Dark matter: from initial conditions to the formation of the structure of the Universe. What is dark matter

In the articles of the series we examined the structure of the visible Universe. We talked about its structure and the particles that form this structure. About nucleons playing main role, since it is from them that all visible matter consists. About photons, electrons, neutrinos, and also about the supporting actors involved in the universal play that unfolds 14 billion years after the Big Bang. It would seem that there is nothing more to talk about. But that's not true. The fact is that the substance we see is only a small part of what our world consists of. Everything else is something we know almost nothing about. This mysterious “something” is called dark matter.

If the shadows of objects did not depend on the size of these latter,
and if they had their own arbitrary growth, then perhaps
soon there would be no left at all globe not a single bright place.

Kozma Prutkov

What will happen to our world?

After Edward Hubble's discovery of redshifts in the spectra of distant galaxies in 1929, it became clear that the Universe was expanding. One of the questions that arose in this regard was the following: how long will the expansion last and how will it end? The forces of gravitational attraction acting between individual parts of the Universe tend to slow down the retreat of these parts. What the braking will lead to depends on the total mass of the Universe. If it is large enough, gravitational forces will gradually stop the expansion and it will be replaced by compression. As a result, the Universe will eventually “collapse” again to the point from which it once began to expand. If the mass is less than a certain critical mass, then the expansion will continue forever. It is usually customary to talk not about mass, but about density, which is related to mass by a simple relationship, known from school course: Density is mass divided by volume.

The calculated value of the critical average density of the Universe is approximately 10 -29 grams per cubic centimeter, which corresponds to an average of five nucleons per cubic meter. It should be emphasized that we're talking about specifically about average density. The characteristic concentration of nucleons in water, earth and in you and me is about 10 30 per cubic meter. However, in the void that separates clusters of galaxies and occupies the lion's share of the volume of the Universe, the density is tens of orders of magnitude lower. The nucleon concentration value, averaged over the entire volume of the Universe, was measured tens and hundreds of times, carefully counting the number of stars and gas and dust clouds using different methods. The results of such measurements differ somewhat, but the qualitative conclusion is unchanged: the density of the Universe barely reaches a few percent of the critical value.

Therefore, until the 70s of the 20th century, the generally accepted forecast was the eternal expansion of our world, which should inevitably lead to the so-called heat death. Heat death is a state of a system when the substance in it is distributed evenly and its different parts have the same temperature. As a consequence, neither the transfer of energy from one part of the system to another, nor the redistribution of matter is possible. In such a system nothing happens and can never happen again. A clear analogy is water spilled on any surface. If the surface is uneven and there are even slight differences in elevation, water moves along it from higher to lower places and eventually collects in the lowlands, forming puddles. The movement stops. The only consolation left was that heat death would occur in tens and hundreds of billions of years. Consequently, you don’t have to think about this gloomy prospect for a very, very long time.

However, it gradually became clear that the true mass of the Universe is much greater than the visible mass contained in stars and gas and dust clouds and, most likely, is close to critical. Or perhaps exactly equal to it.

Evidence for dark matter

The first indication that something was wrong with the calculation of the mass of the Universe appeared in the mid-30s of the 20th century. Swiss astronomer Fritz Zwicky measured the speeds at which galaxies in the Coma cluster (one of the largest clusters known to us, it includes thousands of galaxies) move around a common center. The result was discouraging: the velocities of the galaxies turned out to be much greater than could be expected based on the observed total mass of the cluster. This meant that the true mass of the Coma cluster was much greater than the apparent mass. But the main amount of matter present in this region of the Universe remains, for some reason, invisible and inaccessible to direct observations, manifesting itself only gravitationally, that is, only as mass.

The presence of hidden mass in galaxy clusters is also evidenced by experiments on the so-called gravitational lensing. The explanation for this phenomenon follows from the theory of relativity. In accordance with it, any mass deforms space and, like a lens, distorts the rectilinear path of light rays. The distortion that galaxy clusters cause is so great that it is easy to notice. In particular, from the distortion of the image of the galaxy that lies behind the cluster, it is possible to calculate the distribution of matter in the lens cluster and thereby measure its total mass. And it turns out that it is always many times greater than the contribution of the visible matter of the cluster.

40 years after Zwicky’s work, in the 70s, American astronomer Vera Rubin studied the speed of rotation around the galactic center of matter located on the periphery of galaxies. In accordance with Kepler's laws (and they directly follow from the law universal gravity), when moving from the center of the galaxy to its periphery, the rotation speed of galactic objects should decrease in inverse proportion to square root from the distance to the center. Measurements have shown that for many galaxies this speed remains almost constant at a very significant distance from the center. These results can be interpreted only in one way: the density of matter in such galaxies does not decrease when moving from the center, but remains almost unchanged. Since the density of visible matter (contained in stars and interstellar gas) rapidly falls towards the periphery of the galaxy, the missing density must be supplied by something that for some reason we cannot see. To quantitatively explain the observed dependences of the rotation rate on the distance to the center of galaxies, it is required that this invisible “something” be approximately 10 times larger than ordinary visible matter. This “something” was called “dark matter” (in English “ dark matter") and still remains the most intriguing mystery in astrophysics.

Another important piece of evidence for the presence of dark matter in our world comes from calculations simulating the process of galaxy formation that began about 300,000 years after the Big Bang. These calculations show that the forces of gravitational attraction that acted between the flying fragments of the matter generated during the explosion could not compensate for the kinetic energy of the expansion. The matter simply should not have gathered into galaxies, which we nevertheless observe in modern era. This problem was called the galactic paradox, and for a long time it was considered a serious argument against the Big Bang theory. However, if we assume that particles of ordinary matter in the early Universe were mixed with particles of invisible dark matter, then everything falls into place in the calculations and the ends begin to meet - the formation of galaxies from stars, and then clusters of galaxies, becomes possible. At the same time, as calculations show, at first a huge number of dark matter particles accumulated in galaxies and only then, due to gravitational forces, elements of ordinary matter collected on them, total mass which accounted for only a few percent of the total mass of the Universe. It turns out that the familiar and, it would seem, studied to detail visible world, which we only recently thought was almost understood, is only a small addition to something that the Universe actually consists of. Planets, stars, galaxies and you and me are just a screen for a huge “something” about which we have not the slightest idea.

Photo fact

The galaxy cluster (at the lower left of the circled area) creates a gravitational lens. It distorts the shape of objects located behind the lens - stretching their images in one direction. Based on the magnitude and direction of the stretch, an international group of astronomers from the Southern European Observatory, led by scientists from the Paris Institute of Astrophysics, constructed a mass distribution, which is shown in the bottom image. As you can see, the cluster contains much more mass than can be seen through a telescope.

Hunting dark, massive objects is a slow process, and the results don't look the most impressive in photographs. In 1995, the Hubble Telescope noticed that one of the stars in the Large Magellanic Cloud flashed brighter. This glow lasted for three seconds. extra month, but then the star returned to its natural state. And six years later, a barely luminous object appeared next to the star. It was a cold dwarf that, passing at a distance of 600 light years from the star, created a gravitational lens that amplified the light. Calculations have shown that the mass of this dwarf is only 5-10% of the mass of the Sun.

