the universe to even greater distances, ie to earlier periods, can be studied using quasars. Quasars are giant black holes in the center of galaxies that absorb a large amount of surrounding gas in a large accretion disk, part of which is ejected along the axis of rotation in massive jets - see §4.8 passage "Thick accretion disks. Quasars". The absolute magnitude (actual radiant power) of quasars is different, but it turns out that this absolute magnitude is related to the spectrum of quasar radiation, especially to the ratio of ultraviolet and X-ray radiation (§4.8, passage "Quasars as standard candles"). Quasars with spectrometric analysis can then in principle be used as " standard candles " for measuring the greatest cosmological distances .
At present, these spectrometric measurements are performed on a large number of quasars of different distances.

^{The influence of dark energy on the evolution of universe}
Dark energy is very dilute but ubiquitous and its effect is cumulative. It is imperceptible on terrestrial scales and within the solar system, but it may be dominant on a cosmological scale throughout the universe.
   According to current estimates, in the universe, about 70% of dark energy, about 25% of dark (hidden, non-radiant) matter, and only »4% of ordinary ("luminous" or absorbent) matter are accessible to observation (see table below, at the end of this chapter). Therefore, if the existence of dark energy (or non-zero cosmological constant) is really definitively proven, it will change our ideas about the dynamics of the evolution of the universe, which instead of the previous two phases consisted of 3 stages :

• è Initial iflational phase with rapid expansion dynamics a(t) ~ e ^Hi ^{. t} , where H_i is the "inflation Hubble constant-rate" reaching very high values (§5.5).
    
• è. Standard Fridman expansion of the universe, initially with radiation dominance a(t) ~ t^1/2, later matter a(t) ~ t^2/3 (§5.3 and 5.4). The rate of expansion of the universe slows down with the gravitational action of matter (visible and above all hidden). As the universe expands, its density of matter (both visible and dark) dilutes.
    
• è After sufficient dilution of matter in the universe, dark energy begins to dominate (equivalent to the term L.g_ik in Einstein's equations with the cosmological constant L), the rate of expansion of the universe stops slowing down and begins conversely to accelerate *). The universe will gradually behave as an (almost empty) de Sitter universe with  exponential expansion a(t) ~ e ^{H. t} caused by a repulsive cosmological member. It is thus a kind of late "2nd inflation phase", which is, however, very slow compared to primordial inflation; the vacuum energy density, the cosmological constant and the Hubble constant H are here many orders of magnitude lower than at the beginning. However, this phase of late accelerated expansion would in any case lead to an open universe, leading to "thermal death".
  *) According to supernovae observations, this "tipping point" situation between deceleration and acceleration of space expansion occurred about 5-7 billion years ago. At that time, there was a fatal "tipping of the weighing pans" to the side of antigravity forces caused by dark energy.

The previous Figure 5.2 from §5.3, showing the evolution of the closed universe, will be redrawn and supplemented here again, with an emphasis on the open universe and the dynamics of accelerated expansion (Fig. 5.2'c) :

Fig.5.2´. Different possibilities of the dynamics of the evolution of the universe. a) Closed space. b) Open space. c) Open universe with final accelerated expansion.

Hidden (dark, non-radiant) matter and hidden (dark) energy play essentially opposite roles in the universe :
¨ Hidden matter - holds the universe and its structures together, inhibits - slows down - the expansion of the universe. The formation of large structures - galaxies and clusters of galaxies - was caused mainly by the distribution of hidden matter in the early stages of the universe (at the beginning of the matter era). And this dark matter still holds the galaxies and clusters of galaxies together by gravity.
¨ Hidden energy - if it prevails, with its repulsive effects, on the contrary, it stops the formation of structures and forces the universe to expand faster and faster globally.
   The new cosmological model, extended by the implementation of hidden matter and energy, is sometimes referred to as LCDM - Lambda Cold Dark Matter (Lambda Cold Dark Matter), where the cosmological constant "lambda" L indicates the acceleration of the expansion (cf. also §5.3, passage "Relative omega W - parameterization of cosmological models").
   In the early universe, dark energy played no role (with the exception of the inflationary stage - §5.5), while in the distant future it may acquire a decisive influence; it is even able to "blow" the universe and dissolve it in "nothingness" (see "The Great Rip? " below).
   Thus, if the concept of dark (hidden) matter and energy turns out to be true, the ultimate fate of the universe in the future will be determined by the "duel" between dark matter and dark energy, between their attractive and repulsive gravitational effects. The visible glowing substance, due to its small representation, plays only a secondary role in the dynamics of the universe - it is "passively" carried away by dark matter and energy - the global structure of spacetime generated by them. However, luminous matter serves as a source of electromagnetic signal, an "indicator" that allows us to map the distribution and dynamics of the motion of matter - luminous and hidden - in distant space.

