It is somewhat of an irony of nature that the most abundant form of energy in the Universe is also the most mysterious. After the stunning discovery of the accelerating expansion of the Universe, a consistent picture quickly emerged indicating that 2/3 of the cosmos is “made” of “dark energy” - some kind of gravitationally repulsive material. But is the evidence convincing enough to support these exotic new laws of nature? Maybe there are simpler astrophysical explanations for these results?
The prototype of this note was recently published in the popular science section of Habr, although under lock and key, so perhaps not everyone interested got it. In this version, quite significant additions have been made, which should be of interest to everyone.
The history of dark energy began in 1998, when two independent teams explored distant supernovae. in order to detect the rate at which the expansion of the Universe is slowing down. One of them, Supernova Cosmology Project, began work in 1988, and was led by Saul Perlmutter. Another, led by Brian Schmidt High-z Supernova Search Team, joined the research in 1994. The result shocked them: the Universe has been in an accelerated expansion mode for quite a long time.
Like detectives, cosmologists around the world were compiling a dossier on the accused responsible for the acceleration. Its special features: gravitationally repulsive, prevents the formation of galaxies (clustering of matter into galaxies), manifests itself in the stretching of space-time. The nickname of the accused is “dark energy.” Many theorists have suggested that the accused is a cosmological constant. It certainly corresponded to the scenario of accelerated expansion. But was there enough evidence to fully identify dark energy with the cosmological constant?
The existence of gravitational-repulsive dark energy would have dramatic consequences for fundamental physics. The most conservative assumption was that the Universe is filled with a homogeneous sea quantum energy zero-point vibrations or a condensate of new particles whose mass is $((10)^(39))$ times less than an electron. Some researchers have also suggested the need for change general theory relativity, in particular, new long-range forces that weaken the effect of gravity. But even the most conservative proposals had serious shortcomings. For example, the zero-point energy density turned out to be 120 implausible orders of magnitude less than theoretical predictions. From the point of view of these extreme assumptions, it seemed more natural to look for a solution within the framework of traditional astrophysical concepts: intergalactic dust (the scattering of photons on it and the associated weakening of the photon flux) or the difference between new and old supernovae. This possibility has been supported by many cosmologists keeping watch in the night.
Observations of supernovae and their analysis carried out by S. Perlmutter, B. Schmidt and A. Riess made it clear that the decrease in their brightness with distance occurs noticeably faster than would be expected according to the cosmological models accepted at that time. More recently, this discovery was noted. This additional dimming means that a given redshift corresponds to some effective distance addition. But this, in turn, is possible only when the cosmological expansion occurs with acceleration, i.e. The speed at which the light source moves away from us does not decrease, but increases with time. The most important feature of the new experiments was that they made it possible not only to determine the very fact of accelerated expansion, but also to draw an important conclusion about the contribution of various components to the density of matter in the Universe.
Until recently, supernovae were the only direct evidence of accelerated expansion and the only convincing support for dark energy. Accurate measurements of the cosmic microwave background, including WMAP (Wilkinson Microwave Anisotropy Probe) data, have provided independent confirmation of the reality of dark energy. The same was confirmed by data from two more powerful projects: the large-scale distribution of galaxies in the Universe and the Sloan Digital Sky Survey (SDSS).
A combination of data from WMAP, SDSS and other sources found that the gravitational repulsion generated by dark energy is slowing the collapse of super-dense regions of matter in the Universe. The reality of dark energy immediately became significantly more acceptable.
Space expansion
Cosmic expansion was discovered by Edwin Hubble in the late 1920s and may be the most important feature of our Universe. Not only astronomical bodies move under the influence gravitational interaction their neighbors, but large-scale structures are also stretched to an even greater extent by cosmic expansion. A popular analogy is the movement of raisins in a very large cake in the oven. As the pie rises, the distance between any pair of raisins embedded in the pie increases. If we imagine that one particular highlight represents our galaxy, then we will find that all other highlights (galaxies) are moving away from us in all directions. Our Universe expanded from the hot, dense cosmic soup created by the Big Bang into the much cooler, thinner collection of galaxies and galaxy clusters we see today.
