Why does something exist and not nothing? - precise tuning of the universe

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. Fridman's dynamic models of the universe
5.4. Standard cosmological model. Big Bang.
5.5. Microphysics and cosmology. Inflationary universe.
5.6. The future of the universe
5.7. Anthropic principle and existence of multiple universes
5.8. Cosmology and physics

5.7. Anthropic principle and the existence of multiple universes

Finally, we will mention another more or less speculative "information channel" about the global structure and evolution of the universe, which is the so-called anthropic principle [67], [40], [57]. Some experts in astrophysics and cosmology (especially Dicke, Carter, Hawking, Collins, Wheeler, and others) in the 1960s and 1970s pointed out that the very fact of our human existence imposes some important limitations on the initial conditions and course of evolution of the universe, as well as the values of "constants" and parameters in the laws of physics *). Indeed, we live in a globally homogeneous and isotropic universe (but showing on a smaller scale significant inhomogeneities such as galaxies), containing a predominance of matter over antimatter and an expanding velocity close to critical, simply because in an inhomogeneous, anisotropic, baryon symmetric, or strongly closed or open universe, life would not be possible.
*) The beginnings of the anthropic principle were foreshadowed by reflections on the wonderful relationships and relations between the "big numbers" characterizing the physical constants of the universe and the microworld. (e.g. the ratio of the size of the universe and the atomic nucleus, and the ratio of binding constants of the interacting species), which is already in the 30s Dirac point out. These are dimensionless numbers expressing the ratios between the electromagnetic and gravitational force (between electrons and protons), between the dimension of the visible universe and the dimension of the atomic nucleus, or between the mass of the observable universe and the mass of the proton. Whether certain conspicuous coincidences in the proportions of these numbers (differing by tens of orders) are they random, or do they have a deeper meaning? The very name Anthropic Principle first used in 1968 by B.Carter.
After all, the term " principle " is perhaps somewhat unfortunate and misleading - it is not a central principle in physical, astronomical or scientific knowledge in general. The anthropic "principle" is rather a kind of "conglomerate" of specific ideas, concepts and contexts, having something to say to the mystery of the origin and development of our so specific universe.
Why is there "something" and not "nothing" ? 
Our world is filled with a lot of interesting things - billions of galaxies, nebulae, trillions of stars, planets and other structures in space. On our planet (and perhaps some of it on other planets) are beautiful natural formations - mountains, rivers, sea, trees and countless other plants and animals, we humans. Why do all these interesting and complex things even exist ?: "Why is there 'something' instead of 'nothing'..?.." - this is the most serious question of fundamental physics.
  The basic laws of physics, including the theory of relativity, quantum and particle physics, suggest that the universe should most likely be a rather boring place - it should be dark, inhospitable, without macroscopic structures and therefore, of course, without life... We cannot explain the special properties of the universe. A certain way to understand this would be the hypothesis, that we live in a multiverse. In most individual universes there is almost nothing, in complete emptiness and darkness the fluctuating fields incoherently propagate and only a quantum of fields and particles move, without any structures. But we live in one of the few universes, where the laws of physics allow 'something' to exist - so that more complex structures can be created and evolved (see "Multi-universe concept" below).
Very precise tuning !
The physically possible states that the universe can acquire allow the origin of life only in a very narrow range; a slight deviation is enough and the universe will continue to exist physically, but life will no longer be possible in it.

The origin and development of life is possible only in situations where the rate of expansion of the universe lies in a narrow "allowable range" around the critical rate.

