What is the singular state of matter? quantum theory of gravity

According to this model, our world appeared about thirteen billion years ago as a result of the Big Bang of a certain superdense state of our Universe - a singularity. What preceded this event, how the singularity arose, where its mass came from, was completely incomprehensible - there is no theory of such a state. The further fate of the expanding Universe was also unclear: whether its expansion would continue forever, or whether it would be replaced by contraction until the next singularity.

The theory of cosmogenesis, developed recently by Russian researchers and first reported in May last year at an international conference at the Physical Institute. P. N. Lebedev of the Russian Academy of Sciences, shows that the singularity is a natural product of the evolution of a massive star that has turned into a black hole. A single black hole can give rise to numerous "offspring" in subsequent universes. And this process goes on continuously, branching, like the Tree of the World from Scandinavian legends. The many-sheeted hyperuniverse is infinite both in space and in time.

World Tree

COSMOLOGICAL MODEL

"In the beginning was the Word, and the Word was with God, and the Word was God." Briefly and clearly, but incomprehensibly. Fortunately, in addition to theology, there is also cosmology - the science of the universe. The cosmological picture of the world is, by definition, objective, non-religious in nature and therefore interesting to any person who appreciates the facts.

Until the beginning of the 20th century, cosmology remained a speculative discipline: it was not yet physics based on empirical experience and independent experiment, but natural philosophy based on the views, including religious ones, of the scientist himself. It was only with the advent of the modern theory of gravity, known as general relativity, that cosmology received a theoretical basis. Numerous discoveries in both astronomy and physics gave our heroine observational justification. Numerical experiment became an important aid for theory and observations. Note that, contrary to some assertions, there are no contradictions between general relativity, on the one hand, and observations and experiment, on the other. After all, on the basis of general relativity, they not only calculated the deflection of a light beam in the gravitational field of the Sun, which, frankly, is not fundamentally important for the national economy, but also calculate the orbits of planets and spacecraft, as well as the technical parameters of accelerators, including the Large Hadron Collider. Of course, this does not mean that general relativity is the ultimate truth. However, the search for a new theory of gravity goes in the direction of generalizing the existing one, and not abandoning it.

The definition we have given to cosmology - the science of the universe - is quite broad. As Arthur Eddington rightly remarked, all science is cosmology. Therefore, it is logical to explain with specific examples which tasks and problems are related to cosmological ones.

Building a model of the Universe is, of course, a cosmological task. It is now generally accepted that the universe is homogeneous and isotropic on large scales (greater than 100 megaparsecs). This model is called the Friedman model after its discoverer Alexander Fridman. On a small scale, the matter of the Universe is subject to the process of gravitational twisting due to gravitational instability - the force of attraction acting between bodies tends to bring them together. Ultimately, this leads to the emergence of the structure of the Universe - galaxies, their clusters, etc.

The Universe is non-stationary: it is expanding, and with acceleration (inflationary) due to the presence of dark energy in it - a kind of matter, the pressure of which is negative. The cosmological model is described by several parameters. These are the amount of dark matter, baryons, neutrinos and the number of their varieties, the values ​​of the Hubble constant and spatial curvature, the shape of the spectrum of initial density perturbations (a set of perturbations of different sizes), the amplitude of primary gravitational waves, the redshift and the optical depth of the secondary ionization of hydrogen, as well as others, less important parameters. Each of them deserves a separate discussion, the definition of each is a whole study, and all this relates to the tasks of cosmology. The cosmological parameter is not only a number, but also the physical processes that govern the world in which we live.

EARLY UNIVERSE

Perhaps an even more important cosmological problem is the question of the origin of the Universe, of what was in the Beginning.

For centuries, scientists have imagined the universe to be eternal, infinite, and static. The fact that this is not so was discovered in the 20s of the 20th century: the non-stationarity of the solutions of the equations of gravity was theoretically revealed by the already mentioned A. A. Fridman, and the observations (with the correct interpretation) were made almost simultaneously by several astronomers. It is methodically important to emphasize that space itself does not expand anywhere: we are talking about volumetric expansion of a large-scale flow of matter, spreading in all directions. Speaking of the Beginning of the Universe, we have in mind the question of the origin of this cosmological flow, which was given an initial impetus for expansion and given a certain symmetry.

The idea of ​​an eternal and infinite Universe, through the works of many researchers of the 20th century, sometimes contrary to their personal convictions, has lost ground. The discovery of the global expansion of the Universe meant not only that the Universe is non-static, but also that its age is finite. After much debate about what it is, and many important observational discoveries, the number has been established: 13.7 billion years. This is very little. After all, two billion years ago, something was already crawling on the Earth. In addition, the radius of the visible Universe is too large (a few gigaparsecs) for such a small age. Apparently, the huge size of the Universe is associated with another - inflationary - stage of expansion that occurred in the past and was replaced by a stage of slow expansion, controlled by the gravity of radiation and dark matter. Later, another stage of the accelerated expansion of the Universe begins, which is already controlled by dark energy. The GR equations show that with accelerated expansion, the size of the cosmological flow increases very quickly and turns out to be larger than the light horizon.

The age of the Universe is known with an accuracy of 100 million years. But, despite such a "low" accuracy, we (mankind) can confidently trace the processes that proceeded extremely close in time to the "moment of the birth of the Universe" - about 10^-35 seconds. This is possible because the dynamics of physical processes occurring at cosmological distances is connected only with gravity and in this sense is absolutely clear. With the theory (GR) available, we can extrapolate the Cosmological Standard Model in the modern Universe into the past and "see" what it looked like in its youth. And it looked simple: the early Universe was strictly determined and was a laminar flow of matter expanding from superhigh densities.

SINGULARITY

Thirteen billion years is about 10^17 seconds. And the "natural" beginning of the cosmological flow with such an extrapolation coincides with the Planck time - 10^-43 seconds. Total 43 + 17 = 60 orders. It makes no sense to talk about what happened before 10^-43 seconds, since, due to quantum effects, the Planck scale is the minimum interval for which the concept of continuity and extension is applicable. At this point, many researchers gave up. Like, it is impossible to go further, because we have no theory, we do not know quantum gravity, etc.

However, it cannot really be said that the universe was “born” right at this age. It is quite possible that the flow of matter "slipped through" the superdense state in a very short (Planckian) time, that is, something forced it to go through that short-term stage. And then there is no logical impasse with Planck's time and Planck's constant. You just need to understand what could precede the beginning of the cosmological expansion, for what reason and what "dragged" the gravitating matter through the state of superhigh density.

