In an attempt at answering these questions in this work, we have to leave the territory of physical cosmology and enter the field of philosophy. We shall consider the properties of the universe on the four levels: the level of facts obtained from direct astronomical observations by physical methods, the classical and quantum theories of Big Bang and the metaphysical level. The latter lead to a certain general model of reality and this model can provide answers to the fundamental existential questions. Moreover, the model offers a holistic and consistent view of the reality, in full agreement with contemporary physics.  However, because astronomically large numbers appear rather a lot, the power notation has been used: for instance a milliard (american - billion) seconds is written as 10⁹ s, and one millionth fraction of a meter is 10^-6 m.  One of the most profound questions of science is that about the origin, evolution and structure of the universe. It has been for ages the subject of interest of philosophers and theologians, but the answer was far beyond science. Only the rapid development of sciences in the 20^th century has made it possible to attempt at answering it in a consistent and general way. The 20^th century witnessed the birth of a new field of science – cosmology (known also as physical cosmology) – concerned with the study of the universe as a whole. Unfortunately, cosmology, which is a science based on empirical and mathematical methodology of physics, cannot provide answers to such fundamental questions as: Is there any sense in the existence of the universe? What was before the universe came into being? Why is the universe rational? What is the man’s position in the universe?

First, I will give a description of the basic astronomical facts and observations. Secondly,  presents basic information on the three main branches of physical cosmology: classical, inflation and quantum approaches. Transcosmology providing answers to all fundamental existential questions and explaining the sense of existence of man and the universe. This new formulation of transcosmology also indicates the source of existence and rational character of the universe.

Astrophysics has proved that:

 In the observable part of the universe there are no objects older than 20 milliard years.

This is a very important fact enabling a determination of the size of the observable universe. According to Albert Einstein’s theory of relativity information cannot be sent at a speed greater than that of light in vacuum of 300 000 km/s. Thus, we can observe astronomical objects which are not farther away from the Earth than 20 milliard (american - billion) light years. This distance determines the horizon of our observations. Therefore, the observable universe has the shape of a sphere of the radius smaller than 20 milliard (american - billiob) light years, so smaller than 4 x 10²⁵m, with the Earth at its centre. This sphere is the largest system accessible for investigation with physical methods. In the physical cosmology this system is treated as the universe. The size of the universe is difficult to imagine. To help it let’s make the following rescaling. Let’s assume that the distance from the Earth to the Sun of about 150 milliard (american - billion) meters, travelled by light within approximately 8 minutes is shrunk to 1 mm. In this scale the distance to the stars closest to the Sun is of the order of 300m. The diameter of the Milky Way, the galaxy composed of at least 100 milliard (american - billion) years (including the Sun) in this scale is of about 6000 km. If we shrink the size of the universe even more and assume that the diameter of the Milky Way is 1 cm, then, in this scale the radius of the sphere of the observable universe is of about 1500m. The sphere is almost uniformly filled with at least 100 milliard (american - billion) galaxies approximately 1 cm long, separated by a few tens centimetres. The galaxies are grouped in clusters and superclusters. The observations have proved that the sphere has also large regions – the size of a few meters in this scale - devoid of galaxies. However, in the large scale – of an order of a 100 metres and more, the spatial distribution of galaxies is isotropic and uniform (independent of the site and direction of observation). Thus, the observable universe can be imagined as a ball uniformly filled with the gas of galaxies.

In a large scale (of the order of milliards light years or more) the observable universe is uniform and isotropic.

Moreover, the observations seem to indicate that:

The space of the observable universe in a large scale has euclidean geometry. This is the geometry which we were taught at school and this fact implies for instance that the sum of the angles of a triangle of side length of milliard light years is 180⁰, irrespectively of the triangle position in the universe.

It is understood that, regarding the finite speed of light, distant objects are observed at the earlier moments of their existence. For example, if the Sun suddenly stopped shining, we would learn about it after 8 minutes time, which is needed for the light to travel from the Sun to the Earth. Astronomical observations prove that the earlier universe was different from that existing today, e.g. it encompassed many more radiogalaxies and quasars. Therefore, the universe has its own history and changes in time. In other words:

The universe in not homogeneous in time.