In particular, the rate of expansion cannot be too different from the critical (escape) rate. If the rate of expansion were significantly less than critical, the expansion of the universe would soon stop and turn into a contraction, so that there would not be enough time for the origin and development of life. Conversely, if the universe is expanding at a rate, substantially higher than the escape, the matter would be too quickly diluted and dissipated, so that gravitationally coupled structures such as galaxies and stars could not form, which are needed for the formation of more complex elements and eventually life. In the time immediately after the creation of the universe, the ratio of particles and antiparticles had to be such that, after their mutual annihilation, exactly as many particles remained as were needed as the building material of matter for the present universe. This matter should not be too dense, otherwise the universe would quickly collapse back into singularity, nor too sparse - matter would disperse very quickly. The density had to be such that stars (1st generation) could form, which formed heavier chemical elements that could become the building material of the planetary systems around the stars. Some of these planets must have the optimal distance from the central star and other necessary properties, see below "Stars, planets, life".
  Similarly, if the physical constants had slightly different values, resp. ratios of values (just a few percent) than it is in reality, the evolution of the universe would also take place otherwise and would not lead to the emergence of life *) - at least not in the forms known to us based on organic carbon compounds **). The exact setting of all these necessary values and specific conditions seems like a very unlikely coincidence; all the more so when it is necessary to "chain" individual improbable states into a continuous sequence of conditions, which results in the emergence of life and ultimately an intelligent observer. Or is there something behind it that escapes astrophysics and cosmology? This is exactly what the anthropic principle seeks to answer.
*) Truth be told, we reach this conclusion when we changeone of the physical laws, or its parameters, while leaving the others unchanged. Then, indeed, only a slight change in one of the laws of physics would change the evolution of the universe so much that it would make life impossible. If we change the parameters in the standard model of particle physics, for example, so that a strong nuclear interaction would be somewhat stronger or weaker, nuclear nucleosynthesis inside stars would produce too little carbon, oxygen, nitrogen and other biogenic elements (as discussed in more detail in §4.1 , part "Thermonuclear reactions inside stars"). Similarly, if the masses of the quarks were somewhat different, for example, a proton could become slightly heavier than a neutron, protons would decay into neutrons, and no atoms would be formed.
  Change of force weak interactions would alter the course of the initial nucleosynthesis at the beginning of the universe (and later the thermonuclear reactions inside the stars), which could also change the representation of elements to the detriment of the more complex elements of organic chemistry and the origin of life. If the strength of the weak interaction were smaller, neutrons would decay more slowly and most of them would merge with helium protons in the lepton-era (a similar effect would occur if the rate of expansion of the universe were lower at the beginning). This would lead to a proton deficiency - matter in the universe would consist mainly of helium, there would not be enough hydrogen to later form the water and hydrocarbons necessary for life (primordial nucleogenesis for the conditions of our universe is discussed in more detail in §5.4 "Standard cosmological model. The Big Bang. Shaping the structure of the universe.", passage "Primordial nucleosynthesis").
  So far, the situation where we would simultaneously change two or more parameters or laws of physics at the same time has not been sufficiently explored (this may be the task of future research in nuclear astrophysics). We can imagine such "clever" changes in two or more parameters, in which it could happen that their consequences for the chemical evolution of the universe are in a sense "compensated". In addition to specific physical laws with parameter values, as we observe in our anthropic universe, there may be other "sets" of laws with different parameter values that may result in the evolution of a universe other than ours, but still allowing complex reactions and formation of life... It is even possible to hypothetically imagine a universe with such a combination of physical laws-constants-parameters, in which the conditions for the origin and development of life would be even more suitable than in ours..?!.. And such alternative universes may indeed arise and there are..?.. - within the concept of more universes ...
**) Carbon - a basic biogenic element 
Carbon, which has 6 protons in its nucleus and therefore 6 electrons in its envelope, has significant chemical properties that allow it to form a huge range of complex molecules, including chaining of macromolecules (proteins, RNA, DNA). Chemists and biochemists are very skeptical about the possibility of a silicon- based life (instead of carbon). Silicon does not provide by far as rich possibilities of easy bonds with other light elements (H, O, N, P, ...) as carbon. No significant amount of more complex silicon compounds was observed in space, while relatively large amounts of complex carbon compounds (eg alcohols, amino acids, ...) were observed.
An interesting alternative, however, could be the possibility of the creation and evolution of a purely electric one processing of information signals on an inorganic basis ...