The answer to these questions, in our opinion, lies in the nature of gravity. Quantum effects play a secondary role here, modifying and modifying the concept of superdense matter within a short time interval. Of course, today we do not know all the properties of effective matter [this “matter” is called effective because it also includes parameters that describe possible deviations of gravity from general relativity. In this regard, we recall that modern science operates with separate physical concepts of matter and space-time (gravity). In extreme conditions near the singularity, such a division is conditional - hence the term "effective matter".] in extreme conditions. But, given the short period of this stage, we are able to describe the entire dynamic process, relying only on the known laws of conservation of energy and momentum and assuming that they always hold in the average metric space-time, no matter what the quantum "theory of everything" will be. created in the future.

COSMOGENESIS

In the history of cosmology, there have been several attempts to circumvent the singularity problem and replace it, for example, with the concept of the birth of the Universe as a whole. According to the hypothesis of birth from “nothing”, the world arose from a “point”, a singularity, a superdense area with very high symmetry and everything else that you can think of (metastability, instability, quantum sub-barrier transition to Friedmann symmetry, etc.). In this approach, the singularity problem was not solved, and the singularity was postulated in the form of an initial superdense vacuum-like state (see "Science and Life" No. 11, 12, 1996).

There have been other attempts to "get away" from the singularity, but their price has always been high. Instead, it was necessary to postulate obscure constructions of either superdense (sub-Planckian) states of matter, or “bounces” of the Friedmann flow from high density (change from compression to expansion), or other hypothetical recipes for the behavior of high-density matter.

Nobody likes the Singularity. The physical picture of the world assumes a changing, evolving, but constantly existing world. We propose to take a different look at the singularity and proceed from the fact that the highly compressed states that a dynamic gravitationally interacting system (in the simplest case, a star) enters and passes through under certain conditions are objective and natural for gravity. Singular regions as temporary bridges or chains connect more extended domains of our world. If this is so, then we need to understand what causes matter to fall into special singular states and how it gets out of them.

As already mentioned, the cosmological expansion begins with a cosmological singularity - mentally turning back time, we inevitably come to a moment when the density of the Universe turns into infinity. We can consider this proposition as an obvious fact based on QSM and GR. Taking it for granted, let's ask ourselves a simple follow-up question: how does a singularity arise, how does gravitating matter get into a supercompressed state? The answer is surprisingly simple: this is caused by the process of gravitational contraction of a massive system (a star or other compact astrophysical system) at the end of its evolution. As a result of the collapse, a black hole is formed and, as a result, its singularity. That is, the collapse ends with a singularity, and cosmology begins with a singularity. We argue that this is a chain of a single continuous process.

The question of the origin of the Universe, after several trials, attempts to formulate it and various interpretations, acquired a solid scientific basis in the 21st century in the form of QSM and its unambiguous extrapolation into the past along the lines of general relativity. Starting in considering this problem from the only Universe known to us, we should not forget about the general physical principle associated with the name of Nicolaus Copernicus. It was once believed that the Earth is the center of the universe, then it was associated with the Sun, later it turned out that our Galaxy is not the only one, but only one among very many (only visible galaxies are almost a trillion). It is logical to assume that there are a lot of universes. The fact that we do not yet know anything about others is due to the large size of our Universe - its scale obviously exceeds the horizon of visibility.

Size (scale) of the Universe is the size of the causally connected area, stretched during its expansion. The size of visibility is the distance that light has "traversed" during the existence of the Universe, it can be obtained by multiplying the speed of light and the age of the Universe. The fact that the Universe is isotropic and homogeneous on large scales means that the initial conditions in regions of the Universe remote from each other were similar.

We have already mentioned that this large scale is due to the presence of an inflationary stage of expansion. In the pre-inflationary period of the Big Bang, the expanding flow could be very small and not at all have the features of the Friedman model. But how to turn a small flow into a large one is not a problem of cosmogenesis, but a technical question of the existence of a final intermediate stage of inflation that can expand the flow, just as the surface of an inflated balloon increases. The main problem of cosmogenesis is not in the size of the cosmological flow, but in its appearance. Just as there is a well-known method for the formation of contracting matter flows (gravitational collapse), there must be a fairly general and simple physical mechanism for gravitational generation ("ignition") of expanding matter flows.

INTEGRABLE SINGULARITIES

So, how to penetrate "beyond" the singularity? And what's behind it?

It is convenient to study the structure of space-time by mentally launching free trial particles into it and observing how they move. According to our calculations, geodesic trajectories [the shortest distances in space of a certain structure. In Euclidean space these are straight lines, in Riemannian space they are arcs of a circle, etc.] of test particles propagate freely in time through singular regions of a certain class, which we called integrable singularities. (The density or pressure diverges in the singularity, but the volume integral of these quantities is finite: the mass of the integrable singularity tends to zero, since it occupies an insignificant volume.) Having passed the black hole, geodesic trajectories find themselves in the space-time domain (from the French domaine - area , possession) of a white hole that is expanding with all the signs of a cosmological flow. This space-time geometry is unified, and it is logical to define it as a black and white hole. The cosmological domain of the white hole is located in the absolute future in relation to the parent domain of the black hole, that is, the white hole is a natural continuation and product of the black hole.

This new concept was born quite recently. The creators announced its appearance in May 2011 at a scientific conference dedicated to the memory of A. D. Sakharov, held at the flagship of Russian physics - the Physical Institute. P. N. Lebedev of the Russian Academy of Sciences (FIAN).

How is this possible and why was such a mechanism of cosmogenesis not considered earlier? Let's start by answering the first question.

Finding a black hole is not difficult, there are many of them around - several percent of the entire mass of the stars of the Universe is concentrated in black holes. The mechanism of their occurrence is also well known. You can often hear that we live in a graveyard of black holes. But can this be called a graveyard (the end of evolution), or do other zones (domains) of our complex world, other universes begin beyond the event horizons of black holes?

We know that inside a black hole there is a special singular region, into which all the matter caught by it “falls down”, and where the gravitational potential rushes to infinity. However, nature does not tolerate not only emptiness, but also infinity or divergence (although no one has canceled large numbers). We were able to “pass through” the singularity region by requiring that the gravitational (metric) potentials in it, and hence the tidal forces, remain finite.