In the mid 60s, it was discovered that the universe was filled with electromagnetic radiation of the properties similar to that used in microwave ovens, characterised by the temperature of about 2.7 K. Later studies have shown that the Earth moves with respect to this radiation at a speed of about 620 km/s towards the constellations of Hydra and Centaur. Moreover, the distribution of this radiation was found to correspond to the isotropic radiation of an absolutely black body. Deviations from isotropy appear only at the level of one hundred thousandth value of the average. Thus:

The universe is filled with highly isotropic microwave radiation of the spectral distribution of the absolutely black body. In different regions of the sky the radiation has slightly different temperature. The differences or temperature fluctuations are small and equal to about 10^-5 K.

The radiation is known as the background or relict radiation. According to physics, electromagnetic radiation can be treated as a set of microparticles which are called photons. Sometimes, instead of a photon we talk about a quantum of electromagnetic radiation. Astrophysical estimations show that:

In the universe there are about 30 milliard photons per a single atom.

This means that the kind of matter found on the Earth is something exceptional. Moreover, according to astronomical observations:

Luminous matter in the universe is composed of hydrogen atoms in 75%, helium atoms in 25% and trace amounts of other elements, mainly lithium, mean density of matter in the universe equals 10^-29 of the density of water.

Also from astronomical observations, in particular from the observations of the dynamics of clusters of galaxies, it follows that:

The majority of matter in the universe is non-luminous (the so-called dark matter) and thus invisible for the observer from the Earth.

It cannot be excluded that dark matter makes more than 90% of the matter in the universe. The composition of dark matter is not known yet. Probably it is a mixture of elementary particles, including exotic ones which have not been observed in laboratories.

In 1929, an American astronomer Edwin Hubble discovered that:

Distant galaxies move away from the Earth at a speed directly proportional to the distance from the Earth. Their speed depends only on the distance and not on the direction in which a given galaxy is observed.

For example a galaxy distanced from the Earth by 100 million light years moves away from the Earth at a speed of 2000 km/s, while that at a distance of a milliard (american - billion) light years – at a speed of 20 000 km/s. This means that the universe expands, and its galaxies move away one from another, so the density of matter in the universe gradually decreases.

Finally:

No rotation of the observable universe has been detected.

All these fundamental facts require explanation, which is the subject of concern of physical cosmology.
 
 

Physical cosmology

In the ancient Greece, cosmology was the natural science. At present it is understood as the knowledge of the universe as a whole and the laws within it. Often the term cosmology is used either as part of philosophy or as a science, therefore, to avoid confusion, we distinguish philosophical cosmology and physical cosmology – which refers to physical investigation of the largest possible system – the observable part of the universe. The physical cosmology is divided into classical and quantum ones. We shall start with a brief description of the basic assumptions and results of the classical physical cosmology based on observations and classical physical theories used for description of its dynamics.

Classical cosmology

The main assumption of the classical cosmology is the so-called Kopernik’s (Copernicus) principle. The essence of the Copernicus approach was the recognition that the Earth is not the centre of the universe. In general, according to this principle, each site in the universe is equally important, and our position is typical. Disregarding the small-scale distribution of matter, in a large scale it is isotropic and uniform. The Copernicus principle is thus a general conclusion following from the observational data. Since the only known forces which can act at intergalactic distances are gravitational forces, therefore, the second basic assumption of the classical physical cosmology is that the gravitational forces determine the dynamics of the universe. Physics has an excellent theory of gravitation formulated in 1915 by Albert Einstein. This theory, known as the general theory of relativity, is at present the best experimentally confirmed physical theory. It has been verified with the accuracy of 1 over 100 billions (10¹⁴). As follows from the uniform and isotropic character of the universe, in a large scale the gravitational forces are, on the average, the same. The general theory of relativity reduces the phenomenon of gravity to the inertial motion in a curved spacetime. Thus, the uniformity of the universe implies that the curvature of its space is the same at each point. It can be proved that there are only three kinds of space characterised by a constant curvature independent of position : the space of spherical geometry (the sum of the angles in a triangle is greater than 180⁰), the space of hyperbolic geometry (the sum of the angles in a triangle is lower than 180⁰) and space of euclidean (planar) geometry. The spherical space has a finite volume and there exists in it the greatest finite distance, whereas in the hyperbolic and planar spaces an object can move away at an infinite distance. For this reason the universe of the spherical space is referred to as closed and the universes of the other two geometries are open. Moreover, the total energy of the universe of the closed geometry is equal to zero. The positive energy of matter in such a universe is exactly compensated by the negative energy of the gravitational field. The total energy of the universe of the hyperbolic or planar geometry is infinite.