The essence of dark energy ?
Dark energy probably does not have the usual material, substance or particle nature, it is rather the field property of spacetime as such. Although recent astronomical observations may make it possible to specify the representation of dark energy and perhaps even estimate its "equation of state" (5.59), ie the relationship between pressure p and density r (cf. also §5.3), about the very nature of dark energy, or alternative explanation of the cause of the accelerated expansion of the universe, it will be possible only to speculate in the foreseeable future. So far, there are basically four possibilities (hypotheses) :
l Vacuum energy with negative pressure. In connection with the concepts of phase transitions in unitary field theories (discussed at the beginning of §5.5 "Microphysics and Cosmology. Inflation Universe."), it was hypothesized that this is a energy density of "false vacuum" of the same kind that caused a massive accelerated inflation expansion on the very beginning of the universe (§5.5 "Microphysics and cosmology. Inflationary universe."). Even the current vacuum could be "somewhat false" according to this hypothesis, but the difference is that its energy density is many orders of magnitude lower than at the beginning and therefore causes only a "slightly" accelerated expansion of the universe. This hypothesis assumes, that the vacuum energy density is constant, unchanges in space and time, is not dependent on the expansion of the universe, and can be equivalently expressed as the cosmological constant L in Einstein's gravitational equations (cf. §5.2, part "Cosmological constant"), case c) in table (5.61). It would be an unchanging *) basal form of energy, immanently "woven" into the imaginary "yarn" of the structure of space-time.
*) Mostly assumed a immutability of the cosmological constant and the dark energy thus generated, but there are also hypotheses about the possible slight variability of some physical "constants"..?..
l A new kind of field - the 5th interaction, sometimes also called quintessence (lat. quinta esentia = fifth essence , figuratively punished, primordial essence ), filling the space of the universe (case b) in the table (5.61)). The field of this interaction will generally no longer be constant, but it will be a dynamic field, the strength of which may change over time and may be different in different parts of the universe. Depending on the ratio of its potential and kinetic energy at a given time, quintessence can be either repulsive (as it seems now) or even attractive. It changes as the universe expands - it should decrease with expansion (if it was initially established with a specific intensity), albeit at a different rate than the density of matter, radiation, or hidden matter. But in general, this unknown field of the 5th interaction can be governed and developed by its own dynamics, of which we know nothing yet, but we can consider three possibilities :
- Its intensity may begin to decrease in the future, so that the universe would cease to expand and eventually begin to shrink - dark energy would become attractive, until it eventually collapsed by a "big crash", as predicted by the closed universe model - Fig.5.2'a (that doesn't seem likely now...).
- Or it may remain approximately constant, leading to a constant slow acceleration in a scenario similar to the vacuum energy of the cosmological constant (Fig.5.2'b).
- Alternativelly, we could also imagine an increase in the intensity of the quintessence field with time, which would cause an unlimited acceleration of the expansion of the universe, at which all structures in the universe could be torn (see "Great rip?" below), Fig.5.2'c.
l Deviations from the general theory of relativity. The cause of the accelerated expansion could be a slightly different dynamics the evolution of the universe at extreme cosmological distances than that resulting from the "classical" general theory of relativity, well validated at shorter "astrophysical" distances. A new theory of gravity needs to be developed..?.. This possibility does not seem very likely, the modification of the existing GTR should not conflict with other successfully explained observations and experiments.
l Dark energy does not exist, accelerated expansion is a mere observational illusion ! What we perceive or interpret as dark energy, may be due to our not entirely adequate cosmological idea of the large-scale structure of the universe. Global homogeneity and isotropy of expansion may not be completely absolute. We can be inside a kind of large "bubble" of slightly reduced Hubble expansion rate, so in other remote areas the expansion may seem faster..?..
But it would require relatively large density fluctuations, around 20% ...
  Anyway, the essence of dark energy is currently the most difficult unresolved issue in astrophysics and cosmology.

The Late Accelerated Expanding Universe
The accelerating expansion of the universe, in co-production with standard gravitational attraction, would dramatically change the appearance of the universe in the distant future compared to the current state. From a global perspective, two opposing events will take place in such a universe :
l All the expanding matter in the universe - distant galaxies that are not gravitationally bound to each other - will rapidly (accelerated) recede until they escape from our wiew beyond the event horizon, visually and causally "disappears", they will be "swept" from our cosmic horizon, will move into the "invisible". We can imagine this as new expanding space is created between distant galaxies so fast, that even light appears slow to keep up with the rate of expansion - it is not enough to transport information between distant galaxies.
l Nearby galaxies, on the other hand, will continue to be attracted to each other by gravity and merge into a single huge "supergalaxy".
   In a few hundred billion years, the visible universe will be formed by a single supergalaxy, surrounded by a vast, insurmountable emptiness. In the distant future (hundreds of trillions of years), individual parts, and eventually the entire galaxy, will collapse into a gigantic black hole; therefore, it would be one variant of the ultimate future of the observable universe... Let's compare this unhappy prognosis with the above-mentioned reflection "Astrophysics and cosmology: - human hopelessness?".
  Note: Since outer space expands homogeneously, they would see the same situation potential observers ("aliens") in distant galaxies. For them, our (and close to us) galaxies would escape from sight and, conversely, their surrounding galaxies would gravitationally merged ...
 Astrophysics and Cosmology in the Late Accelerated Universe ?
The observational and epistemological aspect of this development is also worth thinking about. Let's imagine in a hypothetical science fiction scenario, that in hundreds of billions of years, in the late accelerated expanding universe on a suitable planet around some star in said supergalaxy, life and subsequently an intelligent civilization would develop. These "people" (although they certainly won't physically resemble us...) would develop advanced science and technology, perfect devices for improving life and exploring nature and space. Our civilization and the planet Earth will no longer exist at this time, all our knowledge will disappear *). They will have to build all the knowledge of nature and the universe themselves from the beginning.
*) If, of course, the concept of transhumanism would not be realized in the relatively near future (discussed in the passage "Artificial intelligence and transhumanism - a lawful outcome of biological evolution?" of the work "Anthropic principle or cosmic God").
   These future astronomers would come to completely different conclusions about the universe as a whole than our current astronomers. Even the largest telescopes would not see any distant galaxies in the immeasurable abyss of empty space, whose spectral shift would reveal the expansion of the universe. They would see that they live in one large galaxy (probably elliptical with little gas) in an otherwise empty universe; there are no other galaxies in the universe... Relic radiation (which is now microwave) is so diluted and elongated that it ceases to be measurable. It is hard to say, what kind of cosmological theory these future observers would form? The idea of a universe created by the big bang would probably not even occur to them in a dream..?.. Accelerated expansion will irreversibly "erase" all the evidence about the beginning of the Universe and its earlier evolution..!..
   They would observe a large number of stars of different generations, with different metallicities, they could build a stellar nuclear astrophysics well explaining the formation of heavier elements in the universe. By spectrometric analysis, they would find out the abundance of the light elements hydrogen, deuterium, and helium in interstellar space. It's hard to say what kind of theory they would create for the origin of these elements..?... - it probably wouldn't be primordial nucleosynthesis in the hot early universe...
   From the theoretical level of fundamental physics, they would be able to investigate elementary particles, atoms and other structures based on accelerator experiments. They would create what we now call special relativity and quantum physics. Of course, they would easily examine Newton's current law of gravitation. The question is, would they also build our general theory of relativity, or would they arrive at another relativistic physics of gravitation...?.. By applying the model to the entire homogeneous and isotropic universe (even though their observable universe wouldn't be like that!), they could arrive at an analogy of Fridman's equations. One of their solutions - the universe expanding from a hypothetical singularity - they might find theoretically interesting, but so bizarre that they probably wouldn't relate it to the real universe, which would appear completely different at the time...
   Knowledge in all branches of astronomy is primarily based on observations. Our current understanding of the structure and evolution of the universe is based primarily on four observations :
-> Observed relation between spectral redshift and distance for galaxies, which is indicative of an expanding universe.
-> Dominant representation of light elements everywhere in the universe (in nebulae, galaxies and stars of different generations).
-> Analysis of the properties of cosmic microwave radiation as a remnant of the glow from the hot period of the Big Bang.
-> Large-scale structure of the universe showing the formation, distribution and evolution of galaxies.
   Observational facts, followed by the application of physical laws, provide astrophysical model of the universe. However, the ways in which we discovered these fundamental phenomena in the universe will not be available permanently. Our ability to explore fundamental questions about the structure and evolution of the universe depends on when and where in cosmic history we (happen) to live. This also applies to any possible other civilizations, that may arise in different stages of the universe's evolution.
   From the point of view of the current scenario of space evolution, we can welcome that we are fortunate to live at a suitable time when we have a good view of distant space and by analyzing astronomical observations (not only in optical and electromagnetic) we can get a realistic idea of universe evolution almost to period of its origin...