Finally, the general theory of relativity unambiguously connects the rate of expansion of the Universe with the average density of the matter contained in it. Assuming that the average curvature of space is zero, that is, the geometry of Euclid and not Lobachevsky operates in it (which has been reliably verified, for example, in experiments with cosmic microwave background radiation), this density should be equal to 10 -29 grams per cubic centimeter. The density of visible matter is approximately 20 times less. The missing 95% of the mass of the Universe is dark matter. Note that the density value measured from the expansion rate of the Universe is equal to the critical value. Two values, independently calculated completely in different ways, coincided! If in fact the density of the Universe is exactly equal to the critical density, this cannot be a coincidence, but is a consequence of some fundamental property of our world, which has yet to be understood and comprehended.

What is this?

What do we know today about dark matter, which makes up 95% of the mass of the Universe? Almost nothing. But we still know something. First of all, there is no doubt that dark matter exists - this is irrefutably evidenced by the facts given above. We also know for certain that dark matter exists in several forms. After the beginning of the 21st century, as a result of many years of observations in experiments SuperKamiokande(Japan) and SNO (Canada) it was established that neutrinos have mass, it became clear that from 0.3% to 3% of the 95% of the hidden mass lies in neutrinos that have long been familiar to us - even if their mass is extremely small, but their quantity is in The universe has about a billion times the number of nucleons: each cubic centimeter contains an average of 300 neutrinos. The remaining 92-95% consists of two parts - dark matter and dark energy. A small fraction of dark matter consists of ordinary baryonic matter, built from nucleons; the remainder is apparently accounted for by some unknown massive weakly interacting particles (the so-called cold dark matter). Energy balance in modern universe is presented in the table, and the story about its last three columns is below.

Baryonic dark matter

A small (4-5%) part of dark matter is ordinary matter that emits little or no radiation of its own and is therefore invisible. The existence of several classes of such objects can be considered experimentally confirmed. The most complex experiments, based on the same gravitational lensing, led to the discovery of so-called massive compact halo objects, that is, located on the periphery of galactic disks. This required monitoring millions of distant galaxies over several years. When a dark, massive body passes between an observer and a distant galaxy, its brightness briefly decreases (or increases as the dark body acts as a gravitational lens). As a result of painstaking searches, such events were identified. The nature of massive compact halo objects is not completely clear. Most likely, these are either cooled stars (brown dwarfs) or planet-like objects that are not associated with stars and travel around the galaxy on their own. Another representative of baryonic dark matter is hot gas recently discovered in galaxy clusters using X-ray astronomy methods, which does not glow in the visible range.

Nonbaryonic dark matter

The main candidates for nonbaryonic dark matter are the so-called WIMPs (short for English Weakly Interactive Massive Particles- weakly interacting massive particles). The peculiarity of WIMPs is that they show almost no interaction with ordinary matter. This is why they are the real invisible dark matter, and why they are extremely difficult to detect. The mass of WIMP must be at least tens of times greater than the mass of a proton. The search for WIMPs has been carried out in many experiments over the past 20-30 years, but despite all efforts, they have not yet been detected.

One idea is that if such particles exist, then the Earth, as it orbits the Sun with the Sun around the galactic center, should be flying through a rain of WIMPs. Despite the fact that WIMP is an extremely weakly interacting particle, it still has a very small probability of interacting with an ordinary atom. At the same time, in special installations - very complex and expensive - a signal can be recorded. The number of such signals should change throughout the year because, as the Earth moves in orbit around the Sun, it changes its speed and direction relative to the wind, which consists of WIMPs. The DAMA experimental group, working at Italy's Gran Sasso underground laboratory, reports observed year-to-year variations in signal count rates. However, other groups have not yet confirmed these results, and the question essentially remains open.

Another method of searching for WIMPs is based on the assumption that during billions of years of their existence, various astronomical objects (Earth, Sun, the center of our Galaxy) should capture WIMPs, which accumulate in the center of these objects, and, annihilating each other, give rise to a neutrino stream . Attempts to detect excess neutrino flux from the center of the Earth towards the Sun and the center of the Galaxy were made on underground and underwater neutrino detectors MACRO, LVD (Gran Sasso Laboratory), NT-200 (Lake Baikal, Russia), SuperKamiokande, AMANDA (Scott Station -Amundsen, South Pole), but have not yet led to a positive result.

Experiments to search for WIMPs are also actively carried out at accelerators elementary particles. In accordance with Einstein's famous equation E=mс 2, energy is equivalent to mass. Therefore, by accelerating a particle (for example, a proton) to a very high energy and colliding it with another particle, one can expect the creation of pairs of other particles and antiparticles (including WIMPs), the total mass of which is equal to the total energy of the colliding particles. But accelerator experiments have not yet led to a positive result.

Dark energy

At the beginning of the last century, Albert Einstein, wanting to ensure independence of time for the cosmological model in the general theory of relativity, introduced the so-called cosmological constant into the equations of the theory, which he designated Greek letter"lambda" - Λ. This Λ was a purely formal constant, in which Einstein himself did not see any physical meaning. After the expansion of the Universe was discovered, the need for it disappeared. Einstein very much regretted his haste and called the cosmological constant Λ his biggest scientific mistake. However, decades later it turned out that the Hubble constant, which determines the rate of expansion of the Universe, changes with time, and its dependence on time can be explained by selecting the value of that very “erroneous” Einstein constant Λ, which contributes to the hidden density of the Universe. This part of the hidden mass came to be called “dark energy”.

Even less can be said about dark energy than about dark matter. First, it is evenly distributed throughout the Universe, unlike ordinary matter and other forms of dark matter. There is as much of it in galaxies and galaxy clusters as outside of them. Secondly, it has several very strange properties, which can only be understood by analyzing the equations of the theory of relativity and interpreting their solutions. For example, dark energy experiences antigravity: due to its presence, the rate of expansion of the Universe increases. Dark energy seems to push itself away, accelerating the scattering of ordinary matter collected in galaxies. Dark energy also has negative pressure, due to which a force arises in the substance that prevents it from stretching.

The main candidate for dark energy is vacuum. The vacuum energy density does not change as the Universe expands, which corresponds to negative pressure. Another candidate is a hypothetical super-weak field, called quintessence. Hopes for clarifying the nature of dark energy are associated primarily with new astronomical observations. Progress in this direction will undoubtedly bring radically new knowledge to humanity, since in any case, dark energy must be a completely unusual substance, completely different from what physics has dealt with so far.

So, 95% of our world consists of something about which we know almost nothing. One can have different attitudes towards such a fact that is beyond any doubt. It can cause anxiety, which always accompanies a meeting with something unknown. Or disappointment because such a long and difficult path the construction of a physical theory describing the properties of our world led to the statement: most of the Universe is hidden from us and unknown to us.