Stars, planets, life
A phenomenon as complex as life in the universe, can hardly develop in any empty place in space. At the very least, a source of energy and a suitable material carrier of life must be present. The sources of radiant energy in the universe are stars, and the planets orbiting the stars are suitable material carriers capable of providing long-term stable conditions for the time-consuming process of origin and evolution of life.
We know intimately one such place where life evolved. It is a system: [star = Sun] + [planet = Earth]. However, there is nothing special about our solar system that cannot occur elsewhere in the universe. There are only billions of Sun-like stars in the Milky Way alone, the planetary systems around the stars are a natural consequence of their formation from a rotating germ nebula (planetary systems have already been demonstrated around some stars). However, in order for life to evolve on a planet orbiting a particular star, the star and the planet must have some specific properties :

• Mass of the star
  The respective star must have a reasonable mass (in the range of approx. 0.6 ¸ 10 M_¤ ). It must not be too massive, because massive stars consume their basic fuel, hydrogen, too fast to allow the development of life on any planet. It must not be too light, because the most important thermonuclear reaction H ® He would not be ignited (such a pseudo-star is called a brown dwarf ) and there would not be enough energy for the processes of life formation on potential planets.
• Stable luminosity of the star
  The star must have an almost constant luminosity for a sufficiently long time (min. 10⁹ years). It must not be variable, because large temperature fluctuations on the surrounding planets would not allow the creation and maintenance of a stable life. This property is closely related to the above mass of the star.
• Loneliness star
  1. Star should be "alone" in the sense that it should not be part of the close binary or multiple systems. In such systems, for example, planets are subjected to non-central and variable gravitational forces, so there are no circular and long-term stable orbits of the planets (the condition of the following point is not met).
  2. There should not be too massive stars (with masses higher than about 10 M_¤ in the space around tens of light-years.), which would explode like supernovae, with the emitted high-energy radiation "burning" the evolving life on the planets around nearby stars. This condition is most often met in the outer spiral arms of galaxies, not near the center of galaxies, where there is a high concentration of massive stars (and even there is a risk of hard radiation from a supermassive black hole at the center of the galaxy).
• The orbit of the planet
  Planet enabling life must circulate at a suitable distance from its star. The temperature on the nearby planets is too high, preventing the formation and duration of any complex compounds. On distant planets, the temperature is too low, so complex biogenic reactions do not take place. Only in a narrow range of distances - in the so-called planetary ecosphere or habitable zone, the temperature conditions are suitable (in the solar system, the boundaries of the ecosphere are estimated in the range of about 140-170 million km from the Sun, ie about 20% wide). Orbit should be close to circular, because a strongly eccentric trajectory would lead to large temperature fluctuations, unfavorable for the origin and development of life.
• Planet's mass
  Planets that are too light will not hold their atmosphere due to their gravity. For planets that are too massive, the vast atmosphere creates too much pressure, which does not allow sufficient mobility of the reagents.
• The atmosphere of the planet
  A life-enabled planet should have a gaseous envelope - an atmosphere that maintains a relatively constant surface temperature, protects the surface from the sharp impacts of a large number of tiny cosmic bodies, and contains gases that may be involved in the metabolism of living organisms. The "thermal comfort" required for the origin and development of life also depends on the composition and density of the atmosphere, whether it contains "greenhouse" gases (leading to an increase in temperature) or clouds reflecting back part of the parent star's radiation.
• The magnetic field of the planet
  "Mother" star supplies nearby planets not only with life-giving light and heat radiation, but also with streams of charged particles of the "stellar wind". In addition, high-energy cosmic rays are constantly coming from outer space. The planet's magnetic field can play an important role in life in two ways :
  1. It protects the ecosphere from the harmful effects of ionizing cosmic radiation by deflecting high-energy protons out of the planet.
  2. Protects the atmosphere before the destruction of the "stellar wind" - an intense stream of charged particles coming from the parent star.
  The magnetic field of terrestrial-type planets 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, causing the planet's magnetic field to disappear. For possibly. life on the planet's surface has two adverse consequences :
  a) A large amount of hard ionizing radiation, which is harmful to living organisms, begins to enter the biosphere from outer space.
  b) An intense stream of charged particles emitted by the star 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 is incompatible with the continuation of life on such an affected planet.
• Biogenic elements
  Life based on "organic" carbon compounds can only be where there are biogenic elements - hydrogen, carbon, oxygen, nitrogen, sulfur, calcium, phosphorus, etc. So they must be planets around the stars of the 2nd or next generation. On the planets around the oldest stars of the 1st generation, composed only of hydrogen and helium, life cannot arise.