A big rip ?
If the very intense (case d) in Table (5.61)) "phantom" dark energy continues to drive the expansion of the universe with increasing speed, in about a billion years we will not even see our "fingertips", because everything around us will move away at super-light speed. The exponential course of expansion leads to an ever-accelerating expansion, which could theoretically approach infinite speed in the distant future. Conjecting this scenario "to the end" may lead to the idea that ever-accelerating expansion will not only absolutely distances (beyond the horizon) all distant structures in space, as outlined above in the "Late Accelerated Expanding Universe" passage , but then dark energy will eventually overcome all interactions and binding forces. "Antigravity" will tear apart all bound structures - gradually galaxies, planetary systems, stars. In the final phase, according to some ideas, the atoms would rupture and even the elementary particles themselves and perhaps even the structure of space-time would rupture. Such a scenario of cosmic evolution is sometimes referred to as the "big rip". Opinions on this (purely hypothetical!) question differ :
¨ According to the "moderate" opinion, from the point of view of standard GTR based on the principle of equivalence (§2.2 and 2.3), nothing like this should happen *). Only distant objects that do not have internal integrity would be subject to accelerating expansion. Smaller bound systems develop under the influence of their internal binding forces; we can introduce an approximate locally inertial system for them, within which the laws of physics will not be practically affected by the global cosmological gravitational field of the expanding universe. E.g. the electron orbits in the atoms do not change with the expansion of the universe : they are not bound by gravity, but electrically, while within the locally inertial system these electric forces do not depend in any way on a spread gravitational background. Even in galaxies, cosmological expansion does not occur, because the presence of matter leads to a "positive" curvature of space-time, which overcomes repulsive forces. For a comparison, see also the discussion "What actually expands and does not expand during the expansion of the universe?" in §5.4 .
*) Such a conclusion would apply under the usual assumption of a constant (or decreasing) value of the cosmological constant, or dark energy density, with the expansion of the universe. If, hypothetically, the density of dark energy (as a "quintessence") increased indefinitely over time - "phantom" dark energy - it would support the "big rip" scenario ..?..
¨ An alternative "radical" view, supporting the concept of "big rip", argues, among other things, by analyzing the time dynamics of the event horizon. In any case, with the expansion of the universe, the horizon of events becomes smaller and smaller part of the whole universe. As the expansion exponentially accelerated, this effect would become increasingly dominant. The DeSitter event horizon would shrink to the size of clusters of galaxies, then galaxies whose stars would scatter into expanding space. In the final stages of expansion, the horizon would shrink sharply to the dimensions of the solar system, stars (Sun), planets. All these bound systems would disintegrate and "fly away" from each other. Even with such stable formations as black holes, the deSitter horizon would eventually "beat" the gravitational (Schwarzschild) horizon and the black hole would be destroyed. Eventually, molecules, electron shells of atoms and atomic nuclei would rupture, and the individual elementary particles would move so far apart from each other that they would no longer physically "know about themselves" and no interact. Furthermore, nucleons would be torn into free quarks (repulsive forces of dark energy will surpass the law of "quark trapping"). An immensely vast Universe will still exist, but in a state of "thermal death".
   Finally, the deSitter horizon would fall below the dimensions of the elementary particles that would be torn. Immediately, the structure of spacetime in the discontinuity of the metric tensor g_ik would disappear, similar to the singularity of spacetime (see §3.7, §4.9; unlike the "localized" singularity of a black hole, this singularity would be everywhere). The amorphous manifold formed in the topological foam could then perhaps re-create an inflation-expanding region by quantum fluctuation, which could give rise to a new universe, as described in §5.5, passage "Chaotic inflation and quantum cosmology"). But this hypothetical "new universe" would have nothing to do with the original "our" universe ...
   This radical scenario "unlikely, because the density of dark energy, if constant or does not grow too fast, will never locally exceed the density of matter in galaxies, stars or atoms.
   In any case, these are only purely speculative questions, caused by perhaps somewhat hasty conclusions from so far sporadic astronomical observations ..?..