But most physicists are now feeling encouraged. Experience shows that all the riddles that nature posed to humanity were sooner or later resolved. Undoubtedly, the mystery of dark matter will also be resolved. And this will certainly bring completely new knowledge and concepts that we have no idea about yet. And perhaps we will meet new mysteries, which, in turn, will also be solved. But this will be a completely different story, which readers of “Chemistry and Life” will not be able to read until a few years later. Or maybe in a few decades.

A theoretical construct in physics called the Standard Model describes the interactions of all known to science elementary particles. But this is only 5% of the matter existing in the Universe, the remaining 95% is of a completely unknown nature. What is this hypothetical dark matter and how are scientists trying to detect it? Hayk Hakobyan, a MIPT student and employee of the Department of Physics and Astrophysics, talks about this as part of a special project.

The Standard Model of elementary particles, finally confirmed after the discovery of the Higgs boson, describes the fundamental interactions (electroweak and strong) of the ordinary particles we know: leptons, quarks and force carriers (bosons and gluons). However, it turns out that this whole huge complex theory describes only about 5-6% of all matter, while the rest does not fit into this model. Observations of the earliest moments of our Universe show us that approximately 95% of the matter that surrounds us is of a completely unknown nature. In other words, we indirectly see the presence of this hidden matter due to its gravitational influence, but we have not yet been able to capture it directly. This hidden mass phenomenon is codenamed “dark matter.”

Modern science, especially cosmology, works according to the deductive method of Sherlock Holmes

Now the main candidate from the WISP group is the axion, which arises in the theory of the strong interaction and has a very small mass. Such a particle is capable of transforming into a photon-photon pair in high magnetic fields, which gives hints on how one might try to detect it. The ADMX experiment uses large chambers that create a magnetic field of 80,000 gauss (that's 100,000 times more magnetic field Earth). In theory, such a field should stimulate the decay of an axion into a photon-photon pair, which detectors should catch. Despite numerous attempts, it has not yet been possible to detect WIMPs, axions or sterile neutrinos.

Thus, we have traveled through a huge number of different hypotheses seeking to explain the strange presence of the hidden mass, and, having rejected all the impossibilities with the help of observations, we have arrived at several possible hypotheses with which we can already work.

A negative result in science is also a result, since it gives restrictions on various parameters of particles, for example, it eliminates the range of possible masses. From year to year, more and more new observations and experiments in accelerators provide new, more stringent restrictions on the mass and other parameters of dark matter particles. Thus, by throwing out all the impossible options and narrowing the circle of searches, day by day we are becoming closer to understanding what 95% of the matter in our Universe consists of.

Everything we see around us (stars and galaxies) is no more than 4-5% of the total mass in the Universe!

According to modern cosmological theories, our Universe consists of only 5% of ordinary, so-called baryonic matter, which forms all observable objects; 25% dark matter detected due to gravity; and dark energy, making up as much as 70% of the total.

The terms dark energy and dark matter are not entirely successful and represent a literal, but not semantic, translation from English.

In a physical sense, these terms only imply that these substances do not interact with photons, and they could just as easily be called invisible or transparent matter and energy.

Many modern scientists are convinced that research aimed at studying dark energy and matter will likely help answer global issue: what awaits our Universe in the future?

Clumps the size of a galaxy

Dark matter is a substance that most likely consists of new particles that are still unknown in terrestrial conditions and has properties inherent in ordinary matter itself. For example, it is also capable, like ordinary substances, of gathering into clumps and participating in gravitational interactions. But the size of these so-called clumps can exceed an entire galaxy or even a cluster of galaxies.

Approaches and methods for studying dark matter particles

At the moment, scientists around the world are trying in every possible way to discover or artificially obtain particles of dark matter under terrestrial conditions, using specially developed ultra-technological equipment and many different research methods, but so far all their efforts have not been crowned with success.

One method involves conducting experiments at high-energy accelerators, commonly known as colliders. Scientists, believing that dark matter particles are 100-1000 times heavier than a proton, assume that they should be generated in the collision of ordinary particles accelerated to high energies through a collider. The essence of another method is to register dark matter particles located all around us. The main difficulty in registering these particles is that they exhibit very weak interaction with ordinary particles, which are inherently transparent to them. And yet, dark matter particles very rarely collide with atomic nuclei, and there is some hope of registering this phenomenon sooner or later.

There are other approaches and methods for studying dark matter particles, and only time will tell which of them will be the first to succeed, but in any case, the discovery of these new particles will be the most important scientific achievement.

Substance with anti-gravity

Dark energy is an even more unusual substance than dark matter. It does not have the ability to gather into clumps, as a result of which it is evenly distributed throughout the entire Universe. But its most unusual property at the moment is antigravity.

The nature of dark matter and black holes

Thanks to modern astronomical methods It is possible to determine the rate of expansion of the Universe at the present time and simulate the process of its change earlier in time. As a result of this, information was obtained that at the moment, as well as in the recent past, our Universe is expanding, and the pace of this process is constantly increasing. That is why the hypothesis about the antigravity of dark energy arose, since ordinary gravitational attraction would have a slowing effect on the process of “scattering of galaxies”, restraining the rate of expansion of the Universe. This phenomenon does not contradict the general theory of relativity, but dark energy must have negative pressure - a property that no currently known substance has.

Candidates for the role of "Dark Energy"

The mass of the galaxies in the Abel 2744 cluster is less than 5 percent of its total mass. This gas is so hot that it only glows in X-rays (red in this image). The distribution of invisible dark matter (which makes up about 75 percent of the cluster's mass) is colored blue.

One of the putative candidates for the role of dark energy is vacuum, the energy density of which remains unchanged during the expansion of the Universe and thereby confirms the negative pressure of the vacuum. Another putative candidate is the “quintessence” - a previously unknown ultra-weak field that supposedly passes through the entire Universe. There are also other possible candidates, but not one of them has so far contributed to obtaining an exact answer to the question: what is dark energy? But it is already clear that dark energy is something completely supernatural, remaining the main mystery of fundamental physics of the 21st century.

Today it is a mystery about where it came from. dark matter has not yet been solved. There are theories that suggest that it consists of low-temperature interstellar gas. In this case, the substance cannot produce any radiation. However, there are theories against this idea. They say that the gas is able to heat up, which leads to the fact that they become ordinary “baryonic” substances. This theory is supported by the fact that the mass of gas in a cold state cannot eliminate the deficit that arises.

There are so many questions about dark matter theories that it's worth looking into it a little more.

What is dark matter?

The question of what dark matter is arose about 80 years ago. Back at the beginning of the 20th century. At that time, the Swiss astronomer F. Zwicky came up with the idea that the mass of all galaxies in reality is greater than the mass of all those objects that can be seen with their own gases in a telescope. All the numerous clues hinted that there was something unknown in space that had an impressive mass. It was decided to give the name “dark substance” to this inexplicable substance.

This invisible substance occupies at least a quarter of the entire Universe. The peculiarity of this substance is that its particles interact poorly with each other and with ordinary other substances. This interaction is so weak that scientists cannot even detect it. In fact, there are only signs of influence from particles.