Even with these very specific requirements, there are probably millions of stars in our Galaxy with suitable properties, around which they orbit at appropriate distances the planets of the required sizes. And if life originated about 4 billion years ago from inanimate matter on the tiny cosmic "powder" that our Earth is from the cosmic scale, there is no reason why it could not have originated elsewhere in the universe, albeit at a different time and in a different form. After all, the natural laws by which matter is governed are the same everywhere in the universe. So we can assume that life is perhaps in many places in the distant universe..?.. So far no one knows ...
Global "zones of life" in space  
In which parts of the vast and diverse universe is the origin, maintenance and development of life likely? It turns out that this is not everywhere, that from a global point of view there are only relatively small delimited "zones of life" in the universe, while outside these areas, for astrophysical reasons, there are no conditions for a more complex life. Either there is not enough concentration of stars, which led a low probability of the occurrence of "life-giving" stars and planets. Or, conversely, places with high concetration of stars, especially massive stars that can explode as supernovae, are potentially dangerous to life because the supenova's intense high-energy radiation "sterilizes" a wide range of decades of light years (see "Biological significance of cosmic radiation", pasage "Deadly cosmic rays"). On the other hand, suitable material for building planets and building life occurs only where enough stars have already exploded and enriched gas clouds with heavier elements. Thus, in galaxies, life will initially not be able to occur in the central parts, where "every moment" (every million years), a devastatingly explode the supernova, or entirely on the periphery, where there is not enough "building material". But rather somewhere "in the middle" in the spiral arms.
Note.: More complicated situation is in colliding galaxies, where the rapid formation of massive stars, exploding like supernovae, is likely to cancel potential zones of life even at greater distances from the galaxy's center.
  Habitable zones (around stars and in outer space) are not static, but as the astrophysical situation evolves, the size and distribution of habitable zones change. Some disappear, in other places new ones emerge - again only temporary. Whether life really develops, there is a matter of the complex interplay of many conditions and circumstances. And to what complexity this life could develop, is largely determined by the duration of the life zone.

The questions of the origin and evolution of life are discussed in more detail in the work "Anthropic Principle or Cosmic God", the
passage "Origin and Evolution of Life".

Anthropic principle
Namely on the basis of the question why the real universe is so specific, when the laws of physics allow the existence of the universe with completely different properties with the same right, that the anthropic principle arose. What laws and phenomena have made it possible for creatures, capable of thinking about their origin to have evolved here on Earth (and perhaps in many biospheres elsewhere in the universe) ? During many discussions about the relationship between the universe, life and human consciousness, several conceptions of the anthropic principle have emerged, which can be divided into roughly three groups (the other two variants will be presented at the end) :

This is a sober physical formulation of the anthropic principle, which in this sense is a certain selection principle, selecting from all theoretically possible cosmological models those that lead to the universe as it is, especially, to the universe in which life could have originated. The name "anthropic principle", after all, is not very apt here; cosmology does not require the existence of man, but the existence of stars such as the Sun is sufficient.

Alternativelly, universe must inevitably create the conditions for the existence of observers - in every real universe, the observer must necessarily appear once. From a physical point of view, this seems to be too "philosophically colored" a formulation that sounds somewhat metaphysical. The anthropic principle conceived in this way is, in a sense, an antithesis of the philosophically generalized Copernican principle; it is in accordance with the religious concept that the universe was created by God so that it would be maximally purposeful and that the ultimate goal would be the origin and development of man. There is no physical justification for such a concept.

Indeed, the anthropic principle in trying to answer the question "Why is the world built just like and not differently?" it implicitly offers the assumption of the existence of many differently arranged universes coexisting with our universe, which, however, are (at least now) fundamentally unobservable.