From emptiness to emptiness ?
The combination of the idea of quantum cosmology of the universe by chaotic inflation and accelerated expansion in the late stages of the universe offers a scenario of global universe history from the emptiness of "thermal birth" to the emptiness of "thermal death" of the universe :
¨ The initial state is almost empty space ; --> Quantum field fluctuation occurs in a certain region; --> There will be a rapid inflationary expansion of this fluctuation; --> At the end of inflation, vast outer space is filled with a more slowly expanding, almost evenly distributed primary hot gas; -->After its cooling, the inhomogeneities condense by gravity into clusters of galaxies and galaxies in a slowly expanding universe; --> After a long time, dark energy prevails, accelerating expansion dilutes all scattered matter, galaxies escape beyond the horizon; --> The galaxy collapses into black holes, which then quantum evaporate in the radiation; --> Accelerating expansion infinitely dilutes all remaining radiation; --> The universe is again almost empty space...
¨ And in this empty space there can again be quantum fluctuation, leading to the creation of a new universe... Individual such universes would in this respect be only "episodes in quantum fluctuations" of the eternal basic space ..?..
   Again, it is necessary to emphasize the speculativeness of this scenario, which is a far-reaching extrapolation of the little we know to a large area of the unknown ..!..

Possibilities of a different dynamics of the evolution of universe ?
It should be noted that the above-mentioned (moreover, hypothetical) scenarios of the late global evolution of the universe correspond mainly to the current LCDM idea of dark energy. The question of whether this accelerated expansion must last forever and what are the alternatives was briefly discussed above in the passage "The Essence of Dark Energy?".

The greatest mysteries of nature ?
The existence of hidden or dark matter (substance) and even more "hidden", "darker" and more mysterious dark energies in the universe is a great challenge not only for astrophysics and cosmology, but also for elementary particle physics (if we look for its source at the quantum level). The problem of explaining a non-zero but very small cosmological constant L (corresponding to a density r_L » 0.5.10^-5 GeV/cm³, which is a few atoms per m³), represents a major challenge for unitary field theories (cf. §B.4 "Quantum geometrodynamics" and B.6 "Unification of fundamental interactions. Supergravity. Superstrings."). In the current quantum theories of field with the inclusion of a huge number of quantum fluctuations, the value is obtained of r_L ~ m_p.c²/l_p² » 10¹¹⁸ GeV/cm³ (m_p is the Planck mass, l_p Planck length), which is more than 120 orders of magnitude higher.!?. - §B.5, passage "The Mystery of Quantum Vacuum Energy <-> Cosmological Constant".
   To analyze this problem could perhaps say its own even the anthropic principle (§5.7 "Anthropic principle and the existence of multiple universes", see also the philosophical-naturalistic work "Anthropic principle or cosmic God '). "Anthropic justification" in co-production with the idea of a multiverse - a huge set of different "universes" with different properties of elementary particles, fundamental interactions (and thus the amount of vacuum energy) and even different dimensions of space, could reflect, at least on a philosophical level, these hidden mysterious properties..?..

Brief and simplified final summary 1 : Why "phantom" dark matter and dark energy ?
At the scales of galaxies and galaxy clusters, gravity appears stronger than would correspond to astronomically observed "luminous" or absorbing matter composed of electrons, protons, and neutrons. So gravitational dark-hidden matter is added .
   On the larger cosmological scales, where the universe expands, gravity, on the other hand, appears weaker than would correspond to the overall attraction of particles of ordinary and dark matter. Therefore, "dark energy" is added - a weak antigravity, a force that acts against gravity and independently of matter. Current models of the universe require dark energy to explain the observed acceleration of space expansion resulting from measurements of supernova distances in distant galaxies (which appear to be more distant than they should be if the expansion of the universe did not accelerate).
   However, the issues of dark matter and dark energy are still being discussed, new measurements are being evaluated, and alternative options are being explored ..?..

Brief and simplified final summary 2 : How will the universe "extinct" ?
From all our observation of nature and life follows the experience that everything that has originated, exists and is evolving, must have its end - extinction. We also attribute this property to the whole universe. In this chapter 5.6, in a number of places, we have analyzed astrophysical processes, which in the distant future may gradually end the existing processes and the existence of the universe as we know it and cause its "extinction". Here, for clarity, let's summarize the basic ways in which, according to current astrophysics and cosmology, our universe could to excint :
1. The collapse of the universe - a big "crunch".
If the density of matter in the universe is high enough for its gravitational pull to overcome the cosmological expansion of the universe from the Big Bang, the expansion will stop, followed by a contraction that will gradually accelerate and the universe will end in gravitational collapse - the final very dense and hot end of the universe (theoretically collapses with singularities), called the "big crunch". It is sometimes thought that after this collapse of the universe, the "big bang" and the emergence of a new universe may occur again, but this is only an unsubstantiated hypothesis ... In the 1960s and 1970s, it was estimated that the collapse of the universe would occur in about 100 billion years.
According to the results of recent astronomical observations, this closed space scenario is not very likely, the universe is probably open.
2. Infinite expansion - big freeze, "thermal death" of the universe.
Otherwise, when the gravity of matter in space is not able to slow down and stop cosmological expansion, this adiabatic expansion will continue indefinitely, leading to an infinite dilution of the average density of matter and a drop in temperature to virtually zero. The expanding universe depletes all energy, all processes in the universe cease - "freeze" - "thermal death" occurs (it was described in more detail at the beginning in the passage "Open Universe"). Unlimited cosmological expansion may be due to either the low density of matter in space relative to the rate of cosmological expansion or the antigravity effect of dark energy. From an astrophysical point of view, over the course of 100 billion years, all stars will burn out and no new ones will form in the diluted universe. The material of planets, stellar dwarfs, neutron stars will also succumb to nuclear decomposition (proton instability). Black holes also evaporate quantum. In about 10⁶⁰ years, the universe becomes a cold empty space, containing only constantly diluting radiation.
3. Infinite accelerated expansion - "big rip" of the universe.
This hypothesis reinforces the previous scenario of infinite expansion: if the density of dark energy were high enough, and with the expansion of the universe would possibly increase, the accelerated expansion of the universe could gradually accelerate exponentially indefinitely. This would initially disperse clusters of galaxies, then galaxies, disconnect the planets from the stars. The internal pressure of furiously expanding space would eventually decompose stars, planets, then molecules and atoms, atomic nuclei, elementary particles, and finally the structure of space-time..?.. Whether and when such a thing could happen depends on the magnitude and dynamics of the behavior of the mysterious and phantom dark energiy, about which we know almost nothing yet. So far, only completely vague estimates for 100-200 billion years appear..?..
4. Vacuum instability - quantum transition of "false vacuum".
This somewhat curious scenario was inspired by the quantum cosmology of the very early universe, which assumes so-called inflation expansion (§5.5 "Microphysics and cosmology. Inflation universe.") - an extremely sharp exponential expansion of the universe, accompanied (and caused) by a phase transition from a "false" energetically excited vacuum to a state of "true" vacuum with a lower energy density. There may be a hypothetical notion that even our current vacuum in the universe is not the "real" lowest, but it is also somewhat "false", with a tendency to move to an "true" vacuum with even lower energy. In such a case, somewhere in the universe, a tiny "bubble" of a true low-energy vacuum may arise, that can expand exponentially at super-light speeds and to this state of a new "real" vacuum will eventually succumb to the entire universe. This catastrophic process of vacuum decomposition could theoretically occur at any time. However, the very fact of the peaceful existence of our universe for more than 13 billion years suggests that the probability is very small, it is estimated that in the next perhaps 10¹⁰⁰ years there will be no such catastrophe... Moreover, according to some other hypotheses, this process would did not destroy our universe, but could lead to the creation of a parallel other universe in a topologically different space..?..
   According to current astrophysical knowledge, the most probable way to end the universe appears to be variant No. 2. - "thermal death" of the universe.
Note : 
We did not discuss here some unlikely scenarios based on unsubstantiated hypotheses - such as the oscillating universe, or the possibilities arising from the ecpyrotic model...
   Furthermore, it is necessary to emphasize the great astrophysical uncertainties we have about the global structure of the universe, the dynamics of its evolution, the nature and equations of state of dark matter and dark energy. We know a little bit about the current parameters, maybe only small parts of the metagalaxy, which may change significantly in the distant future. Therefore, none of the possible end-of-the-universe scenarios is guarantied ...