The study of this issue is being carried out by the greatest minds around the world, so even the biggest skeptics in the world believe that it will be possible to catch particles of the substance. The most desirable goal is to do this in a laboratory setting. Work is being carried out in mines at great depths; such conditions for experiments are necessary to eliminate the interference caused by particles of rays from space.

There is a possibility that a lot new information will be possible to obtain thanks to modern accelerators, in particular, with the help of the Large Hadron Collider.

Particles of dark matter have one strange feature - mutual destruction. As a result of such processes, gamma radiation, antiparticles and particles (such as electron and positron) appear. Therefore, astrophysicists are trying to find traces of gamma radiation or antiparticles. For this, various ground and space installations are used.

Evidence for the existence of dark matter

The very first doubts about the correctness of calculations of the mass of the Universe, as already mentioned, were shared by the astronomer from Switzerland F. Zwicky. To begin with, he decided to measure the speed of galaxies from the Coma cluster moving around the center. And the result of his work puzzled him somewhat, because the speed of movement of these galaxies turned out to be higher than he had expected. In addition, he pre-calculated this value. But the results were not the same.

The conclusion was obvious: the real mass of the cluster was much greater than the apparent one. This could be explained by the fact that most of the matter that is in this part of the Universe cannot be seen, and it is also impossible to observe it. This substance exhibits its properties only in the form of mass.

A number of gravitational experiments have confirmed the presence of invisible mass in galaxy clusters. The theory of relativity has some interpretation of this phenomenon. If you follow it, then each mass is capable of deforming space, in addition, like a lens, it bends the direct flow of light rays. The galaxy cluster causes distortion, its influence is so strong that it becomes noticeable. The view of the galaxy that is located directly behind the cluster is most distorted. This distortion is used to calculate how the matter is distributed in this cluster. This is how real mass is measured. It invariably turns out to be several times larger than the mass of visible matter.

Four decades after the work of the pioneer in this area, F. Zwicky, the American astronomer V. Rubin took up this issue. She studied the speed at which matter, which is located at the edges of galaxies, rotates around the center of the galaxy. If we follow Kepler's laws concerning the laws of gravity, then there is a certain relationship between the speed of rotation of galaxies and the distance to the center.

But in reality, measurements showed that the rotation speed did not change with increasing distance to the center. Such data could be explained only in one way - the matter of the galaxy has the same density both in the center and at the edges. But the visible substance had a much greater density in the center and was characterized by sparseness at the edges, and the lack of density could only be explained by the presence of some substance that was not visible to the eye.

To explain the phenomenon, it is necessary that there is almost 10 times more of this invisible matter in galaxies than the matter that we can see. This unknown substance is called “dark matter” or “dark matter”. To date, this phenomenon remains the most interesting mystery for astrophysicists.

There is another argument in favor of evidence of the existence of dark matter. It follows from calculations that describe the process of how galaxies formed. It is believed that this began approximately 300,000 years after the Big Bang occurred. The calculation results say that the attraction between the fragments of matter that appeared during the explosion could not compensate for the kinetic energy from the expansion. That is, the matter could not concentrate in galaxies, but we can see it today.

This inexplicable fact called the galaxy paradox, it was cited as an argument that destroys the Big Bang theory. But you can look at it from the other side. After all, particles of the most ordinary matter could be mixed with particles of dark matter. Then the calculations become correct, and how galaxies were formed in which a lot of dark matter had accumulated, and particles of ordinary matter had already joined them due to gravity. After all, ordinary matter makes up a small fraction of the total mass of the Universe.

Visible matter has a relatively low density compared to dark matter because it is 20 times denser. Therefore, those 95% of the mass of the Universe that are missing according to scientists’ calculations are dark matter.

However, this led to the conclusion that the entire visible world, which had been studied far and wide, so familiar and understandable, was only a small addition to what actually made up.

All galaxies, planets and stars are just a small piece of something that we have no idea about. This is what is exposed, but the real is hidden from us.

Introduction

There are strong arguments that much of the matter in the Universe neither emits nor absorbs anything and is therefore invisible. The presence of such invisible matter can be recognized by its gravitational interaction with radiating matter. Studies of galaxy clusters and galactic rotation curves provide evidence of the existence of this so-called dark matter. So, by definition, dark matter is matter that does not interact with electromagnetic radiation, that is, it does not emit or absorb it.
The first detection of invisible matter dates back to the last century. In 1844, Friedrich Bessel wrote in a letter to Karl Gauss that the unexplained irregularity in the motion of Sirius could be the result of its gravitational interaction with some neighboring body, and the latter in this case should have a fairly large mass. At the time of Bessel, such a dark companion to Sirius was invisible; it was optically discovered only in 1862. It turned out to be a white dwarf, called Sirius-B, while Sirius itself was called Sirius-A.
The density of matter in the Universe, ρ, can be estimated from observations of the motion of individual galaxies. Usually ρ is given in units of the so-called critical density ρ c:

In this formula, G is the gravitational constant, H is the Hubble constant, which is known with low accuracy (0.4< H < 1), к тому же, вероятно, зависит от времени:

V = HR – Hubble’s formula for the expansion rate of the Universe,
H = 100 h km∙s -1 ∙Mpc -1 .

For ρ > ρ с the Universe is closed, i.e. The gravitational interaction is strong enough for the expansion of the Universe to give way to compression.
Thus, the critical density is given by:

ρ с = 2∙1 –29 h 2 g∙cm -3 .

Cosmological density Ω = ρ/ρ с, determined based on the dynamics of galaxy clusters and superclusters, is equal to 0.1< Ω < 0.3.
From observing the nature of the removal of large-scale regions of the Universe using the infrared astronomical satellite IRAS, it was found that 0.25< Ω < 2.
On the other hand, estimating the baryon density Ω b from the luminosity of galaxies gives a significantly smaller value: Ω b< 0.02.
This discrepancy is usually taken as an indication of the existence of invisible matter.
Recently, much attention has been paid to the problem of searching for dark matter. If we take into account all forms of baryonic matter, such as interplanetary dust, brown and white dwarfs, neutron stars and black holes, it turns out that a significant proportion of nonbaryonic matter is needed to explain all observed phenomena. This statement remains valid even after taking into account modern data on the so-called MACHO objects ( M.A. ssive C compact H alo O bjects are massive compact galactic objects) discovered using the gravitational lensing effect.