Light emitted by stars and gas in distant galaxies is similarly stretched, lengthening its wavelength as it travels to Earth. This shift in wavelength is given by the redshift $z=\left(\lambda_(obs)-\lambda_0\right)/\lambda_0$, where $\lambda_(obs)$ is the length of light on Earth and $\lambda_(0) $ is the wavelength of the emitted light. For example, the Lyman alpha transition in the hydrogen atom is characterized by a wavelength of $\lambda_0=121.6$ nanometers (when returning to the ground state). This transition can be detected in the radiation of distant galaxies. In particular, it was used to detect a record high redshift: a stunning z=10 with the Lyman alpha line at $\lambda_(obs)=1337.6$ nanometers. But redshift describes only the change in cosmic scale as light is emitted and absorbed, and does not provide direct information about the distance to the emitter or the age of the universe when the light was emitted. If we know both the distance to the object and the redshift, we can try to get important information about the dynamics of the expansion of the Universe.
Observations supernovas discovered some gravitational-repulsive substance that controls the acceleration of the Universe. This is not the first time that astronomers have encountered the problem of missing matter. The luminous masses of galaxies turned out to be significantly smaller than the gravitating masses. This difference was made up by dark matter - cold, non-relativistic matter, probably mostly composed of particles that interact weakly with atoms and light.
However, observations indicated that the total amount of matter in the Universe, including dark matter, is only 1/3 of total energy. This has been confirmed by the study of millions of galaxies within the 2DF and SDSS projects. But general relativity predicts that there is a precise relationship between expansion and the energy content of the universe. We therefore know that the total energy density of all photons, atoms and dark matter must be supplemented to some critical value determined by the Hubble constant $H_(0)$: $((\rho)_(crit))=3H_(0)^(2)/8\pi\cdot(G)$. The catch is that it doesn't, but that's a completely different story.
Mass, energy and space-time curvature are directly related in general relativity. One explanation, therefore, may be that the gap between the critical density and the observed matter density is filled by some energy density associated with the deformation of space at large scales and observable only at scales on the order of $c/((H)_(0)) \sim 4000\ Mpc$. Fortunately, the curvature of the Universe can be determined using precision ICF measurements. A relic, with an origin 400,000 after the Big Bang, the ICF is black body radiation, the source of which is the primordial plasma. When the Universe cooled below $3000\K$, the plasma became transparent to photons and they were able to freely propagate in space. Today, almost 15 billion years later, we observe a thermal reservoir of photons at a temperature of $2.726\K$, which represents the result of a redshift due to cosmic expansion.
A remarkable image of the ICF was obtained using the WMAP satellite, showing the slightest changes in the photon temperature of the “sky”. These variations, known as ICF anisotropy, reflect small variations in the density and motion of the early Universe. These variations, which arise at the $((10)^(-5))$ level, are the seeds of the large-scale structure (galaxies, clusters) that we observe today.
The coldest/hottest spots in the cosmic microwave background are due to photons that escaped from areas of the highest/least density gravitational potential. The dimensions of these regions are well determined by plasma physics. When we consider the complete universe, the apparent angular size of these anisotropies should be about $((0.5)^(0))$ if the Universe has sufficient curvature to fill the energy gap and twice the angular sizes in the absence of any curvature of space. The easiest way to visualize this geometric effect is to imagine a triangle with a fixed base and sides (just sides?), drawn on surfaces of varying curvature. For a saddle surface/sphere, the interior angles will be smaller/larger than the same triangle drawn on a flat surface (with Euclidean geometry).
Since 1999 it has been held whole line experiments (TOCO, MAXIMA, BOOMERANG, WMAP), which showed that the MCF spots have sizes of the order of $((1)^(0))$. This means that the geometry of the Universe is flat. From the perspective of the missing energy problem, this means that something other than curvature must be responsible for filling the gap. To some cosmologists, this result looked like déjà vu. Inflation, best theory The ICF origin of primordial fluctuations suggests that the very early Universe experienced a period of accelerated expansion that was driven by a particle called an inflaton. The inflaton would stretch out any large-scale curvature, making the geometry of the universe flat or Euclidean. The evidence suggests the existence of a form of energy that prevents galaxy clustering, which is gravitationally repulsive, and which may be due to a particle other than the inflaton.