Revision of the accelerated expansion of universe ?
The accelerated expansion of the universe was inferred in 1998-99 from measurements of about 60 type Ia supernovae and was widely accepted in the following years (discussed above in the section "Accelerated expansion of the universe? Dark energy?"). However, more recent frequency shift measurements and analyzes of 740 Type Ia supernovae scattered in various directions across the sky, likely show a smaller rate of accelerated expansion, than was inferred from the first measurements. Moreover, it has been shown here that this acceleration is not exactly the same in all directions, that it may be a relatively local effect (it is directed along our apparent motion relative to the cosmic microwave radiation) and cannot be unambiguously attributed to dark energy, which would cause the same acceleration in in all directions. This could indicate that the acceleration is an observational artefact of our cosmological location, and perhaps even lead to the abandonment of the concept of accelerated expansion and dark energy..?.. Definitive decisions about the expansion history of our universe will emerge only from spectrometric measurements of a much larger number of supernovae and other very distant ones objects, using large telescopic systems.

What is the basic composition of universe ?
In addition to the global structure and evolution of the universe, the basic task of physical cosmology is also to clarify what mass - matter, field, particles - the universe consists of? In §5.4 "Standard Cosmological Model. The Big Bang. Shaping the Structure of the Universe." we saw that the composition of the matter filling the universe changed significantly during its evolution. From fluctuating fields and quanta in the very early universe immediately after the Big Bang, through quarks and baryons (protons, neutrons), photons, electrons, muons, neutrinos, up to light atomic nuclei of hydrogen and helium after initial nucleosynthesis and finally all heavier atoms formed during nucleosynthesis in stars and during the supernova explosion (§4.1 and 4.2). The composition of the universe has settled down to about 75% hydrogen, 25% helium and a smaller amount of heavier elements according to the graph on "Elements-Abundance" in §4.1. All this is "ordinary" matter made up of baryons, electrons, photons.
   However, the concept of dark matter and dark energy changes significantly - complements - our earlier idea of the composition of the universe. According to current knowledge, the composition of matter-energy in the present universe is as follows :

Mass: ì material - particle, atomic structure î field - distributed form of matter (quantized) Matter in space: ì the observed luminous + lightless - baryonic î non-radiant - dark (hidden) matter                     â æ                                      í dark matter î  dark energy ?   baryonic    ?     nonbaryonic ( nonbaryonic ) According to current estimates, it is in space : about 73% dark energy ; about 23% dark matter (hidden, non-radiant); only » 4% of ordinary matter " luminous"or absorbing, accessible to observation .

These values were obtained by a detailed analysis of the correlation of the LCDM model with extensive astronomical observations and sensitive measurements of intensity, spectrum and subtle fluctuations of relic microwave radiation (most recently by the WMAP and PLANCK space probes).
   This global composition also has a strong gnoseological aspect. Until recently, we thought that by astronomical observation of glowing objects and absorbing clouds of gas and dust in optical, infrared, radio, X or gamma electromagnetic radiation, we would gradually find out everything about the universe, it would be just a matter of larger and more advanced telescopes and other instruments. It now turns out that in this way we are able to observe only about 4% of the matter in the universe. We don't know much about 25% of dark matter yet and about 70% of dark energy is completely unknown to us. Stars, nebulae or galaxies are therefore not an essential component of the universe for the properties of the universe as a whole and for its evolution. This luminous or otherwise astronomically observable matter in space is just the "tip of the iceberg", whose main mass is hidden from us. The universe is made up mostly of something we don't see and unknown. It's a depressing finding of how little we know about the Universe..!?..