. Evidence for dark matter

2.1. Galactic rotation curves

In case spiral galaxies the speed of rotation of individual stars around the center of the galaxy is determined from the condition of constancy of orbits. Equating centrifugal and gravitational forces:

for the rotation speed we have:

where M r is the entire mass of matter inside a sphere of radius r. In the case of ideal spherical or cylindrical symmetry, the influence of mass located outside this sphere is mutually compensated. To a first approximation, the central region of the galaxy can be considered spherical, i.e.

where ρ is the average density.
In the inner part of the galaxy, a linear increase in the rotation rate is expected with increasing distance from the center. In the outer region of the galaxy, the mass M r is almost constant and the dependence of the velocity on distance corresponds to the case with a point mass in the center of the galaxy:

The rotational velocity v(r) is determined, for example, by measuring the Doppler shift in the emission spectrum of He-II regions around O stars. The behavior of the experimentally measured rotation curves of spiral galaxies does not correspond to a decrease in v(r) with increasing radius. A study of the 21-cm line (hyperfine structure transition in the hydrogen atom) emitted by interstellar matter led to a similar result. The constancy of v(r) at large values of the radius means that the mass M r also increases with increasing radius: M r ~ r. This indicates the presence of invisible matter. Stars move faster than would be expected based on the apparent amount of matter.
Based on this observation, the existence of a spherical dark matter halo surrounding the galaxy and responsible for the non-decreasing behavior of the rotation curves was postulated. In addition, a spherical halo could contribute to the stability of the shape of the disk of galaxies and confirm the hypothesis of the formation of galaxies from a spherical protogalaxy. Model calculations carried out for the Milky Way, which were able to reproduce the rotation curves by taking into account the presence of a halo, indicate that a significant part of the mass must be in this halo. Evidence in favor of the existence of spherical halos is also provided by globular clusters - spherical clusters of stars, which are the most ancient objects in the galaxy and which are distributed spherically.
However, recent research into the transparency of galaxies has cast doubt on this picture. By considering the degree of obscurity of spiral galaxies as a function of inclination angle, one can infer the transparency of such objects. If the galaxy were completely transparent, then its total luminosity would not depend on the angle at which this galaxy is observed, since all stars would be visible equally well (ignoring the size of the stars). On the other hand, a constant surface brightness means that the galaxy is not transparent. In this case, the observer always sees only the outer stars, i.e. always the same number per unit surface, regardless of the viewing angle. It was experimentally established that the surface brightness remains constant on average, which could indicate the almost complete opacity of spiral galaxies. In this case, the use of optical methods to determine the mass density of the Universe is not entirely accurate. A more thorough analysis of the measurement results led to the conclusion that molecular clouds are an absorbing material (their diameter is approximately 50 ps and the temperature is about 20 K). According to Wien's displacement law, such clouds should emit in the submillimeter region. This result could provide an explanation for the behavior of the rotation curves without the assumption of additional exotic dark matter.
Evidence for the existence of dark matter has also been found in elliptical galaxies. Gaseous halos with temperatures around 10 7 K have been recorded by their absorption of X-rays. The velocities of these gas molecules are greater than the expansion rate:

v r = (2GM/r) 1/2 ,

assuming that their masses correspond to their luminosity. For elliptical galaxies, the mass-to-luminosity ratio is about two orders of magnitude greater than that of the Sun, which is a typical example of an average star. Such a large value is usually associated with the existence of dark matter.

2.2. Dynamics of galaxy clusters

The dynamics of galaxy clusters provide evidence for the existence of dark matter. When the movement of the system potential energy which is a homogeneous function of coordinates, occurs in a limited spatial region, then the time-averaged values of kinetic and potential energy are related to each other by the virial theorem. It can be used to estimate the density of matter in clusters of a large number of galaxies.
If the potential energy U is a homogeneous function of radius vectors r i of degree k, then U and kinetic energy T are related as 2T = kU. Since T + U = E = E, it follows that

U = 2E/(k + 2), T = kE/(k + 2),

where E is the total energy. For gravitational interaction (U ~ 1/r) k = -1, so 2T = -U. The average kinetic energy of a cluster of N galaxies is given by:

T=N /2.

These N galaxies can interact with each other in pairs. Therefore, there are N(N–1)/2 independent pairs of galaxies, the total average potential energy of which has the form

U = GN(N − 1)m 2 /2r.

With Nm = M and (N − 1) ≈ N for the dynamic mass it turns out M ≈ 2 /G.
Average distance measurements and average speed give a dynamic mass value that is approximately two orders of magnitude higher than the mass obtained from an analysis of the luminosity of galaxies. This fact can be interpreted as further evidence in favor of the existence of dark matter.
This argument also has its own weak points. The virial equation is valid only when averaging over a long time period, when closed systems are in a state of equilibrium. However, measurements of galaxy clusters are something like snapshots. Moreover, galaxy clusters are not closed systems; they are connected to each other. Finally, it is not clear whether they have reached a state of equilibrium or not.

2.3. Cosmological evidence

The definition of the critical density ρ c was given above. Formally, it can be obtained on the basis of Newtonian dynamics by calculating the critical expansion rate of a spherical galaxy:

The relationship for ρ c follows from the expression for E, if we assume that H = r"/r = v/r.
The description of the dynamics of the Universe is based on Einstein's field equations (General Theory of Relativity - GTR). They are somewhat simplified under the assumption of homogeneity and isotropy of space. In the Robertson-Walker metric, the infinitesimal linear element is given by:

where r, θ, φ are the spherical coordinates of the point. The degrees of freedom of this metric are included in the parameter k and the scale factor R. The value of k takes only discrete values (if fractal geometry is not taken into account) and does not depend on time. The value k is a characteristic of the Universe model (k = -1 - hyperbolic metric (open Universe), k = 0 - Euclidean metric (flat Universe), k = +1 - spherical metric (closed Universe)).
The dynamics of the Universe are completely specified by the scale function R(t) (the distance between two neighboring points in space with coordinates r, θ, φ changes over time as R(t)). In the case of the spherical metric, R(t) represents the radius of the Universe. This scale function satisfies the Einstein-Friedmann-Lemaitre equations:

where p(t) is the total pressure, and Λ is the cosmological constant, which, within the framework of modern quantum field theories, is interpreted as the vacuum energy density. Let us further assume that Λ = 0, as is often done to explain experimental facts without introducing dark matter. The coefficient R 0 "/R 0 determines the Hubble constant H 0, where the index "0" marks the modern values of the corresponding quantities. From the above formulas it follows that for the curvature parameter k = 0, the modern critical density of the Universe is given by the expression whose value represents the boundary between the open and a closed Universe (this value separates the scenario in which the Universe is eternally expanding from the scenario in which the Universe expects collapse at the end of the temporary expansion phase):

Density parameter is often used

where q 0 is the braking parameter: q(t) = –R(t)R""(t)/(R"(t)) 2. Thus, three cases are possible:
Ω 0 < 1 − открытая Вселенная,
Ω 0 = 1 – flat Universe,
Ω 0 > 1 – closed Universe.
Measurements of the density parameter gave an estimate: Ω 0 ≈ 0.2, on the basis of which the open nature of the Universe could be expected. However, a number of theoretical concepts are difficult to reconcile with the openness of the Universe, for example, the so-called “flatness” problem and the genesis of galaxies.