The divergence of metric potentials can be eliminated by smoothing the singularity with the help of effective matter, which weakens it, but does not eliminate it completely. (Such an integrable singularity can be compared to the behavior of dark matter as it approaches the center of a galaxy. Its density tends to infinity, but the mass contained inside a decreasing radius tends to zero due to the fact that the volume inside this radius decreases faster than the density increases. Such an analogy is not absolute: the galactic cusp, a region of divergent density, is a spatial structure, and a black hole singularity occurs as an event in time.) So while density and pressure diverge, the tidal forces acting on a particle are finite because they depend on the total mass. This allows test particles to freely pass through the singularity: they propagate in continuous space-time, and information about the distribution of density or pressure is not required to describe their motion. And with the help of test particles, you can describe the geometry - build reference systems and measure the spatial and temporal intervals between points and events.

BLACK AND WHITE HOLES

So, you can go through the singularity. And consequently, it is possible to “see” what is behind it, through what kind of space-time our test particles continue to propagate. And they fall into the region of the white hole. The equations show that a kind of oscillation occurs: the flow of energy from the contracting region of the black hole continues into the expanding region of the white hole. The momentum cannot be hidden: the collapse is inverted into an anti-collapse with the total momentum preserved. And this is already a different universe, since a white hole filled with matter has all the properties of a cosmological flow. This means that our Universe, perhaps, is the product of some other world.

The picture following from the received solutions of the equations of gravitation, develops such. The parent star collapses in the parent universe and forms a black hole. As a result of the collapse, destructive tidal gravitational forces arise around the star, which deform and break the vacuum, giving rise to matter in the previously empty space. This matter from the singular region of the black-and-white hole falls into another universe, expanding under the action of a gravitational impulse received during the collapse of the parent star.

The total mass of particles in such a new universe can be arbitrarily large. It can significantly exceed the mass of the parent star. In this case, the mass of the formed (parent) black hole, measured by an observer located in the outer space of the parent universe, is finite and close to the mass of the collapsed star. There is no paradox here, since the mass difference is compensated by the gravitational binding energy, which has a negative sign. We can say that the new universe is in the absolute future in relation to the parent (old) universe. In other words, you can go there, but you can't go back.

ASTROGENIC COSMOLOGY, OR A MULTIPLE UNIVERSE

Such a complex world resembles the Tree of Life (a family tree, if you like). If in the process of evolution black holes appear in the Universe, then through them particles can get into other branches (domains) of the universe - and so on along the temporary garlands of black and white holes. If black holes are not formed for one reason or another (for example, stars are not born), a dead end arises - the genesis (creation) of new universes in this direction is interrupted. But under favorable circumstances, the flow of "life" can resume and blossom even from one black hole - for this it is necessary to create conditions for the production of new generations of black holes in subsequent universes.

How can “favorable circumstances” arise and what do they depend on? In our model, this is due to the properties of effective matter, which is born under the action of extreme gravity near the singularities of black and white holes. In fact, we are talking about nonlinear phase transitions in a quantum-gravitational material system, which have the character of fluctuations and, therefore, are subject to random (bifurcation) changes. Following contrary to Einstein's catchphrase, we can say that "God throws the dice", and then these dice (initial conditions) can form into deterministic domains of new universes, or they can remain undeveloped "embryos" of cosmogenesis. Here, as in life, there are laws of natural selection. But this is the subject of further research and future work.

HOW TO AVOID THE SINGULARITY

At one time, the concept of an oscillating, or cyclic, Universe was proposed, based on the “bounce” hypothesis. According to her, the Universe exists in the form of an infinite number of cycles. Its expansion is replaced by contraction almost to a singularity, followed by expansion again, and a number of such cycles go into the past and the future. Not a very clear concept, because, firstly, there is no observational evidence that one day the expansion of our world will be replaced by contraction, and secondly, the physical mechanism that causes the Universe to make such oscillatory movements is not clear.

Another approach to the origin of the world is associated with the hypothesis of a self-healing Universe, proposed for many years by the Russian scientist A.D. Linde, who has been living in the USA. According to this hypothesis, the world can be represented as a boiling cauldron. Globally, the Universe is a hot soup with a high energy density. Bubbles appear in it, which either collapse or expand, and, under certain initial conditions, for a long time. It is assumed that the characteristics (any one you can think of, including a set of fundamental constants) of bubbles of emerging worlds have some spectrum and a wide range. Many questions arise here: where did such a “broth” come from, who brewed it and what maintains it, how often the initial conditions are realized, leading to the appearance of universes of our type, etc.

HOW INTEGRABLE SINGULARITIES CAN FORM

As we approach the singularity, the growing tidal forces act on the vacuum of physical fields, deform and break it. There is, as they say, the polarization of the vacuum and the birth of particles of matter from the vacuum - its breakdown.

Such a reaction of the physical vacuum to the external intense action of a rapidly changing gravitational field is well known. This is, in fact, the effect of quantum gravity - gravitational tensions are transformed into material fields, there is a redistribution of physical degrees of freedom. Today, such effects can be calculated in the weak field approximation (the so-called semiclassical limit). In our case, we are talking about powerful nonlinear quantum-gravitational processes, where it is necessary to take into account the inverse gravitational influence of the born effective matter on the evolution of the average metric that determines the properties of the four-dimensional space-time (when quantum effects in gravity become strong, the metric becomes “trembling” and we can only talk about it in the middle sense).

This direction, of course, requires further research. However, it can already be assumed that, according to Le Chatelier's principle, the reverse influence will lead to such a rearrangement of the metric space that the growth of tidal forces, which causes the unlimited birth of effective matter, will be stopped and, consequently, the metric potentials will cease to diverge and remain finite and continuous.

Doctor of Physical and Mathematical Sciences Vladimir Lukash,
Candidate of Physical and Mathematical Sciences Elena Mikheeva,
Candidate of Physical and Mathematical Sciences Vladimir Strokov (Astrospace Center of FIAN),

The universe we live in is described by the Cosmological Standard Model. According to this model, our world appeared about thirteen billion years ago as a result of the Big Bang of a certain superdense state of our Universe - a singularity. What preceded this event, how the singularity arose, where its mass came from, was completely incomprehensible - there is no theory of such a state. The further fate of the expanding Universe was also unclear: whether its expansion would continue forever, or whether it would be replaced by contraction until the next singularity.

The theory of cosmogenesis, developed recently by Russian researchers and first reported in May last year at an international conference at the Physical Institute. P. N. Lebedev of the Russian Academy of Sciences, shows that the singularity is a natural product of the evolution of a massive star that has turned into a black hole. A single black hole can give rise to numerous "offspring" in subsequent universes. And this process goes on continuously, branching, like the Tree of the World from Scandinavian legends. The many-sheeted hyperuniverse is infinite both in space and in time.