Astrophysics and cosmology: - human hopelessness ?
If we reflect from our human point of view the knowledge of contemporary astrophysics and cosmology about the evolution of the universe (and combine it with other risks), it will inevitably evoke in us a sense of hopelessness in the ultimate perspective and the meaning of our existence - the duration of human civilization! The danger to humanity is in several directions (listed in chronological order according to potential acuteness) :
¨ From human society
We prepare the most acute danger ourselves. Greed, selfishness, and pride (especially among "celebrities" - the rich and powerful of this world, who makes a claim to dominate and manipulate other people) breed hatred and murderous wars (often with religious pretexts). Using current weapons of mass destruction, potential global wars could threaten entire human civilization. The consumer society leads to a waste of natural raw materials, waste contamination and total devastation of the environment. There is an overpopulation of people, especially unproductive individuals, who will parasitize nature and society - especially Africa and India (including Pakistan) , other Islamic countries and some problematic minorities in Western countries. Unless extensive enlightenment is provided and effective birth control, this population explosion can lead to bloody wars and the devastation of nature, threatening entire human civilization. In order of nonviolent peaceful development, it will also be necessary to eliminate or transform unjust social systems based on human inequality, as well as to eradicate religious superstitions and prejudices (which divide people), especially dogmatic and radical trends - many "believers" are indoctrinated (or more aptly "stupided") criminal religious ideology, in in the name of which are capable to murder their neighbors..!..
   Only if humanity kind in harmony "it will pull on one rope together", it will hopefuly avert some terribl dangeres in the future, mentioned below..!..
¨ From the Earth's atmosphere
The Earth's atmosphere plays a significant role in the appropriate climate (temperature, humidity, pressure) for various species of life, including us humans. Now there is often a discussion about increasing the concentration of so-called greenhouse gases (especially CO₂), which can lead to an unfavorable increase in temperature in our biosphere; in extreme cases except for temperatures incompatible with life. The extent to which human activity contributes to this is the subject of professional discussions. The Earth gradually loses its atmosphere by evaporation into the surrounding universe and could eventually end up completely without an atmosphere - a "dead planet" (cf. the atmosphere destruction scenario in the next paragraph) .
¨ From the planet Earth 
We are also in mortal danger from our "Mother Earth". We live on a thin shell of the earth's crust (broken into a series of lithospheric plates), under which a hellish hearth of molten rocks rages. Earthquakes and volcanic activity occur at the junction of lithospheric plates. Under the thin shell of the earth's crust, in the earth's mantle, like a "time bomb", massive streams of hot molten rocks rise by thermal convection. If it melts to the surface, lava gushes violently under great pressure like a destructive supervolcano. Such a supervolcano can not only destroy an area of hundreds of kilometers, but the amount of volcanic gas and dust (thousands of km³) can block sunlight and cause a planet-wide ecological catastrophe with radical climate change. Yelowstone National Park in North America is considered to be one of the areas most threatened by a devastating supervolcano.
   Another risk in the distant future may be the weakening of the Earth's magnetic field, which protects it from a stream of charged particles from the Sun. The Earth's magnetic field is generated in the rotating semi-fluid outer part of the nucleus, which acts as a magnetohydrodynamic "dynamo". In the later stages of the planet's evolution, this nucleus cools and solidifies, weakening the magnetic field and eventually disappearing. For possibly life on the surface of a planet has two adverse consequences. Larger amounts of hard ionizing radiation, harmful to living organisms, begin to enter the biosphere from outer space. Furthermore, an intense stream of charged particles emitted by a star ("solar wind") it destroys the atmosphere and can "spray" it into the surrounding universe. The loss of the atmosphere leads to faster evaporation of water, whose steam is also carried into space by the stellar wind. The loss of the atmosphere and water would be incompatible with the continuation of life on our planet.
¨ From near space - asteroids
In the solar system, not only well-known planets or our Earth orbit the Sun, but also a large number of smaller bodies of various sizes, from fractions of millimeters, several centimeters and meters (meteorites) to tens or hundreds of kilometers - small "planets" or asteroids (name "asteroid ", which means " star - like" arose from the fact that the sun illuminated by nearby bodies of ground-based telescopes look like tiny points of light, like distant stars, unlike the stars but move across the sky like planets). Some of these objects cross the orbits of the planets, can be collide with them, be captured by their gravity, and hit their surface at high speeds of tens of kilometers per second. All terrestrial planets are densely littered with impact craters after the impacts of these bodies.
   Thousands of the above-mentioned bodies also cross the Earth's orbit. Small bodies "burn" in the atmosphere like meteors; it is estimated that such a meteor fallout represents millions of tonnes each year. We are effectively protected from small "space projectiles" by the Earth's atmosphere, in which small meteor bodies burn and do not fall to the surface at all. Even larger meteorites that hit the earth's surface do not pose a greater danger, as they lose almost all their kinetic energy by friction in the atmosphere (and most of their mass evaporates).
   Unfortunately, the orbits of larger bodies and asteroids also intersect the Earth's orbit, fortunately mostly at a time when the Earth is not in the given place. However, there is a certain probability that the asterioid will hit the collision path with the Earth and the Earth will collide with an asteroid - "we live in a space shooting range", astronomers say. There is a real danger from larger bodies with a diameter of tens of meters and a weight of over 1000 tons (it would cause "only" a local catastrophe). An impact of a planet several kilometers long weighing more than 10¹² kg would suddenly release energy greater than 10²² J, which corresponds to the explosion of more than a million thermonuclear bombs. In addition to the immediate destruction of an area of thousands of kilometers, this would cause (similar to the above-mentioned supervolcano) ejection of huge amounts of rocks, gas and dust into the atmosphere. The fall of molten rocks to the surface would cause fiery meteor shower, which could burn a large part of the earth's surface. Large amounts of ejected dust could remain in the atmosphere for several years, which would significantly weaken the sun's radiation for a longer period of time. This would lead to a global environmental catastrophe with radical climate change. Humanity probably wouldn't survive! Such an asteroid crash is thought to have occurred 65 million years ago, when dinosaurs and most species of fauna and flora at the time became extinct. The Earth collided with asteroid-sized cosmic bodies several times in the past and is likely to continue to do so in the future - with fatal consequences for the continuation of human civilization; we do not yet have the opportunity to prevent such a cosmic catastrophe ...
How to prevent a collision with an asteroid ?
Current astronomical technology is gradually making it possible to find "risky" asteroids and predict a possible cosmic collision. There are basically two basic possible ways to avert an impending catastrophe :