The geometry of the universe depends on the average density of matter in it. If this density is lower than a certain critical value, the universe has the space of the hyperbolic geometry. If it is equal to a certain critical value, the space of the universe is planar (euclidean), and if it is higher than a certain critical value – spherical.

At present astronomical observations and theoretical calculations do not provide an unambiguous answer to the question whether the density of matter in the universe is lower or higher than the critical value. We can only say that this density is not much different from the critical one. In combination with Fact 4, it means that the observed part of the universe is a small fragment of a finite or infinite universe.

If the density of matter was lower or equal to the critical value, the theory predicts that this density would gradually decrease, tending to zero, with no time limitations. If it was greater than the critical value, it would decrease for at least 100 milliard (10¹¹) years and then it would start to grow to reach the infinite value over the next 200 milliard (american - billion) years. At this moment, according to the general theory of relativity, the universe will end – the spacetime and the matter it contains will disappear.

In all types of space of a constant curvature, when we go back in time, the density of matter increases to infinity. By extrapolation we find that about 15 milliard (american - billion) years ago, this density had an infinite value. Such a state is known as the initial singularity. According to the laws of thermodynamics, an increase in the density of the universe implies an increase in its temperature. In the state of the initial singularity, the temperature, similarly as the density, takes an infinite value.

According to the laws of classical physics, the history of the universe could be described as a gigantic explosion from the state of the initial singularity; that is why the theoretical model describing this history is often called the Big Bang theory.

The temperature of the universe can be treated as a physical quantity, which is a measure of the mean kinetic energy of particles. The greater the mean velocity of particles, the higher the temperature of the universe. In contemporary accelerators, we are able to carry out collisions of particles of kinetic energy corresponding to a temperature of about 10¹⁵ K According to the Big Bang theory, the universe had this temperature for the time of 10^-11s after the initial singularity, which in cosmology is denoted as the zero moment t=0. In the earlier time, 0<t<10^-11s, the universe had the characteristics which we are not able to reproduce in our laboratories. Therefore, the cosmology of the universe younger than 10^-11s is based on extrapolations of the known physical theories or their hypothetical generalisations over the temperatures and energies inaccessible for experimental studies.

There is a physical theory known as the standard model of elementary particles, which well describes the behaviour of particles of energies equal or lower than that corresponding to the temperature of 10¹⁵ K. Therefore, we can say that our knowledge allows us to reproduce, at least in general, the history of the universe from t=10^-11 s after the Big Bang till the present. At t=10^-11 s, the density of matter was 10²⁸ times greater than that of water. At present the ratio of the difference between the matter density in the universe and the critical density (corresponding to the euclidean geometry) was lower than 3, at t=10^-11 s it was lower than10^-8, which means that at that time, the universe geometry could be well assumed as euclidean.

Assuming the above physical conditions implying that at t=10^-11 s the universe was filled with hot matter of the temperature of 10¹⁵ K and density of 10²⁸ times greater than that of water, composed of the known elementary particles: quarks, leptons, gauge bosons and dark matter of not ideally homogeneous density, we are able to reconstruct the history of the universe. We can explain the contemporary structure of the universe, composition of matter, distribution of radiation, etc.

The following main stages of the universe evolution can be distinguished:

This amazing scenario of the universe evolution is known as the Big Bang theory. It has been a great achievement of human thought as it gives the first scientific description of the universe history, quantitative and consistent with observations. This theory is attributed to Alexander Friedman, Georges Lemaî tre and Gieorgij Gamov.

Although the theory provides explanations of a great number of problems, many are still left unanswered. Some of them are:

To answer these questions we should first of all learn what happened in the universe in the time t<10^-11 s. Partial answer is provided by the so-called inflation cosmology.