Cosmic harmony
CMB and supernova data have consistently confirmed that the source of cosmic acceleration is dark energy. But that was only the beginning. By combining precision ICF measurements from WMAP with radio, optical and X-ray sensing of large-scale matter distributions, astrophysicists have obtained further evidence of an accelerating rate of expansion of the Universe. It turned out that the gravitational potential holes of density and compaction in the Universe were stretched and smoothed over time, as if under the influence of repulsive gravity. This effect is known as the integral effect (Sachs-Wolfe (ISW)). It leads to a correlation between temperature anisotropy in the CMB and the large-scale structure of the Universe. Although the primordial plasma became transparent to photons as the Universe cooled, photons do not travel unimpeded. Space is riddled with irregularities that are strong at short distances (where matter clusters into stars, galaxies and nebulae) and gradually weaken over large length scales... During their flight, photons fall into and out of gravitational holes.
After cosmic rays were first detected (about 40 years ago), Sachs and Wolff showed that a time-varying potential should result in an energy shift in the ICF of photons passing through it. A photon gains energy when it falls into a gravitational hole and spends it when it gets out of it. If the potential became deeper during this process, then the photon as a whole would therefore lose energy. If the potential becomes shallower, the photon will gain energy.
In a Universe where the full critical density is formed only by atoms and dark matter, weak gravitational potentials at very large spatial scales (which correspond to gentle waves of matter density) evolve too slowly to leave noticeable traces in ICF photons. Denser regions simply absorb surrounding matter at the same rate at which cosmic expansion lengthens the waves, leaving the potential unchanged. However, with more rapid expansion With a universe driven by dark energy, matter accretion cannot compete with stretching. Effectively, the gravitational collapse is slowed down by repulsive dark matter. Consequently, the gravitational potential tends to flatten and photons gain energy when passing through these areas. Likewise, photons lose energy when passing through regions of low density. (Not trivial!)
Negative pressure
The greatest mystery of cosmic acceleration is not that it implies that 2/3 of the substance filling the Universe is not visible to us, but that it imposes the existence of matter with gravitational repulsion. To consider this strange property of dark energy, it is useful to introduce the quantity $w=((p)_(dark))/((\rho )_(dark))$. This expression resembles the equation of state of a gas. In general relativity, the rate of change of cosmic expansion is proportional to $-\left(((\rho )_(total))+3((p)_(total)) \right)$. For accelerated expansion this value must be positive. Since $((\rho )_(total))$ is positive, and the average pressure of ordinary and dark matter is negligible (because it is cold and non-relativistic), we arrive at the requirement $3w\times ((\rho )_(dark ))+((\rho )_(total))
Why does pressure affect the expansion of the Universe? Einstein showed that matter and energy bend space-time. Therefore, for a hot gas, the kinetic energy of its atoms contributes to their gravitational forces, as measured by measuring the acceleration of distant bodies. However, the forces required to contain or isolate the gas work against this excess pressure. The universe on the other hand is neither isolated nor limited. The expansion of space filled with hot gas will effectively occur more slowly (due to self-gravity) than the expansion of a universe filled with cold gas. By the same logic, a medium with such negative pressure that $((\rho )_(total))+3p
Negative pressure is not such a rare occurrence. Water pressure in some tall trees becomes negative as nutrition rises through their vascular system. In a uniform electric or magnetic field, configurations with negative pressure can also be found. In these cases, the pressure is something like a stretched spring under tension caused by internal forces. At the microscopic level, the reservoir of Higgs bosons (the hypothetical particles that generate particle mass in the Standard Model) creates negative pressure when its thermal or kinetic excitations are small. Indeed, the inflaton can be considered as a heavy version of the Higgs boson. One proposed version of dark energy—quintessence—may even be a lighter version of the Higgs.