1. If we knew well in advance (several years) the future orbit of such a potentially dangerous cosmic body, we could avert an impending collision by changing its trajectory - deflecting it or changing the speed of the body so to cross the Earth's orbit when the Earth is not there. Such a deflection of the path could be effected by the application of a force, preferably perpendicular to the instantaneous direction of movement. Usage is discussed nuclear charge, the energy of which would explode would cause a "rocket effect" (primarily by ejecting molten material from the crater), leading to a deflection of the asteroid's orbit. Or shelling with high-power laser beams. The launch of a spacecraft in orbit near an asteroid is also being considered, which would gravitationally deflect the asteroid's orbit.
2. Another possibility would be to break the body of the explosion, but a number of fragments would move in their original orbit and land on Earth. The individual fragments might not cause a global catastrophe..?.. But it is a discutable and not very optimal way, suitable only for smaller asteroids (fragments of which would mostly burned in the atmosphere).
   However, we do not yet have sufficient missile technology for any of these interventions (perhaps in 50 years? - provided that humanity does not waste its forces on senseless political and religious disputes, armaments and wars!). Meanwhile, we have to stand idly by as the asteroid "falls on our head"...
¨ From the distant universe - supernovae, gamma-ray bursts ,
If some of the closer or "nearby" stars within a distance of about 30 light-years across, exploded as a supernova, enormous amounts of radiant energy, especially hard ionizing radiation, that would hit the Earth would probably cause a huge natural disaster which could seriously jeopardize the very existence of life here on Earth! Even from an even more distant universe, hundreds or thousands of light-years, narrowly collimated gamma-ray bursts emitted by collapsing objects - massive stars, neutron star collisions, accretion disks around black holes - can be potentially dangerous to us, if their rotational axis is turned toward us (they would affect not only the Earth, but the entire solar system ...). From an astrophysical point of view, these high-energy events are discussed in §4.2, section "Supernova explosion. Neutron star. Pulsars." and §4.8, section "Accretion disks around black holes. Quasars.".
   The risk of cosmic radiation from catastrophic processes in space is discussed in the treatise "Cosmic radiation", part "Biological significance of cosmic radiation", passage "Deadly cosmic radiation" §1.6 monograph "Nuclear physics and physics of ionizing radiation".
¨ From the Sun
Even if we can avert the catastrophe of the Earth's collision with asteroids, devastating wars, survive supervolcanoes and various ecological catastrophes, protect the Earth from a massive flash of cosmic rays from a nearby supernova explosion or neutron star fusion, our life-giving star Sun will destroy us. Over the next 3 billion years, the Sun will increase its current radiant power by about 40 %. The temperature on Earth will rise by tens of degrees, the oceans will evaporate and all life will end. In about 5 billion years, the Sun will deplete the supply of thermonuclear fuel (especially hydrogen) and reach the final stages of its evolution (see §4.1, section "Late Stages of Stellar Evolution"). The Sun then "inflates" and, like a red giant, first absorbs and evaporates all the inner planets, including the Earth *), creating a "planetary" nebula and later becoming a white dwarf itself.
*) The Sun in the stage of the red giant will be large enough to engulf Mercury, Venus, Earth and Mars, if they orbit at the same distance as today. But Earth and Mars might be able to avoid this fate due to the following effect :
   In the late stages, with increased radiant power, the Sun will emit significantly more "solar wind", which will carry a considerable amount of the Sun's material away into space outside the solar system. This will reduce the total mass of the Sun, which will increase the radius of the planet's orbits. If the mass of the Sun is reduced sufficiently in this way, the Earth can orbit at an already safe distance, where the inflated surface of the Sun cannot reach..?.. However, even if this favorable development took place, the Earth would be a desolate planet with a hot dried surface on which life could no longer exist!
   The only way to maintain the Earth's habitability in the long run against the rising radiant power of the Sun is to gradually increase the orbital distance of Earth around the Sun. It would be enough very slowly, on the order of millimeters per year. Currently, it is sci-fi, we have no technical means to do so. In the distant future, however, our offspring are likely to have much greater energy resources. In addition, gravity and asteroid energy could in principle be used to bring the Earth into higher orbit, which could be carefully guided into a close coronary orbit with the Earth so that it gravitationally transfers kinetic energy to the Earth in the direction of orbit. In this way, at least in principle, the habitability of the Earth could be preserved by life for about 5 billion years. In the final stages of the Sun's development, however, this would already be a problem, because its radiation changes relatively quickly. The earth would be hit by high-energy gas streams from an expanding envelope. Then it would be "useful" the radiance of the Sun - the white dwarf - sharply reduced and the hard ultraviolet component would predominate in the radiation. The earth in distant orbit would freeze, it would need to be quickly moved to nearby orbit. If we moved the Earth to a very close orbit to maintain the temperature (in the sci-fi concept), intense UV radiation would destroy the atmosphere and life. At that time, however, human civilization, if it survives at all, will certainly be transformed into a completely different form - see the passage "Artificial intelligence and transhumanism" in work"Anthropic Principle, or cosmic God "...
¨ For Global Evolution - extinction of the Universe
Until then, humans may (perphas?) manage to escape from the Earth and the solar system and populate other suitable objects in space (so far it's pure sci-fi!). But what's next? If the universe were closed and collapsed it into a "fiery furnace" big crash, we should probably no hope. If the universe was open, so fatal end we would fundamentally threatened, at least not in the foreseeable future. However, in an expanding and ever-cooling universe, it would be increasingly difficult to find areas of local entropy fluctuation, where there are still available energy sources *) for the development and maintenance of civilization. The "thermal death of the universe" would ultimately mean the death of human civilization (discussed at the beginning of this chapter, the "Open Universe" passage).
*) Living matter receives food, which is an ordered form of energy, and converts most of it into a heat - disordered form of energy. Even if in the distant future there is a transformation of civilization and intelligent processing of information from the environment of living matter, eg into electronic form (as discussed in the passage "Artificial Intelligence and Transhumanism" of work "Anthropic principle or cosmic God"), the basic thermodynamic process would not change in principle (however, the energy efficiency of information processing would increase dramatically!). Even the arrangement of electronic memory elements in a certain state requires energy, while a part of it is always dissipated in the form of heat and thus increases the clutter of the whole system; according to the laws of thermodynamics, this increase in disorder is always higher than the increase in order in memory. This concept would only delay the demise of civilization by thermal death.
   Some, but only imaginary hope of eternal duration of life, could represent the concept of "multiverse" - an infinite number universes (§5.5 "Microphysics and cosmology. Inflationary universe.", part "Chaotic inflation", passage "The emergence of multiple universes"). Although a single specific universe "die" by collapse or heat death, multiverse as a whole will live on - forever, in individual universes can arise a new life. But this is no hope for us..!..
   In any case, we can state that the knowledge and theories of contemporary astrophysics and cosmology unfortunately do not show us any real perspective of the eternal existence and development of our human civilization ! However, we can console ourselves that our present knowledge is certainly not absolute and final. There is a lot we don't know yet and maybe we don't even we have no idea... And from this ignorance of ours we can perhaps draw some hope..?..