Flatness problem

As you can see, the density of the Universe is very close to critical. From the Einstein-Friedmann-Lemaitre equations it follows (at Λ = 0) that

Since the density ρ(t) is proportional to 1/R(t) 3, then using the expression for Ω 0 (k is not equal to 0) we have:

Thus, the value Ω ≈ 1 is very unstable. Any deviation from the perfectly flat case increases greatly as the Universe expands. This means that during the original nuclear fusion the Universe must have been significantly flatter than it is now.
One possible solution to this problem is provided by inflation models. It is assumed that the expansion of the early Universe (in the interval between 10 -34 s and 10 -31 s after the Big Bang) occurred exponentially in the inflation phase. In these models, the density parameter is usually independent of time (Ω = 1). However, there are theoretical indications that the value of the density parameter in the range of 0.01< Ω 0 < 2 также согласуется с моделью инфляции.

Genesis of galaxies

For the genesis of galaxies, density inhomogeneities are necessary. Galaxies had to arise in such spatial regions where the densities were greater than around them, so that as a result of gravitational interaction these regions managed to cluster faster than their rarefaction occurred due to general expansion.
However, this type of accumulation of matter could begin only after the formation of atoms from nuclei and electrons, i.e. approximately 150,000 years after the Big Bang at temperatures of about 3000 K (since in the early stages matter and radiation were in a state of dynamic equilibrium: any resulting clump of matter was immediately destroyed under the influence of radiation and at the same time radiation could not escape beyond the boundaries of matter ). Noticeable fluctuations in the density of ordinary matter at that time were excluded down to very low levels by the isotropy of background radiation. After the stage of formation of neutral atoms, the radiation ceases to be in a state of thermal equilibrium with matter, thus the subsequent fluctuations in the density of matter are no longer reflected in the nature of the radiation.
But if we calculate the evolution over time of the process of compression of matter, which just then began, it turns out that the time that has passed since then is not enough for such large structures as galaxies or their clusters to form. Apparently, it is necessary to require the existence of massive particles released from a state of thermal equilibrium at an earlier stage, so that these particles have the opportunity to manifest themselves as some seeds for the condensation of ordinary matter around them. Such candidates could be so-called WIMP particles. In this case, it is necessary to take into account the requirement that the background cosmic radiation is isotropic. A small anisotropy (10 -4) in the cosmic microwave background radiation (temperature about 2.7 K) was discovered only recently using the COBE satellite.

III. Dark matter candidates

3.1. Baryonic dark matter

The most obvious candidate for dark matter would be ordinary baryonic matter, which does not emit and has a corresponding abundance. One possibility could be realized by interstellar or intergalactic gas. However, in this case, characteristic emission or absorption lines should appear that are not detected.
Another candidate could be brown dwarfs - cosmic bodies with masses significantly less than the mass of the Sun (M< 0.08M солнца). Гравитационного давления внутри этих объектов оказывается недостаточно для создания температур, при которых начинает процесс слияния протонов в гелий. Из-за отсутствия ядерного синтеза излучение коричневых карликов очень слабо, если не считать излучения тех из них, которые находятся на ранней стадии своего развития. Планеты также могли бы входить в эту группу. Однако из-за отсутствия знания о происхождении звезд и планет, а также из-за ограниченности фотометрической детектируемости celestial bodies At a distance of several light years, it is especially difficult to estimate the number of such objects.
Very compact objects in the final stages of stellar development (white dwarfs, neutron stars and black holes) could also be part of dark matter. Since virtually every star reaches one of these three final stages during its lifetime, a significant portion of the mass of earlier and heavier stars must be present in non-radiating form as white dwarfs. neutron stars or black holes. Some of this matter returns to interstellar space through supernova explosions or other ways and takes part in the formation of new stars. In this case, stars with masses M should not be taken into account< 0.9M солнца, так как их время жизни больше, чем возраст Вселенной, и они еще не достигли конечных стадий в своем развитии.
Upper bounds on the possible density of baryonic matter in the Universe can be obtained from data on the initial nuclear fusion, which began approximately 3 minutes after the Big Bang. Measurements of the current abundance of deuterium are especially important −
(D/H) 0 ≈ 10 -5, since during the initial nuclear fusion it was mainly deuterium that was formed. Although deuterium also appeared later as an intermediate product of nuclear fusion reactions, the total amount of deuterium did not increase significantly due to this. Analysis of the processes occurring at the stage of early nuclear fusion gives an upper limit − Ω o,b< 0.1–0.2 для плотности возможной барионной материи во Вселенной. При этом учтена вся материя, которая была сформирована во время ядерного синтеза в ранней Вселенной. Данное значение хорошо согласуется с оценками, полученными из рассмотрения характера вращения галактик.
On the other hand, it is now completely clear that baryonic matter by itself is not able to satisfy the requirement Ω = 1, which follows from inflationary models. In addition, the problem of galaxy formation remains unresolved. All this leads to the need for the existence of nonbaryonic dark matter, especially in the case when the condition Ω = 1 at zero cosmological constant is required.

3.2. Nonbaryonic dark matter

Theoretical models provide large selection possible candidates for the role of nonbaryonic dark matter, including: light and heavy neutrinos, supersymmetric particles of SUSY models, axions, cosmions, magnetic monopoles, Higgs particles - they are summarized in the table. The table also contains theories that explain the experimental data without introducing dark matter (the time-dependent gravitational constant in non-Newtonian gravity and the cosmological constant). Designations: DM - dark matter, GUT - Grand Unified Theory, SUSY - supersymmetric theories, SUGRA - supergravity, QCD - quantum chromodynamics, QED - quantum electrodynamics, GTR - general relativity. The concept WIMP (weakly interacting massive particles) is used to denote particles with a mass greater than a few GeV/c 2 that participate only in weak interactions. Taking into account new measurements of the cosmic microwave background radiation from the COBE satellite and the redshift from the IRAS satellite, the distribution of galaxies at large distances and the formation of large-scale structures in our galaxy have recently been re-examined. Based on the analysis of various models of structure formation, it was concluded that only one satisfactory model of the Universe is possible with Ω = 1, in which dark matter is of a mixed nature: 70% exists in the form of cold dark matter and 30% in the form of hot dark matter, with the latter consists of two massless neutrinos and one neutrino with a mass of 7.2 ± 2 eV. This means a revival of the previously discarded mixed dark matter model.

Light neutrinos

Unlike all other dark matter candidates, neutrinos have the distinct advantage of being known to exist. Their prevalence in the Universe is approximately known. In order for neutrinos to be candidates for dark matter, they certainly must have mass. To achieve the critical density of the Universe, neutrino masses must lie in the region of several GeV/c 2 or in the region from 10 to 100 eV/c 2 .
Heavy neutrinos are also possible as such candidates, since the cosmologically significant product m ν exp(-m ν /kT f) becomes small even for large masses. Here Tf is the temperature at which heavy neutrinos cease to be in a state of thermal equilibrium. This Boltzmann factor gives the abundance of neutrinos with mass m ν relative to the abundance of massless neutrinos.
For each type of neutrino in the Universe, the neutrino density is related to the photon density by the relation n ν = (3/11)n γ. Strictly speaking, this expression is valid only for light Majorana neutrinos (for Dirac neutrinos, under certain circumstances, it is necessary to introduce another statistical factor equal to two). The photon density can be determined based on the background cosmic microwave background radiation 3 K and reaches n γ ≈ 400 cm -3 .