 Inflationary cosmology

The standard model of elementary particles has explained many phenomena of high-energy physics, however, for some reasons it cannot be considered a final and fundamental physical theory. First of all this model uses over 60 different elementary particles involved in many interactions but fails to explain the reasons for the diversity. Moreover, the model gives a separate description of weak electric and strong nuclear interactions, disregarding gravitational forces. The model has been formulated with 18 constants, which we are not able to calculate. For these reasons, if we wish to study the initial moments of the universe evolution, we have to make use of theories, which are generalisations of the standard model. Direct generalisation of the standard model has led to the development of a group of theories of grand unification known as GUT. Different formulations of GUT have been proposed, and at present no experimental verification can be suggested to verify which of them is true. All formulations proposed have certain common features.

The grand unification programme aims at combining the weak electromagnetic interactions with strong nuclear ones in a common theoretical scheme. At first glance such an attempt is bound to fail as these interactions have much different intensity and concern different elementary particles. However, it was shown that the intensity of these interactions depends on the temperature of the medium, and although in the present universe they differ substantially, in the early hot universe they were similar. According to GUT these interactions were identical for t   10^-35 s, when the temperature of the universe was of the order of 10²⁸ K, and the matter density was 10⁷⁶ that of water. At that time the presently observed part of the universe was a ball of only 4 mm. The size of the universe observed at that time was 10^-27 m. So in this early epoch, the region which has expanded to the presently observed universe was 10²⁴ greater than the universe observable at that time. Therefore, the presently observable universe should not be uniform and should contain many magnetic monopoles, which are the simplest topological defects (the so-called Higgs fields) appearing according to the theory of grand unification at the border of misadjusted regions. The mass of the monopoles was estimated as about 10¹⁶ that of the hydrogen atom, and their density in the universe is predicted as comparable to that of atoms.

At present we are not able to verify GUT but we can study its implications. Unification of the above mentioned interactions demands the existence of the so-called gauge bosons transferring the interactions and changing certain particles into others (quarks into leptons and leptons into quarks). The gauge bosons must have mass great enough to be produced in large numbers by collisions of particles at temperatures of the order of 10²⁸ K. The grand unification theories predict the presence of two kinds of particles: the X particles which are heavy gauge bosons and magnetic monopoles. .

The X gauge bosons, in contrast to other known elementary particles permit the transformation of matter into antimatter. This property of X particles is of the key importance in explaining why the present universe is almost entirely composed of matter as the X particles and their antiparticles do not disintegrate at the same rate. Consequently, the initial state of the universe in which the matter and antimatter were in equilibrium could in ~ 10^-35 s evolve into the asymmetric state with a significant domination of matter. The X bosons are short-lived, so they quickly break up into leptons and quarks, whereas the magnetic monopoles are permanent particles. Their contribution in the matter density is so high that our universe should have already ceased to exist as the time of its existence would be of only 10⁴ years. Moreover, there is no experimental evidence for their presence in the presently observed universe. Therefore, GUT’s implications do not agree with the observations. Thus, either GUT is incorrect and should be rejected or there is a way of removing magnetic monopoles from the observable universe.

In 1981, Alan Guth, an American physicist, suggested a solution. He assumed that in the time t=10^-35 s to 10^-33 s, after the beginning of expansion, the universe went through a rapid exponential expansion. This kind of expansion implies that roughly every 10^-35 s all distances in the universe doubled. Consequently, in a fraction of a second all distances expanded e.g. 2²⁰⁰=1.6x10⁶⁰ times. This rapid swelling of the universe is called inflation. The hypothesis of inflation developed into a separate discipline -– inflationary cosmology, which is at present the central problem in the studies of the early universe.

If the universe went through the process of inflation, the whole presently observed universe could have developed from a region smaller than the universe observed at t=10^-35 s. Homogeneity and isotropy of the presently observed universe become understandable as we see only an expanded image of the region which was small enough to get smoothed before the inflation. The inhomogeneities apparently exist, although they were moved out of the observable part of the universe.

Inflation excludes the possibility of observation of rotations of the universe as a whole, because, even if the universe rotated very fast before the inflation, as a result of its expansion as demanded by the law of conservation of the moment of momentum, the rotation would become too slow to be observed.