Brief recap :
Origin, structure and evolution of the universe
For better clarity, a large amount of knowledge and hypotheses about the origin and evolution of the universe, discussed in §5.2 - 5.6, will be expedient to briefly and simplified recapitulate within the framework of the current standard cosmological model in several points, capturing the basic processes :
-> Creation of the universe
is assumed to have occurred approximately 13.8 billion years ago in an explosively hot so-called big bang. The hypothetical initial singularity was rather a "topological foam" of spacetime. In the beginning there was no causality or any laws of physics, all physical forces were connected. At the Planck time of 10^-43 s, gravity began to operate; the strong, weak and electromagnetic interactions were still unified. Spacetime was created, followed by the rapid expansion of the universe.
-> Inflationary expansion of the universe
it occurred almost immediately after the big bang and after gravity became independent,, at 10^-35 seconds. It was very violent but short, after about 10^-32 seconds it stopped and the universe was already expanding according to Fridman's model. The inflationary expansion of the very early universe ensured that the universe became globally smooth and flat. The energy of inflationary expansion was transformed into elementary particles - leptons, quarks, gluons..... The strong interaction separated from the electro-weak one. Quarks and gluons were initially free, forming the so-called quark-gluon plasma. It is assumed that as yet unknown particles of so-called dark matter were also created here..?.
-> Hadron era
After the first microsecond, due to the strong interaction in the quark-gluon plasma, the free quarks combine into hadrons, mainly protons, neutrons and unstable mesons. Due to the so-called baryon asymmetry, slightly more matter than antimatter was created (in a ratio of 1:10⁹).
-> Lepton era
In a time of 10^-4 s. the nucleons and antinucleons annihilated each other (into pions which decayed into muons, electrons and neutrinos), only a small excess of 10^-9 nucleons remained. An equilibrium mixture of light particles - leptons - electrons, positrons, neutrinos, mixed with photons prevailed.
-> Primordial cosmological nucleosynthesis
In the time of 10 s. - approx. 1000 s., the fusion of protons and the remaining free neutrons took place to form the nuclei of deuterium ²H, tritium ³H, helium ⁴He and ³He, in a small amount of beryllium, lithium, boron. The final result of this primordial nucleosynthesis was the representation of atomic nuclei: 75% hydrogen ¹H, 25% helium ⁴He, a small amount of deuterium ²H (~4×10^-2 %), helium ³He (~2×10^-3 %) and a trace amount of Li, Be, B. Heavier elements could have formed much later, in stars.
-> Photon era of radiation
In all the above-mentioned early periods of the universe, there was a high temperature - great kinetic energy of particles and photons, the matter in the universe was in a plasmatic state. In the period ~10 s. ÷ 10¹³ s., radiation-dominated photon plasma prevailed in space.
-> Formation of atoms ("recombination") - Era of matter
In about 380,000 years, when the temperature dropped below 3000 °K, protons and helium nuclei combine with electrons to form neutral atoms of hydrogen and helium. The universe becomes transparent to light, its mass is made up of gaseous hydrogen and helium.
-> Formation of large-scale structures - creating of galaxies and stars
After the formation of atoms ("recombination"), the "dark age" occurred, because the radiation from the early hot universe had already died out and there were no stars yet. Cold matter, gaseous hydrogen and helium, begins to organize itself into large-scale structures through gravitational contraction, galaxies and clusters of galaxies are formed (the formation of large structures was also greatly assisted by the so-called dark matter). Gravitational contraction of denser gas clouds creates the first generation of stars, which end the "dark age" with their radiation. Massive stars thermonuclearly synthesize heavier elements from hydrogen and helium, explode as supernovae and enrich the surrounding matter with heavy elements. The stars of the next generations are then created from this substance, including our Sun. After their formation, stars are surrounded by clouds of residual gas ("protoplanetary disks"), in which planets orbiting the central star (such as the planets of the solar system, including Earth) gradually form.
-> Late evolution, the future of the universe
During all these processes, the expansion of the universe was still taking place, which was gradually slowed down by the attractive gravitational action of all the matter of the universe, including dark matter. However, this deceleration of expansion lasted only about 7 billion years. After sufficient dilution of the gravitating matter, the so-called dark energy, which has anti-gravitational effects, began to prevail. The deceleration of the expansion gradually decreased until it turned into an acceleration of the expansion. This situation continues even now and the continued accelerated expansion of the universe is expected in the future. In the distant future (~ hundreds of billions of years) this would lead to the "heat death of the universe" - complete cooling to practically absolute zero, stopping of all processes, stretching of all structures beyond the event horizon (sometimes the so-called "big rip" of everything is also discussed... ?..).

5.5. Microphysics and cosmology. Inflationary universe.		5.7. Anthropic principle and the existence of multiple universes

Vojtech Ullmann