Particle	Weight	Theory	Manifestation
G(R)	-	Non-Newtonian gravity	Transparent DM at scale
Λ (space constant)	-	GTO	Ω=1 without DM
Axion, marjoram, goldstone. boson	10 -5 eV	QCD; violation of sim. Pechei-Quina	Cold DM
Ordinary neutrino	10-100 eV	GUT	Hot DM
Light higgsino, photino, gravitino, axino, sneutrino	10-100 eV	SUSY/DM
Paraphoton	20-400 eV	Modifier QED	Hot, warm DM
Right neutrinos	500 eV	Superweak force	Warm DM
Gravitino, etc.	500 eV	SUSY/SUGRA	Warm DM
Photino, gravitino, axion, mirrors. particles, Simpson neutrino	keV	SUSY/SUGRA	Warm/cold DM
Photino, sneutrino, higgsino, gluino, heavy neutrino	MeV	SUSY/SUGRA	Cold DM
Shadow Matter	MeV	SUSY/SUGRA	Hot/cold (like baryons) DM
Preon	20-200 TeV	Composite Models	Cold DM
Monopoly	10 16 GeV	GUT	Cold DM
Pyrgon, maximon, pole Perry, newtorite, Schwarzschild	10 19 GeV	Theories of higher dimensions	Cold DM
Superstrings	10 19 GeV	SUSY/SUGRA	Cold DM
Quark "nuggets"	10 15 g	QCD, GUT	Cold DM
Space strings, domain walls	(10 8 -10 10)M sun	GUT	The formation of galaxies may not contribute much to
Cosmion	4-11 GeV	Neutrino problem	Formation of a neutrino flux on the Sun
Black holes	10 15 -10 30 g	GTO	Cold DM

Primak J.R., Seckel D., Sadoulet B., 1988, Ann. Rev. Nucl. Part.Sci., 38, 751 It turns out that the neutrino mass density is close to critical if the condition is met

where g ν is a statistical factor that takes into account the number of different helicity states for each type of neutrino. For Majorana neutrinos this factor is equal to 2. For Dirac neutrinos it should be equal to 4. However, it is usually assumed that the right-handed components left the state of thermal equilibrium much earlier, so we can also assume that g ν = 2 for the Dirac case.
Since the neutrino density is of the same order of magnitude as the photon density, there are about 10 9 times more neutrinos than baryons, so even a small neutrino mass could determine the dynamics of the Universe. To achieve Ω = ρ ν /ρ с = 1, neutrino masses m ν c 2 ≈ 15–65 eV/N ν are required, where N ν is the number of light neutrino types. The experimental upper bounds for the masses of the three known types of neutrinos are: m(ν e)< 7.2 эВ/c 2 , m(ν μ) < 250 кэВ/c 2 , m(ν τ) < 31 МэВ/c 2 . Таким образом, электронное нейтрино практически исключается в качестве кандидата на доминирующую фракцию темной материи. Экспериментальные данные для остальных двух типов нейтрино не столь критичны, так что мюонные и тау-нейтрино остаются среди возможных кандидатов. Нейтрино вышли из состояния термического равновесия примерно через 1 с после Большого Взрыва при температуре 10 10 К (что отвечает энергии 1 МэВ). В это время они обладают релятивистскими энергиями и тем самым считаются частицами горячей темной материи. Нейтрино также могут давать вклад в процесс формирования галактик. В расширяющейся Вселенной, в которой доминируют частицы массой m i , согласно критерию Джинса, та масса, которая может коллапсировать за счет гравитационных сил, равна

In a Universe dominated by neutrinos, the required degree of compression could be established at a relatively late stage, the first structures would correspond to superclusters of galaxies. Thus, galaxy clusters and galaxies could develop through the fragmentation of these primary structures (top-down model). However, this approach faces problems when considering the formation of very small structures such as dwarf galaxies. To explain the formation of quite massive compressions, one also needs to take into account the Pauli principle for fermions.

Heavy neutrinos

According to LEP and SLAC data related to precision measurements of the decay width of the Z 0 boson, there are only three types of light neutrinos and the existence of heavy neutrinos up to mass values of 45 GeV/c 2 is excluded.
When neutrinos with such large masses left the state of thermal equilibrium, they already had non-relativistic speeds, which is why they are called cold dark matter particles. The presence of heavy neutrinos could lead to early gravitational compression of matter. In this case, smaller structures would form first. Clusters and superclusters of galaxies would have formed later by the accumulation of individual groups of galaxies (bottom-up model).

Axions

Axions are hypothetical particles that arise in connection with the problem of CP violation in the strong interaction (θ problem). The existence of such a pseudoscalar particle is due to the violation of Pechey-Quin chiral symmetry. The mass of the axion is given by

The interaction with fermions and gauge bosons is described by the following coupling constants, respectively:

Axion decay constant f a is determined by the vacuum average of the Higgs field. Because f a is a free constant that can take any value between the electroweak and Planck scales, then the possible values of the axion masses vary by 18 orders of magnitude. A distinction is made between DFSZ axions, which directly interact with electrons, and so-called hadronic axions, which interact with electrons only in the first order of perturbation theory. Axions are generally thought to make up cold dark matter. In order for their density not to exceed the critical value, it is necessary to have f a< 10 12 ГэВ. Стандартный аксион Печеи-Куина с f a ≈ 250 GeV has already been excluded experimentally; other options with lower masses and, accordingly, larger coupling parameters are also significantly limited by various data, primarily astrophysical.

Supersymmetric particles

Most supersymmetric theories contain one stable particle, which is a new candidate for dark matter. The existence of a stable supersymmetric particle follows from the conservation of the multiplicative quantum number, the so-called R-parity, which takes a value of +1 for ordinary particles and –1 for their superpartners. It's there R-parity conservation law. According to this conservation law, SUSY particles can only form in pairs. SUSY particles can only decay into an odd number of SUSY particles. Therefore, the lightest supersymmetric particle must be stable.
It is possible to violate the law of conservation of R-parity. The quantum number R is related to the baryon number B and the lepton number L by the relation R = (–1) 3B+L+2S, where S is the spin of the particle. In other words, violation of B and/or L may lead to R-parity failure. However, there are very tight limits on the possibility of R-parity violation.
It is assumed that the lightest supersymmetric particle (LSP) does not participate in either electromagnetic or strong interactions. Otherwise, it would combine with ordinary matter and presently appear as an unusual heavy particle. Then the abundance of such an LSP, normalized to the abundance of the proton, would be equal to 10 -10 for the strong interaction, and 10 -6 for the electromagnetic one. These values are inconsistent with the experimental upper bounds: n(LSP)/n(p)< 10 -15 - 10 -30 . Приведенные оценки зависят от масс и в данном случае отвечают области масс 1 ГэВ < m LSP c 2 < 10 7 ГэВ. Поэтому был сделан вывод о том, что легчайшая SUSY-частица, помимо гравитационного взаимодействия, принимает участие только в слабом.
Among the possible candidates for the role of the neutral lightest supersymmetric particle are photino (S = 1/2) and zino (S = 1/2), which are usually called gaijino, as well as higgsino (S = 1/2), sneutrino (S = 0) and gravitino (S = 3/2). In most theories, an LSP particle is a linear combination of the spin-1/2 SUSY particles mentioned above. The mass of this so-called neutralino should most likely be greater than 10 GeV/c 2 . Considering SUSY particles as dark matter is of particular interest, since they appeared in a completely different context and were not specifically introduced to solve the problem of (nonbaryonic) dark matter. Cosmions Cosmions were originally introduced to solve the problem of solar neutrinos. Thanks to its high speed these particles pass through the surface of the star almost unimpeded. In the central region of the star they collide with nuclei. If the loss of energy is great enough, then they cannot leave this star again and accumulate in it over time. Inside the Sun, captured cosmions influence the nature of energy transfer and thereby contribute to the cooling of the central region of the Sun. This would result in a lower probability of neutrino production from 8 V and would explain why the neutrino flux measured on Earth is less than expected. To solve this neutrino problem, the cosmion mass must lie in the range from 4 to 11 GeV/c 2 and the cross section for the interaction of cosmions with matter must have a value of 10 -36 cm 2. However, experimental data seem to rule out such a solution to the solar neutrino problem.