World Tree

COSMOLOGICAL MODEL

"In the beginning was the Word, and the Word was with God, and the Word was God." Briefly and clearly, but incomprehensibly. Fortunately, in addition to theology, there is also cosmology - the science of the universe. The cosmological picture of the world is, by definition, objective, non-religious in nature and therefore interesting to any person who appreciates the facts.

Until the beginning of the 20th century, cosmology remained a speculative discipline: it was not yet physics based on empirical experience and independent experiment, but natural philosophy based on the views, including religious ones, of the scientist himself. It was only with the advent of the modern theory of gravity, known as general relativity, that cosmology received a theoretical basis. Numerous discoveries in both astronomy and physics gave our heroine observational justification. Numerical experiment became an important aid for theory and observations. Note that, contrary to some assertions, there are no contradictions between general relativity, on the one hand, and observations and experiment, on the other. After all, on the basis of general relativity, they not only calculated the deflection of a light beam in the gravitational field of the Sun, which, frankly, is not fundamentally important for the national economy, but also calculate the orbits of planets and spacecraft, as well as the technical parameters of accelerators, including the Large Hadron Collider. Of course, this does not mean that general relativity is the ultimate truth. However, the search for a new theory of gravity goes in the direction of generalizing the existing one, and not abandoning it.

The definition we have given to cosmology - the science of the universe - is quite broad. As Arthur Eddington rightly remarked, all science is cosmology. Therefore, it is logical to explain with specific examples which tasks and problems are related to cosmological ones.

Building a model of the Universe is, of course, a cosmological task. It is now generally accepted that the universe is homogeneous and isotropic on large scales (greater than 100 megaparsecs). This model is called the Friedman model after its discoverer Alexander Fridman. On a small scale, the matter of the Universe is subject to the process of gravitational twisting due to gravitational instability - the force of attraction acting between bodies tends to bring them together. Ultimately, this leads to the emergence of the structure of the Universe - galaxies, their clusters, etc.

The Universe is non-stationary: it is expanding, and with acceleration (inflationary) due to the presence of dark energy in it - a kind of matter, the pressure of which is negative. The cosmological model is described by several parameters. These are the amount of dark matter, baryons, neutrinos and the number of their varieties, the values ​​of the Hubble constant and spatial curvature, the shape of the spectrum of initial density perturbations (a set of perturbations of different sizes), the amplitude of primary gravitational waves, the redshift and the optical depth of the secondary ionization of hydrogen, as well as others, less important parameters. Each of them deserves a separate discussion, the definition of each is a whole study, and all this relates to the tasks of cosmology. The cosmological parameter is not only a number, but also the physical processes that govern the world in which we live.

EARLY UNIVERSE

Perhaps an even more important cosmological problem is the question of the origin of the Universe, of what was in the Beginning.

For centuries, scientists have imagined the universe to be eternal, infinite, and static. The fact that this is not so was discovered in the 20s of the 20th century: the non-stationarity of the solutions of the equations of gravity was theoretically revealed by the already mentioned A. A. Fridman, and the observations (with the correct interpretation) were made almost simultaneously by several astronomers. It is methodically important to emphasize that space itself does not expand anywhere: we are talking about volumetric expansion of a large-scale flow of matter, spreading in all directions. Speaking of the Beginning of the Universe, we have in mind the question of the origin of this cosmological flow, which was given an initial impetus for expansion and given a certain symmetry.

The idea of ​​an eternal and infinite Universe, through the works of many researchers of the 20th century, sometimes contrary to their personal convictions, has lost ground. The discovery of the global expansion of the Universe meant not only that the Universe is non-static, but also that its age is finite. After much debate about what it is, and many important observational discoveries, the number has been established: 13.7 billion years. This is very little. After all, two billion years ago, something was already crawling on the Earth. In addition, the radius of the visible Universe is too large (a few gigaparsecs) for such a small age. Apparently, the huge size of the Universe is associated with another - inflationary - stage of expansion that occurred in the past and was replaced by a stage of slow expansion, controlled by the gravity of radiation and dark matter. Later, another stage of the accelerated expansion of the Universe begins, which is already controlled by dark energy. The GR equations show that with accelerated expansion, the size of the cosmological flow increases very quickly and turns out to be larger than the light horizon.

The age of the Universe is known with an accuracy of 100 million years. But, despite such a "low" accuracy, we (mankind) can confidently trace the processes that proceeded extremely close in time to the "moment of the birth of the Universe" - about 10^-35 seconds. This is possible because the dynamics of physical processes occurring at cosmological distances is connected only with gravity and in this sense is absolutely clear. With the theory (GR) available, we can extrapolate the Cosmological Standard Model in the modern Universe into the past and "see" what it looked like in its youth. And it looked simple: the early Universe was strictly determined and was a laminar flow of matter expanding from superhigh densities.

SINGULARITY

Thirteen billion years is about 10^17 seconds. And the "natural" beginning of the cosmological flow with such an extrapolation coincides with the Planck time - 10^-43 seconds. Total 43 + 17 = 60 orders. It makes no sense to talk about what happened before 10^-43 seconds, since, due to quantum effects, the Planck scale is the minimum interval for which the concept of continuity and extension is applicable. At this point, many researchers gave up. Like, it is impossible to go further, because we have no theory, we do not know quantum gravity, etc.

However, it cannot really be said that the universe was “born” right at this age. It is quite possible that the flow of matter "slipped through" the superdense state in a very short (Planckian) time, that is, something forced it to go through that short-term stage. And then there is no logical impasse with Planck's time and Planck's constant. You just need to understand what could precede the beginning of the cosmological expansion, for what reason and what "dragged" the gravitating matter through the state of superhigh density.

The answer to these questions, in our opinion, lies in the nature of gravity. Quantum effects play a secondary role here, modifying and modifying the concept of superdense matter within a short time interval. Of course, today we do not know all the properties of effective matter [this “matter” is called effective because it also includes parameters that describe possible deviations of gravity from general relativity. In this regard, we recall that modern science operates with separate physical concepts of matter and space-time (gravity). In extreme conditions near the singularity, such a division is conditional - hence the term "effective matter".] in extreme conditions. But, given the short period of this stage, we are able to describe the entire dynamic process, relying only on the known laws of conservation of energy and momentum and assuming that they always hold in the average metric space-time, no matter what the quantum "theory of everything" will be. created in the future.

COSMOGENESIS

In the history of cosmology, there have been several attempts to circumvent the singularity problem and replace it, for example, with the concept of the birth of the Universe as a whole. According to the hypothesis of birth from “nothing”, the world arose from a “point”, a singularity, a superdense area with very high symmetry and everything else that you can think of (metastability, instability, quantum sub-barrier transition to Friedmann symmetry, etc.). In this approach, the singularity problem was not solved, and the singularity was postulated in the form of an initial superdense vacuum-like state (see "Science and Life" No. 11, 12, 1996).