In principle, there is no lower limit to pressure in the Universe. Although strange things happen if $w$ drops to a value less than $-1.$ Isolated pieces of such material can have negative mass. …..But one thing is obvious. Such a strong negative pressure does not occur for normal particles and fields in general relativity. Numerous observations lead to a narrower range of dark energy parameters than those that follow from the above general reasoning.
Combination of different predictions theoretical models And best observations cosmic microwave background radiation, large-scale structures and supernovae lead to $$\Omega_(dark)= 0.728^(+0.015)_(-0.016)$$ $$w= -0.980\pm0.053 $$
A Brief History of Dark Energy
Dark energy, or something similar to it, has appeared many times in the history of cosmology. Pandora's box was opened by Einstein, who introduced into his equations gravitational field. Cosmic expansion had not yet been discovered and the equations correctly “suggested” that the Universe containing matter could not be static without the mathematical addition of the cosmological constant, which is usually denoted by $\Lambda$. The effect is equivalent to filling the Universe with sea negative energy, in which stars and nebulae drift. The discovery of the extension eliminated the need for this ad hoc addition to the theory.
In subsequent decades, desperate theorists periodically introduced $\Lambda$ in an attempt to explain new astronomical phenomena. These returns were always short-lived and usually resulted in more plausible explanations for the data obtained. However, since the 60s, the idea began to emerge that the vacuum (zero) energy of all particles and fields should inevitably generate a term similar to $\Lambda$. In addition, there is reason to believe that the cosmological constant could naturally arise in the early stages of the evolution of the Universe.
In 1980, the theory of inflation was developed. In this theory, the early Universe experienced a period of accelerated exponential expansion. The expansion was obliged negative pressure, due to the new particle – . Inflaton proved to be very successful. He allowed a lot. These paradoxes include the problems of the horizon and the flatness of the Universe. The theory's predictions were in good agreement with various cosmological observations.
Dark energy and the future of the Universe
With the discovery of dark energy, ideas about what the distant future of our Universe might be like have changed dramatically. Before this discovery, the question of the future was clearly associated with the question of curvature three-dimensional space. If, as many previously believed, the curvature of space determined 2/3 modern pace expansion of the Universe, and there was no dark energy, then the Universe would expand without limit, gradually slowing down. Now it is clear that the future is determined by the properties of dark energy.
Since we know these properties poorly now, we cannot yet predict the future. You can only consider different options. It is difficult to say what is happening in theories with new gravity, but other scenarios can be discussed now. If dark energy is constant over time, as is the case with vacuum energy, then the Universe will always experience accelerated expansion. Most galaxies will eventually move away from ours to an enormous distance, and our Galaxy, along with its few neighbors, will turn out to be an island in the void. If dark energy is quintessential, then in the distant future the accelerated expansion may stop and even be replaced by compression. IN the latter case The Universe will return to a state with hot and dense matter, a “Big Bang in reverse” will occur, back in time.
Energy budget of our Universe. It is worth paying attention to the fact that the share of familiar matter (planets, stars, the entire world around us) accounts for only 4 percent, the rest is made up of “dark” forms of energy.
An even more dramatic fate awaits the Universe if dark energy is a phantom, and such that its energy density increases without limit. The expansion of the Universe will become more and more rapid, it will accelerate so much that galaxies will be torn out of clusters, stars from galaxies, planets from solar system. Things will get to the point where electrons will break away from atoms, and atomic nuclei split into protons and neutrons. There will be, as they say, a big break.
Such a scenario, however, does not seem very likely. Most likely, the phantom's energy density will remain limited. But even then, the Universe may face an unusual future. The fact is that in many theories, phantom behavior - an increase in energy density over time - is accompanied by instabilities. In this case, the phantom field in the Universe will become highly inhomogeneous, its energy density in different parts of the Universe will be different, some parts will rapidly expand, and some may experience collapse. The fate of our Galaxy will depend on which region it falls into.
All this, however, relates to the future, distant even by cosmological standards. In the next 20 billion years, the Universe will remain almost the same as it is now. We have time to understand the properties of dark energy and thereby more definitely predict the future - and perhaps influence it.