Until recently, the idea of many universes was purely speculative *). Now, however, a relatively realistic conception of several different universes is emerging on the basis of cosmological applications of modern unitary theories. In connection with the inflationary model was in §5.5 "Microphysics and cosmology" noted, that due to the quantum fluctuations could spontaneously arise more independent universes, that as a result of various amplitudes and scope of quantum fluctuations and various types of spontaneous symmetry breaking will have a different structure and global properties of physical fields and matter (more detailed discussion of the possibility of more universes in §5.5, part "Chaotic inflation", passage "Origin of more universes"). In some of these universes, then, according to the anthropic principle, it can develop life.
*) We will not discuss here the hypothesis of parallel existence of infinitely many universes with various course of physical processes based on physically not completely justified application of stochastic quantum laws to the whole universe. According to this hypothesis (expressed by Everett and Wheeler [79] in the 1950s), in each interaction leading to a certain quantum-mechanical state in a given universe, even all other possible states are actually realized, but in other universes. Figuratively speaking, in other universes, all "wasted chances" from our universe are realized. Each historical event took place differently in all possible variants in different parallel worlds. So these are not different universes in terms of space-time, but the space of states; in this configuration space, the individual universes are orthogonal to each other, so that from the classical point of view there is no possibility of interconnection between them.
Considerations about the possibility of the existence of more universes also arose in connection with some geometric-topological properties of space-time around black holes - see §3.5 and 4.4, especially the passage "Black holes - bridges to other universes?".

According to these concepts, our entire universe is just a "bubble" in a bubble multiverse made up of lots of bubbles; each "bubble" is a different universe with different fundamental constants and different physical laws. Or another analogy: our universe is just a "grain of sand" on the gigantic "beach" of the multiverse. The key to the mystery of the uniqueness of our anthropic universe could be statistical laws in the multiverse ...
  Quantum fluctuations of the vacuum may everywhere and are constantly "spewing" new and new universes with various properties. The whole Universe thus appears to be a bubbling "foam" of expanding "bubbles" - separate universes, each governed by its own  laws of physics, he lives his "own life". Our entire visible universe is just a small area in one of these bubbles. Otherwise, very few bubbles have physical and geometric properties suitable for creating more complex structures - galaxies, stars, planets and ultimately life.

For little refreshment, we can mention the charming Indian legend of the creation of many universes.

In connection with the concept of many universes, the anthropic principle can also help to solve the problem of the dimension of our spacetime, ie the question of why space-time is just four-dimensional (and space three-dimensional). The question of the dimension of physical space and spacetime (which previously seemed entirely academic, even almost scholastic) was raised more seriously after the creation of multidimensional unitary theories, namely Kaluz-Klein's five-dimensional theory (see Appendix B, §B.2). The original Kaluz and Klein unitary theories were not successful and for a long time they practically fell into oblivion. Recently, interest in them began to rise again because it turned out that extended supergravity theories can be built geometrically in spaces of dimension n = 10 or n = 11 [59], [283].
  In generalized unitary theories of the Kaluz-Klein type (see also §B.2 and B.6), a space of dimension n> 4 is considered, while all dimensions n-4 spontaneously "compactifying" - closing in on themselves, so that the radius of curvature of space in their directions it is very small (of the order l_p » 10^-33 cm), so no macroscopic object can move in these directions and spacetime effectively appears to be four-dimensional. However, the question remains unclear why they compacted the dimensions n-4 and not n-3, n-2, n-5 or the like, ie why the resulting continuum is not three-dimensional, two-dimensional, 5-dimensional, etc.?
  However, within the co-production of the inflation model of the universe and the anthropic principle, a certain possibility opens up to solve this problem even under the general assumption that spontaneous compaction can transform the original n-dimensional space not only into 4-dimensional space, but also into spaces with other number of dimensions. Such compaction will then take place independently in distant causally unrelated parts of the universe, so that after the compaction the effective dimension of space may be different in different parts of the universe (although microscopically the dimension of space will be equal to the default value of n everyvhere). If inflationary expansion of the universe occurs after (or during) compaction, the variously compacted regions will strongly expand and move away, so that upon completion, the universe will consist of many separate "mini-universes" with different dimensions, including dimension 4 corresponding to our spacetime. And here comes the word anthropic principle: it turns out that the existence of atoms and planetary systems (necessary for the origin and development of life) is possible only within four-dimensional space-time. This problem was already dealt with by P.Ehrenfest in 1917, who showed that in spaces of dimension higher than 4, gravitational and electromagnetic forces would decrease too quickly with distance**) and could not lead to the formation of stable bound systems such as atoms or planetary systems. According to GTR, in spaces of dimension smaller than 4, gravitational action between bodies would not occur at all. According to this concept, we live in that metagalaxy (in one of the many "mini-universes"), in which the 3 + 1-dimensionality of space enabled the origin and development of life.
**) In n-dimensional space (n+1-dimensional spacetime), the equation of the gravitational potential generated by a point source would have the form (in Newtonian approximation) N_n²j = G.M.dⁿ(r), where Ñ_n is the n-dimensional Hamiltonian operator, dⁿ(r) s d(x₁).d(x₂)....d(x_n) is an n-dimensional Dirac function, r is a position vector in n-dimensional space. For a spherically symmetric case, the n-dimensional Gauss theorem gives a solution in the form j(r) ~ 1/r^n-2, so that the force action depends on the distance according to the law F(r) ~ 1/r^n-1. Analogous to electrostatic field. In §1.2 we have shown that the existence of stable orbits is conditioned by the shape of the effective potential (1.14); the equation of motion d²r/dt² = -N_nj has a solution in the form of stable orbits only if the effective potential V_ef(r) has a minimum at r ¹ 0, r ¹ ¥ . Ehrenfest showed that the equation of motion d²r/dt² = -N_nj has no solution in the form of closed orbits at n> 3 - the test body either falls on the attractive center or moves away from it to infinity.
  Although the considerations we have just outlined are somewhat speculative, in addition to the traditional notion of a globally homogeneous and isotropic universe, the idea of a heterogeneous island universe consisting of many locally homogeneous and isotropic "mini-universes" - metagalaxies - is increasingly emerging in contemporary cosmology. In each such "miniverse" properties of elementary particles, fundamental interactions (and thus the size of the vacuum energy) and even the dimension of the space, may be different . Although current experimental and theoretical knowledge does not provide any direct evidence for the existence of other metagalaxies ("universes"), this possibility cannot be ruled out a priori. Observable universe (our metagalaxy) from physical point of view is not so exclusive, that had to be considered unique. Physically, they could exist, resp. coexist, other metagalaxies (causally separated "universes") with different properties different from our metagalaxy. Interestingly, these concepts are in line with the views of I.Kant, who dealt with the question of the dimension of space from a philosophical point of view: "If there can be formations with other dimensions, God has probably actually placed them somewhere" (1746).
  So there are some indications that we live in a multiverse, but other universes are forever beyond our reach. We can't get there in any way (physically or by signals), there is no way to know if they exist or not..?..