There have been other attempts to "get away" from the singularity, but their price has always been high. Instead, it was necessary to postulate obscure constructions of either superdense (sub-Planckian) states of matter, or “bounces” of the Friedmann flow from high density (change from compression to expansion), or other hypothetical recipes for the behavior of high-density matter.

Nobody likes the Singularity. The physical picture of the world assumes a changing, evolving, but constantly existing world. We propose to take a different look at the singularity and proceed from the fact that the highly compressed states that a dynamic gravitationally interacting system (in the simplest case, a star) enters and passes through under certain conditions are objective and natural for gravity. Singular regions as temporary bridges or chains connect more extended domains of our world. If this is so, then we need to understand what causes matter to fall into special singular states and how it gets out of them.

As already mentioned, the cosmological expansion begins with a cosmological singularity - mentally turning back time, we inevitably come to a moment when the density of the Universe turns into infinity. We can consider this proposition as an obvious fact based on QSM and GR. Taking it for granted, let's ask ourselves a simple follow-up question: how does a singularity arise, how does gravitating matter get into a supercompressed state? The answer is surprisingly simple: this is caused by the process of gravitational contraction of a massive system (a star or other compact astrophysical system) at the end of its evolution. As a result of the collapse, a black hole is formed and, as a result, its singularity. That is, the collapse ends with a singularity, and cosmology begins with a singularity. We argue that this is a chain of a single continuous process.

The question of the origin of the Universe, after several trials, attempts to formulate it and various interpretations, acquired a solid scientific basis in the 21st century in the form of QSM and its unambiguous extrapolation into the past along the lines of general relativity. Starting in considering this problem from the only Universe known to us, we should not forget about the general physical principle associated with the name of Nicolaus Copernicus. It was once believed that the Earth is the center of the universe, then it was associated with the Sun, later it turned out that our Galaxy is not the only one, but only one among very many (only visible galaxies are almost a trillion). It is logical to assume that there are a lot of universes. The fact that we do not yet know anything about others is due to the large size of our Universe - its scale obviously exceeds the horizon of visibility.

Size (scale) of the Universe is the size of the causally connected area, stretched during its expansion. The size of visibility is the distance that light has "traversed" during the existence of the Universe, it can be obtained by multiplying the speed of light and the age of the Universe. The fact that the Universe is isotropic and homogeneous on large scales means that the initial conditions in regions of the Universe remote from each other were similar.

We have already mentioned that this large scale is due to the presence of an inflationary stage of expansion. In the pre-inflationary period of the Big Bang, the expanding flow could be very small and not at all have the features of the Friedman model. But how to turn a small flow into a large one is not a problem of cosmogenesis, but a technical question of the existence of a final intermediate stage of inflation that can expand the flow, just as the surface of an inflated balloon increases. The main problem of cosmogenesis is not in the size of the cosmological flow, but in its appearance. Just as there is a well-known method for the formation of contracting matter flows (gravitational collapse), there must be a fairly general and simple physical mechanism for gravitational generation ("ignition") of expanding matter flows.

INTEGRABLE SINGULARITIES

So, how to penetrate "beyond" the singularity? And what's behind it?

It is convenient to study the structure of space-time by mentally launching free trial particles into it and observing how they move. According to our calculations, geodesic trajectories [the shortest distances in space of a certain structure. In Euclidean space these are straight lines, in Riemannian space they are arcs of a circle, etc.] of test particles propagate freely in time through singular regions of a certain class, which we called integrable singularities. (The density or pressure diverges in the singularity, but the volume integral of these quantities is finite: the mass of the integrable singularity tends to zero, since it occupies an insignificant volume.) Having passed the black hole, geodesic trajectories find themselves in the space-time domain (from the French domaine - area , possession) of a white hole that is expanding with all the signs of a cosmological flow. This space-time geometry is unified, and it is logical to define it as a black and white hole. The cosmological domain of the white hole is located in the absolute future in relation to the parent domain of the black hole, that is, the white hole is a natural continuation and product of the black hole.

This new concept was born quite recently. The creators announced its appearance in May 2011 at a scientific conference dedicated to the memory of A. D. Sakharov, held at the flagship of Russian physics - the Physical Institute. P. N. Lebedev of the Russian Academy of Sciences (FIAN).

How is this possible and why was such a mechanism of cosmogenesis not considered earlier? Let's start by answering the first question.

Finding a black hole is not difficult, there are many of them around - several percent of the entire mass of the stars of the Universe is concentrated in black holes. The mechanism of their occurrence is also well known. You can often hear that we live in a graveyard of black holes. But can this be called a graveyard (the end of evolution), or do other zones (domains) of our complex world, other universes begin beyond the event horizons of black holes?

We know that inside a black hole there is a special singular region, into which all the matter caught by it “falls down”, and where the gravitational potential rushes to infinity. However, nature does not tolerate not only emptiness, but also infinity or divergence (although no one has canceled large numbers). We were able to “pass through” the singularity region by requiring that the gravitational (metric) potentials in it, and hence the tidal forces, remain finite.

The divergence of metric potentials can be eliminated by smoothing the singularity with the help of effective matter, which weakens it, but does not eliminate it completely. (Such an integrable singularity can be compared to the behavior of dark matter as it approaches the center of a galaxy. Its density tends to infinity, but the mass contained inside a decreasing radius tends to zero due to the fact that the volume inside this radius decreases faster than the density increases. Such an analogy is not absolute: the galactic cusp, a region of divergent density, is a spatial structure, and a black hole singularity occurs as an event in time.) So while density and pressure diverge, the tidal forces acting on a particle are finite because they depend on the total mass. This allows test particles to freely pass through the singularity: they propagate in continuous space-time, and information about the distribution of density or pressure is not required to describe their motion. And with the help of test particles, you can describe the geometry - build reference systems and measure the spatial and temporal intervals between points and events.

BLACK AND WHITE HOLES

So, you can go through the singularity. And consequently, it is possible to “see” what is behind it, through what kind of space-time our test particles continue to propagate. And they fall into the region of the white hole. The equations show that a kind of oscillation occurs: the flow of energy from the contracting region of the black hole continues into the expanding region of the white hole. The momentum cannot be hidden: the collapse is inverted into an anti-collapse with the total momentum preserved. And this is already a different universe, since a white hole filled with matter has all the properties of a cosmological flow. This means that our Universe, perhaps, is the product of some other world.