The theory of inflation solves the problem of magnetic monopoles, as the presently observed part of the universe could have developed from a region so small that it could have contained at least one linear topological defect conditioning the existence of a magnetic monopole. However, in order to solve the problem of magnetic monopoles, the process of inflation should last at least 100 times longer than the age of the universe at the moment the inflation began. If so, the observable universe may contain one or at most a few magnetic monopoles. If the time of expansion was long enough to explain why we do not detect any magnetic monopoles, the average density of matter should differ from that of the critical density by no more than its one millionth fraction.

This result is very interesting for the following three reasons. First of all it explains the euclidean geometry of the observed universe. Secondly, if the density of matter in the universe is so close to the critical value, we will never be able to experimentally discern whether we live in the universe of spherical or hyperbolic geometry, since our observations cannot be made at the accuracy of one part per million. Thirdly, the observed density of the luminous matter is at least 10 times lower than the critical one, so if the inflation hypothesis is true, over 90% of the matter must occur in the non-luminous form, so not as stars or galaxies.

Thus it seems that the universe is mainly composed of dark matter. The abundance of helium 3 and deuterium suggests that if the universe is filled with dark matter of a density close to the critical one, the matter cannot have the form which can take part in nuclear reactions. This could mean that the major part of matter in the universe occurs in the form completely different from the elementary particles we know.

If the inflation process had not taken place, the universe space geometry would have been spherical and the universe would have existed only for a short time. Thanks to the inflation expansion, the universe can survive very long, even billions of years. Because of a large number of magnetic monopoles, the GUT theories suggest the spherical geometry of the universe. If so, the universe has a huge but finite size and will exist for a finite time. The observable part of the universe is so small that it seems flat. Likewise, a fisherman would not notice that the surface of the pond at which he catches fish on a windless day is not really flat because of the spherical shape of the Earth.

Taking into account the rapid character of the inflation, the universe could have been forced out of the thermodynamical equilibrium for a fraction of a second, and this, together with the earlier discussed properties of gauge bosons X would lead to a certain domination of matter over antimatter. The remainder matter and antimatter would annihilate producing a large number of protons. This process can explain why there are 30 milliard photons per a single atom.

The question is however, what induced inflation and why the matter in the universe was heated up to 10²⁸ K. According to the classical cosmology, the inflation takes place in the time when the density of matter is constant in spite of a rapid expansion of the universe. This would imply that matter is produced during the inflation. The matter is endowed with positive energy and satisfaction of the energy conservation law requires that it is produced at the expense of the negative energy of gravitational field. As mentioned earlier, such a full compensation of energies takes place only in the universe of spherical geometry, so in a closed universe. The occurrence of inflation would suggest that our universe has this very geometry. In such a universe, everything comes into being from nothing. The only requirement is the existence of a microscopic region of spherical geometry and the configuration permitting the beginning of inflation, which in a fraction of a second would produce a space of the size greater than the presently observed universe.

The conditions needed for the inflation to start are still a mystery. Different theories and mechanisms have been proposed to explain the generation of inflation and the heating up of the universe at the end of this process, however, the results are not satisfactory. In spite of increasingly refined theoretical constructions, the problems have not been solved in full agreement with observations.

Although the inflation cosmology is not a closed chapter yet, it has been an important step in understanding the universe evolution. The hypothesis of inflation is one of the most important ideas in contemporary cosmology. It provides simple and convincing explanations of many questions, which could not be answered before. It seems that the difficulties of the inflation cosmology are of technical nature and will be solved in future. Therefore, it is supposed that the process of inflation really took place in the early moments of the universe evolution. The inflation cosmology explains many properties of the observable universe, irrespective of its actual origin. This is a very important feature as it allows prediction of the current state of the universe without the need of accurate knowledge of its initial state. On the other hand, this feature is a kind of impediment in understanding the origin of the universe because its current state has developed, in great extent, irrespective of its pre-inflation state. Although the process of inflation effectively obscures the information on the initial state of the universe, we shall try to answer the following questions:

1. What existed before the process of inflation?

2. Where from did the microscopic space of spherical geometry appear?

These questions have been answered by the quantum cosmology.

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