For the sake of completeness, let us mention two more speculative versions of the (strong) anthropic principle, which emphasize the role of the observer :

From a philosophical point of view, the participatory anthropic principle, originated by J.A.Wheeler, is justified by the theory of knowledge - gnoseology, noetics. From the physical point of view, it is partially supported by the so-called Copenhagen interpretation of quantum mechanics, according to which a certain state of the physical system is creaded only by measuring it. General: No phenomenon is a phenomenon until it is observed. And so is the universe. Therefore, if the universe is to be real, its properties must allow the existence of an observer. In a sense, the universe and the observer are placed on the same level here, their existence is conditioned by each other. However, this overestimation of the role of the observer is highly debatable from a physical and philosophical point of view..?..

The intelligent observer is a goal that makes sense of the existence of the universe.
Any physical justification for the final anthropic principle is currently lacking; it even contradicts current cosmological concepts, according to which no structures in the universe can be eternal - they end in either the collapse or the infinite dilution and decay in the open universe - see §5.6 (cf. also the passage "Astrophysics and Cosmology - Human Hopelessness?"). The final anthropic principle is only a product of our faith, respectively pious desire ...

From a philosophical point of view, the role of the anthropic principle is discussed in the work the Anthropic Principle or the Cosmic God.

Different meanings of the term "universe"
To at least partially clarify some terminological ambiguities in philosophical considerations of cosmology, it is be useful to realize that the term "universe" is used in several senses, the basic three of which are :

• Universalistic - "everything that is" - everything that "physically" whenever and wherever it exists.
• Causal - includes everything that has interacted with our area in the past, interacts now, or will interact at any time in the future.
• Metagalaxy - a system of causally interacting objects, which is either isolated (causally) from other systems, or separated by such large distances that there is practically no interaction for the duration of the structure of the system.

5.6. The future of the universe		5.8. Cosmology and physics

Vojtech Ullmann