The picture following from the received solutions of the equations of gravitation, develops such. The parent star collapses in the parent universe and forms a black hole. As a result of the collapse, destructive tidal gravitational forces arise around the star, which deform and break the vacuum, giving rise to matter in the previously empty space. This matter from the singular region of the black-and-white hole falls into another universe, expanding under the action of a gravitational impulse received during the collapse of the parent star.

The total mass of particles in such a new universe can be arbitrarily large. It can significantly exceed the mass of the parent star. In this case, the mass of the formed (parent) black hole, measured by an observer located in the outer space of the parent universe, is finite and close to the mass of the collapsed star. There is no paradox here, since the mass difference is compensated by the gravitational binding energy, which has a negative sign. We can say that the new universe is in the absolute future in relation to the parent (old) universe. In other words, you can go there, but you can't go back.

ASTROGENIC COSMOLOGY, OR A MULTIPLE UNIVERSE

Such a complex world resembles the Tree of Life (a family tree, if you like). If in the process of evolution black holes appear in the Universe, then through them particles can get into other branches (domains) of the universe - and so on along the temporary garlands of black and white holes. If black holes are not formed for one reason or another (for example, stars are not born), a dead end arises - the genesis (creation) of new universes in this direction is interrupted. But under favorable circumstances, the flow of "life" can resume and blossom even from one black hole - for this it is necessary to create conditions for the production of new generations of black holes in subsequent universes.

How can “favorable circumstances” arise and what do they depend on? In our model, this is due to the properties of effective matter, which is born under the action of extreme gravity near the singularities of black and white holes. In fact, we are talking about nonlinear phase transitions in a quantum-gravitational material system, which have the character of fluctuations and, therefore, are subject to random (bifurcation) changes. Following contrary to Einstein's catchphrase, we can say that "God throws the dice", and then these dice (initial conditions) can form into deterministic domains of new universes, or they can remain undeveloped "embryos" of cosmogenesis. Here, as in life, there are laws of natural selection. But this is the subject of further research and future work.

HOW TO AVOID THE SINGULARITY

At one time, the concept of an oscillating, or cyclic, Universe was proposed, based on the “bounce” hypothesis. According to her, the Universe exists in the form of an infinite number of cycles. Its expansion is replaced by contraction almost to a singularity, followed by expansion again, and a number of such cycles go into the past and the future. Not a very clear concept, because, firstly, there is no observational evidence that one day the expansion of our world will be replaced by contraction, and secondly, the physical mechanism that causes the Universe to make such oscillatory movements is not clear.

Another approach to the origin of the world is associated with the hypothesis of a self-healing Universe, proposed for many years by the Russian scientist A.D. Linde, who has been living in the USA. According to this hypothesis, the world can be represented as a boiling cauldron. Globally, the Universe is a hot soup with a high energy density. Bubbles appear in it, which either collapse or expand, and, under certain initial conditions, for a long time. It is assumed that the characteristics (any one you can think of, including a set of fundamental constants) of bubbles of emerging worlds have some spectrum and a wide range. Many questions arise here: where did such a “broth” come from, who brewed it and what maintains it, how often the initial conditions are realized, leading to the appearance of universes of our type, etc.

HOW INTEGRABLE SINGULARITIES CAN FORM

As we approach the singularity, the growing tidal forces act on the vacuum of physical fields, deform and break it. There is, as they say, the polarization of the vacuum and the birth of particles of matter from the vacuum - its breakdown.

Such a reaction of the physical vacuum to the external intense action of a rapidly changing gravitational field is well known. This is, in fact, the effect of quantum gravity - gravitational tensions are transformed into material fields, there is a redistribution of physical degrees of freedom. Today, such effects can be calculated in the weak field approximation (the so-called semiclassical limit). In our case, we are talking about powerful nonlinear quantum-gravitational processes, where it is necessary to take into account the inverse gravitational influence of the born effective matter on the evolution of the average metric that determines the properties of the four-dimensional space-time (when quantum effects in gravity become strong, the metric becomes “trembling” and we can only talk about it in the middle sense).

This direction, of course, requires further research. However, it can already be assumed that, according to Le Chatelier's principle, the reverse influence will lead to such a rearrangement of the metric space that the growth of tidal forces, which causes the unlimited birth of effective matter, will be stopped and, consequently, the metric potentials will cease to diverge and remain finite and continuous.

Doctor of Physical and Mathematical Sciences Vladimir Lukash,
Candidate of Physical and Mathematical Sciences Elena Mikheeva,
Candidate of Physical and Mathematical Sciences Vladimir Strokov (Astrospace Center of FIAN),

Everyone who came across the term "singularity" sought to realize what it is? If we make a literal translation from Latin, it turns out that this is a singularity of some event, creature, phenomenon. The concept of singularity (feature) is common in many fields of science and technology, and has a certain specificity. Depending on this, the singularity can be:

  • mathematical;
  • gravity;
  • cosmological;
  • technological;
  • biological.

But if you look more philosophically, then the singularity is the whole universe in a tiny point. And this is not only the entire substance of the Universe, but also our life, with its awareness, significance and feelings.

Cosmological singularity

Otherwise, this is the state that the Universe had at the very first moment of the Big Bang. It is characterized by the presence of infinite values ​​of the density and temperature of the substance. This state, which has become an example of a gravitational singularity, was predicted by Einstein in the provisions of the general theory of relativity. It is incredibly difficult to imagine that the Sun can be compressed to the size of an atomic nucleus, but it is even more difficult to imagine that the entire Universe was compressed to a point that was much smaller than this nucleus. Nonetheless, The universe arose from such an object, called a singularity. This version of events is mathematically calculated and is the main theory of the emergence of the surrounding world. But there are certain difficulties not explained by this theory.

  1. No one knows exactly where the point from the core of which our Universe was born was located.
  2. It is not clear how this feature "gave birth" to endless amounts of energy and matter.
  3. The heterogeneity of the universe is also not entirely clear. According to all the canons, it should have become homogeneous, but this uniformity was not even in the primary gas.
  4. The physical laws known to us, which help to describe the world familiar to us, do not work in the case of a singularity. It follows from this that it is possible to describe only those events that happened after the Big Bang, but not the explosion itself and not the threshold of it.