Topological defects of space-time

Besides the above particles, topological defects can also contribute to dark matter. It is assumed that in the early Universe at t ≈ 10 –36 s, E ≈ 10 15 GeV, T ≈10 28 K, a violation of GUT symmetry occurred, which led to the separation of interactions described by the groups SU(3) and SU(2)×U (1). The Higgs field of dimension 24 acquired a certain alignment, and the orientation of the phase angles of spontaneous symmetry breaking remained arbitrary. As a consequence of this phase transition, spatial regions with different orientations should have formed. These areas grew larger over time and eventually came into contact with each other.
According to modern concepts, topologically stable defect points were formed on the boundary surfaces where regions with different orientations met. They could have dimensions from zero to three and consist of a vacuum of unbroken symmetry. After breaking the symmetry, this initial vacuum has a very high energy and density of matter.
The most important are the point-like defects. They must carry an isolated magnetic charge, i.e. be magnetic monopoles. Their mass is related to the phase transition temperature and is about 10 16 GeV/c 2. Until now, despite intensive searches, the existence of such objects has not been registered.
Similar to magnetic monopoles, linear defects - cosmic strings - can also form. These thread-like objects have a characteristic linear mass density of the order of 10 22 g∙cm –1 and can be either closed or open. Due to gravitational attraction, they could serve as seeds for the condensation of matter, as a result of which galaxies were formed.
Large masses would make it possible to detect such strings through the effect of gravitational lenses. The strings would bend the surrounding space in such a way that a double image of the objects behind them would be created. Light from very distant galaxies could be deflected by this string according to the laws of the general theory of gravity. An observer on Earth would see two adjacent mirror images of galaxies with identical spectral composition. This gravitational lensing effect has already been discovered for distant quasars, where a galaxy located between the quasar and Earth served as a gravitational lens.
The possibility of a superconducting state in cosmic strings is also discussed. Electrically charged particles such as electrons in the symmetrical vacuum of a string would be massless because they only acquire their masses through symmetry breaking through the Higgs mechanism. Thus, particle-antiparticle pairs moving at the speed of light can be created here with very little energy expenditure. The result is a superconducting current. Superconducting strings could become excited by interacting with charged particles, and this excitation would be removed by emitting radio waves.
Higher dimensional defects are also considered, including two-dimensional "domain walls" and, in particular, three-dimensional defects or "textures". Other exotic candidates

Shadow matter. Assuming that strings are one-dimensional extended objects, superstring theories attempt to replicate the success of supersymmetric models in eliminating divergences also in gravity and to penetrate the energy regions beyond the Planck mass. From a mathematical point of view, anomaly-free superstring theories can only be obtained for the SO(32) and E 8 *E 8" gauge groups. The latter splits into two sectors, one of which describes ordinary matter, while the other corresponds to shadow matter (E 8 "). These two sectors can only interact with each other gravitationally.
"Quark Nuggets" were proposed in 1984. These are stable macroscopic objects of quark matter, consisting of u-, d- and s-quarks. The densities of these objects lie in the nuclear density region of 10 15 g/cm 3, and the masses can range from several GeV/c 2 to the masses of neutron stars. They form during a hypothetical QCD phase transition, but are generally considered very unlikely.

3.3. Modified theories (cosmological constant, MOND theory, time-dependent gravitational constant)

Initially, the cosmological constant Λ was introduced by Einstein into the field equations of general relativity to ensure, according to the views of that time, the stationarity of the Universe. However, after Hubble discovered the expansion of the Universe at the end of the 20s of our century, it turned out to be unnecessary. Therefore, they began to believe that Λ = 0. However, within the framework modern theories field, this cosmological constant is interpreted as the vacuum energy density ρ v . The following equation holds:

The case Λ = 0 corresponds to the assumption that vacuum does not contribute to the energy density. This picture corresponds to the ideas of classical physics. In quantum field theory, the vacuum contains various quantum fields that are in a state with the lowest energy, which is not necessarily zero.
Taking into account the non-zero cosmological constant, using the relations

we obtain a lower critical density and higher value density parameter than expected according to the formulas given above. Astronomical observations based on galaxy counts provide an upper bound for the modern cosmological constant
Λ < 3·10 -56 см –2 . Поскольку критическая плотность ρ с0 не может быть отрицательной, легко оценить верхнюю границу

where for H 0,max the value of 100 km∙s –1 ∙Mpc –1 is used. While a non-zero cosmological constant has proven necessary to interpret the early phase of evolution, some scientists have concluded that a non-zero Λ could play a role in later stages of the universe's development.
Cosmological constant

could lead to the value Ω(Λ = 0), although in fact Ω(Λ ≠ 0). The parameter Ω(Λ = 0) defined from ρ 0 would provide Ω = 1, as required in inflationary models, provided that the cosmological constant is

Using the numerical values H 0 = 75 ± 25 km∙s −1 ∙Mpc −1 and Ω 0,obs = 0.2 ± 0.1 leads to
Λ= (1.6 ± 1.1)∙10 −56 cm −2. A vacuum energy density corresponding to this value could resolve the contradiction between the observed value of the density parameter and the value Ω = 1 required by modern theories.
In addition to introducing a nonzero cosmological constant, there are other models that remove at least some of the problems without involving the dark matter hypothesis.

MOND Theory (Modified Newtonian Dynamics)

This theory assumes that the law of gravity differs from the usual Newtonian form and is as follows:

In this case, the attractive force will be greater and must be compensated by a faster periodic motion, which can explain the flat behavior of the rotation curves.

Time dependent gravitational constant

The time dependence of the gravitational constant G(t) could be of great importance for the process of galaxy formation. However, so far precision measurements have not given any indication of the temporal variation of G.

Literature