The very fact of the emergence of a cosmological singularity, if we continue back in time the solution that describes the dynamics of the expansion of the Universe, was proved by S. Hawking in 1967. But he noted that the singularity is knocked out of the laws of physics. It is impossible for density and temperature to have infinite values ​​at the same time. Infinite density implies that the measure of chaos (entropy) tends to zero, and this does not fit with infinite temperature. The cosmological singularity (and the very fact of its existence) has become one of the main problems of cosmology. This follows from the fact that all the available information about what happened after the Big Bang does not provide absolutely any information about the phenomena that preceded this grandiose event. But the scientific world is constantly trying to solve this problem, and these attempts are taking place in different directions:

  • It is assumed that it will be possible to describe the dynamics of the field, where there are no given singularities, with the help of quantum gravity, the theory of which has not yet been built;
  • It is believed that if quantum effects in non-gravitational fields are taken into account, it is possible to violate the condition of energy dominance, namely, Hawking emphasized it;
  • There are other theories of gravity that do not appeal to the singularity. In them, the substance, compressed to the limit, with the help of gravitational forces, experiences not attraction, but repulsion.

Gravitational Singularity

If we speak in the dry language of physical terms, then this is a point located in space-time, through which there is no way to evenly lay a geodesic line. Often, the gravitational singularity makes the quantities that describe the gravitational field infinite or indefinite. These quantities include, for example, the energy density or the scalar curvature. implies that singularities must occur during the formation of a black hole. If they are below the event horizon, then they cannot be observed. In the case of the Big Bang, there is a bare singularity - its observation is quite possible, unless, of course, you are nearby. Unfortunately, it is impossible to see it directly, therefore, based on the level of development of modern physics, it is only a theoretical object. When the provisions of quantum gravity are developed, it will be possible to describe the space-time in the vicinity of these objects.

Every black hole has two main features - an event horizon and a singularity, which is the center of this hole. There is a distortion here, as well as a gap in space-time. In fact, the laws of physics lose their logic here. There are theories that at such points it is quite possible to make a transition to other worlds. A mathematical model has been developed - the "Einstein-Rosen bridge", confirming this option. This can be done by jumping through the singularity. It is here that the layers of the Universe intersect, forming a kind of subspace transition. It is a combination of two holes - black and white. This is a kind of time machine, and the very fact of the transition does not conflict with the principle of causality. Jumping through the singularity of a spinning black hole will make time travel possible in any direction. Since the black hole is surrounded by an event horizon, the singularity cannot be seen in the naked state. But still, models are being created that allow this to be done with varying degrees of realism.

If you spin a black hole up to a certain speed, the event horizon can separate. However, there are some difficulties here. To spin a black hole, you need to pour additional mass into it, which is not very realistic due to the presence of a clear limit, beyond which the rotation of the hole is impossible. But it is usually assumed that the mass is added to an already very rapidly rotating hole. And if we assume that the rotation has just begun? This option allows you to spin the black hole to a state where its singularity becomes open. It is likely that black holes are traveling through the universe, flaunting a bare singularity.

Singularity in mathematics

The mathematical concept of a given singularity is a certain point at which a mathematical function tends to infinity. Either the function has other irregularities of behavior (in particular, a critical point).

Technological Singularity

This concept refers mainly to the field of futurology, a doctrine that tries to predict the future. In this case, some existing trends in technology, economics, social phenomena are taken as a basis, and then they are extrapolated. It is believed that a moment will soon come when progress in science and technology will become beyond the understanding of human mind. This will probably become real after the possibility of creating artificial intelligence appears and the production of machines that reproduce themselves will be adjusted. The integration of a person with computers or a sharp change in the functionality of the human brain with the use of biotechnology will lead to the same result. This will become the technological singularity that some scientists predict in the near future. V. Widge believes that this will happen already in 2030, and R. Kurzweil postpones the revolution to the year 2045.

Singularity in biology

In biology, this concept is not often used. It is usually used as some generalization in the evolutionary process.

Conclusions and meaning

If the mathematical, technical and biological singularities have quite tangible parameters, then the situation is more complicated with the features of other options. It is difficult to operate with concepts that cannot be “felt” and evaluated. Mathematical calculations are a reliable thing, but only if the objects of research are material enough. The Singularity is different. It is not only not material, but has not yet been proven. Therefore, its application, even hypothetical, raises questions. If you can travel through it to get into other dimensions, then how to stay whole, passing through the gravitational Scylla and Charybdis? Probably, physicists will eventually find answers to all questions. And we will definitely recognize them and finally understand what a singularity is.

Hello, dear readers of the blog site. In conversations with people, we sometimes hear rare, incomprehensible to most, the word "singularity". To give significance to his own person, a person uses such words, but is not able to answer exactly what it means.

A literal translation from Latin is easy to find. Word singularis means special, unique, indicates uniqueness any event, being, phenomenon. It seems much easier, but here the incomprehensibility begins.

This concept is applicable in different spheres of human life, science, technology, philosophy. In each area it is explained specifically. To an inexperienced citizen it seems that we are talking about completely different things. There is no agreement even in understanding the meaning of the word.

Meaning of the word

As if on purpose, to confuse everything completely, scientific minds came up with several varieties of singularity. According to Wikipedia there are:

Singularity in plain language

Yes, it doesn't get any easier! You are confused and indignant: “What is this, cannot be explained in simple words?”. Let's try. Let's take for example the two interpretations mentioned above and explain all this as simply as possible (on the fingers):

  1. Gravity. Suppose there is an open hatch on the road. The road surface is space, the edge of the hatch is the event horizon (the boundary of space curvature, or more beautifully, the event horizon). You don't see everything that happens inside the pit, but the hole is formed by a singular object. You throw one stone into the hatch, you missed - the stone remained in our space. The next one - they hit, it flew over the boundary of the horizon and got into the zone of singularity (uncertainty);
  2. Cosmological. Imagine a small ball with unrealistically high temperature and density. At some point, it explodes with great force, forming a pile of fragments, particles and dust. Imagine everything that happened to the ball at the time of the explosion? This is called the singularity state.

Two common interpretations of this phenomenon are able to describe its main distinguishing features:

The correspondence of something to at least one of these signs indicates that you have a singularity in front of you.

On both grounds, the singularity illustrates most clearly black hole. It is believed that in its center the indicators of all physical characteristics are infinite, the laws of physics do not apply, and time flows according to rules unknown to us. Since it is impossible to predict the behavior of such an object, then forecasting loses all meaning.

Do you think that everything described far in time, space does not concern us? I'll show you that it's not.

Singularity in our lives

Most of the processes in society, economy, history, biology occur under conditions that imply a singularity point at a certain point in time. The development of this phenomenon is based on the law of hyperbole. Right now, processes that originated billions of years ago are approaching their denouement around us.

Humanity and the global product

The most understandable example is the increase in the population of the Earth and the increase in the world's reserves of the product. Relationships conditioned by certain conditions have been built for thousands of years. If we leave these dependencies unchanged now and continue them into the future, very soon we will come to the point of singularity.

The number of people on the planet and the world product have long been calculated by scientists. Two or three decades ago, it became clear that the number of people is increasing according to a quadratic hyperbole, and production - according to a simple one, that is, 2 times slower.

Forecasts showed that in the period from 2005 to 2020 the time of the singularity point will come. That is, today we are inside this phenomenon. Tell me, do you observe all-embracing abundance and wealth around you?

And again the technological singularity

The very point when the complexity of developing technologies will be inaccessible to human understanding is not far off. Presumably we will meet her from 2030 to 2045. The scenario of probable events is known to everyone from science fiction films.

Biological revolutions

Singularity in the biology of the Earth is a common thing. occurred with hyperbolic population growth up to a certain point. For example, dinosaurs were the masters of the planet. But after the revolutionary events, they almost disappeared. Unless crocodiles modestly occupy an insignificant niche.

When pundits analyzed the periodicity of the dates of the revolutions that took place in biology, and then added human unrest to this information, they noticed a clear connection with the singularity point in the region of 2010-2050.

Singularity in history

This phenomenon happened quite often. Remember the history of states and empires. For example, Ancient Rome at the beginning of its development developed according to the law of hyperbole.

Population growth caused the seizure of territories, determined some technical development. This continued until several plague epidemics, when up to a third of the population died. After that, humanity thought about the density of inhabitants in one place.

Attempts to restore the number of people allowed the empire to hold out for some more time. But still, the state fell apart for many reasons. So, the algorithm is a sharp increase, imbalance, small fluctuations, a change in the balance of resources and death.

Similar predestinations have been found in:

  1. science;
  2. demographics;
  3. economy;
  4. culture and other areas of human life.

conclusions

In the specified historical period, something incredibly important should happen, comparable to the release of living organisms on land, which will radically change the future.

Just do not say that everything is lost and we are destined for the fate of crocodiles. After all, Rome did not disappear without a trace. Yes, we are different from dinosaurs. We can think, make predictions, look for solutions and adapt the environment to our needs.

The main thing is to understand what is happening and change the conditions of the game in time to prevent irreversible processes.

Because the singularity is a point of infinite density, where all the laws of physics are violated, and the assumptions about the future are unknown. Everything in it loses its meaning. And comprehension of what is happening also does not matter.

Good luck to you! See you soon on the blog pages site

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We turn to the consideration of the most important issue of cosmology - the question of the beginning of cosmological expansion, the question of the singularity. The generalizing result of the previous sections is that the Universe is expanding isotropically and uniformly, starting at least from the moment when the equality was satisfied and with a high degree of probability was described by the Friedman model much earlier, starting from the epoch of the synthesis of chemical elements, i.e., i.e., from the first seconds of expansion and from densities of order

What was before? Did the Friedmannian Universe expand starting from the singularity (or at least from the "Planckian" moment, or was the early epoch essentially non-Friedmannian? Did the matter of the Universe pass through infinitely greater density (or at least through the "Planckian" density or did the contraction of the Universe at an even earlier epoch give way to expansion at a finite density [see, for example, Alfven (1971)]?

According to Friedman's model, the expansion of the Universe started from a singularity. Since the 1930s, for decades, cosmology has faced whether the presence of a singularity at the beginning of the expansion is a special property of the Friedman model (and other sufficiently symmetric models), will the singularity disappear when small peculiar velocities of matter or rotation are introduced?

The analogy with the mechanical problem of expanding the ball in Newton's theory supported such assumptions. Indeed, if we consider in Newton's theory the expansion of gravitating particles that simultaneously fly out along the radii from one point, then the expansion starts from a singularity. However, in the presence of small peculiar velocities, the points fly past each other near the Center, the particle density is always finite, and there are no singularities.

arise. Perhaps a similar situation is possible in the cosmological problem of Einstein's theory?

Here it is essential to note one circumstance, which is emphasized by Lifshitz and Khalatnikov (1963a, b). If there was no singularity in the past and the observed expansion of the Universe in the past was preceded by contraction, then the cosmological model describing the passage of matter through the density maximum and subsequent expansion must be stable, i.e., refer to the “general solution” in the terminology of Lifshitz and Khalatnikov. In other words, let there be some model without a singularity that describes the compression of matter to a finite density (without a singularity) and then its expansion, and let a small change in the model parameters in the compression phase lead to the appearance of a singularity. Then, obviously, this model cannot be implemented in reality, since there will always be random fluctuations leading the model away from a solution without a singularity. Thus, a solution without a singularity should not be exceptional, not degenerate, but general in order to claim to describe the real Universe.

However, if the extension starts from a singularity, then the requirement for the generality of the solution near the singularity is no longer necessary. Indeed, in this case, the initial conditions that determine the solution are given by some unknown processes at huge curvatures of space-time, i.e., under conditions that are not described by modern theory. Perhaps the processes in this case lead to special initial conditions for the expansion of the Universe, for example, to almost complete homogeneity and isotropy [see. Peebles (1971a)]. Therefore, even if it were possible to prove that the general solution does not contain a singularity, this would still not mean that the expansion did not start from a singularity.

So, cosmology faced two different questions: 1) is there a general (in the sense of "stable") cosmological solution without a singularity? and 2) was there a singularity in the past under the conditions that take place in the real universe?

In the late 1960s, a positive answer was given to the second question (Penrose, Hawking, Geroch). It has been proven that the expansion of the Universe began with a singularity (if, of course, GR is valid, but the change in GR itself, if it is due to a large curvature, requires "almost" a singularity), however, how exactly the expansion proceeded near the singularity - according to Friedman or more complex way, has not been established. After these works, the acuteness of the first question for cosmology disappeared. Indeed, the structure of the solution near the singularity does not necessarily correspond to the general solution, and the problem arises: in some way

establish the true nature of the beginning of the expansion of the real universe.

In 1972, after lengthy work, Belinsky, Lifshitz, and Khalatnikov constructed a general (stable) solution with a singularity, i.e., they gave a positive answer to the first question.

In terms of its properties, the general solution turned out to be qualitatively the same as the solution near the singularity for the “mixed” world model (see §§ 4 and 5 of Chap. 21).

In the further presentation, we will focus on the proof of the presence of a singularity in the past in the Universe and on physical processes near the singularity itself. It can be hoped that in the future an analysis of these processes and their consequences will make it possible to establish the true nature of the expansion of the Universe at the earliest stages, at densities substantially exceeding the nuclear one.