Just a hundred years ago, scientists discovered that our Universe is rapidly increasing in size.
A hundred years ago, ideas about the Universe were based on Newtonian mechanics and Euclidean geometry. Even a few scientists, such as Lobachevsky and Gauss, who admitted (only as a hypothesis!) physical reality non-Euclidean geometry, considered outer space eternal and unchanging
In 1870, the English mathematician William Clifford came to a very profound idea that space can be curved, and unequally at different points, and that over time its curvature can change. He even admitted that such changes were somehow related to the movement of matter. Both of these ideas, many years later, formed the basis of the general theory of relativity. Clifford himself did not live to see this - he died of tuberculosis at the age of 34, 11 days before Albert Einstein was born.
Redshift
The first information about the expansion of the Universe was provided by astrospectrography. In 1886, English astronomer William Huggins noticed that the wavelengths of starlight were slightly shifted compared to the terrestrial spectra of the same elements. Based on the formula for the optical version of the Doppler effect, derived in 1848 by the French physicist Armand Fizeau, the radial velocity of a star can be calculated. Such observations make it possible to track the movement of a space object.
Just a hundred years ago, ideas about the Universe were based on Newtonian mechanics and Euclidean geometry. Even a few scientists, such as Lobachevsky and Gauss, who assumed (only as a hypothesis!) the physical reality of non-Euclidean geometry, considered outer space eternal and unchanging. Due to the expansion of the Universe, it is not easy to judge the distance to distant galaxies. The light that arrived 13 billion years later from the galaxy A1689-zD1, 3.35 billion light years away (A), “reddens” and weakens as it travels through expanding space, and the galaxy itself moves away (B). It will carry information about the distance in redshift (13 billion light years), in angular size (3.5 billion light years), in intensity (263 billion light years), while the real distance is 30 billion light years. years.
A quarter of a century later, this opportunity was used in a new way by Vesto Slifer, an employee of the observatory in Flagstaff in Arizona, who, since 1912, had been studying the spectra of spiral nebulae with a 24-inch telescope with a good spectrograph. To obtain a high-quality image, the same photographic plate was exposed for several nights, so the project moved slowly. From September to December 1913, Slipher studied the Andromeda nebula and, using the Doppler-Fizeau formula, came to the conclusion that it was approaching the Earth by 300 km every second.
In 1917, he published data on the radial velocities of 25 nebulae, which showed significant asymmetries in their directions. Only four nebulae approached the Sun, the rest ran away (and some very quickly).
Slifer did not seek fame and did not promote his results. Therefore, they became known in astronomical circles only when the famous British astrophysicist Arthur Eddington drew attention to them.
In 1924, he published a monograph on the theory of relativity, which included a list of the radial velocities of 41 nebulae found by Slipher. The same four blue-shifted nebulae were present there, while the remaining 37 had spectral lines red-shifted. Their radial velocities varied between 150 and 1800 km/s and were on average 25 times higher than the known velocities of the Milky Way stars at that time. This suggested that nebulae participate in different movements than “classical” luminaries.
Space Islands
In the early 1920s, most astronomers believed that spiral nebulae were located on the periphery of the Milky Way, and beyond there was nothing but empty, dark space. True, back in the 18th century, some scientists saw giant star clusters in nebulae (Immanuel Kant called them island universes). However, this hypothesis was not popular, since it was impossible to reliably determine the distances to the nebulae.
This problem was solved by Edwin Hubble, working on the 100-inch reflecting telescope at California's Mount Wilson Observatory. In 1923-1924, he discovered that the Andromeda nebula consists of many luminous objects, including variable stars of the Cepheid family. It was already known then that the period of change in their visible brightness is associated with absolute luminosity, and therefore Cepheids are suitable for calibrating cosmic distances. With them using Hubble estimated the distance to Andromeda at 285,000 parsecs (according to modern data, it is 800,000 parsecs). The diameter of the Milky Way was then believed to be approximately 100,000 parsecs (in reality it is three times less). It followed that Andromeda and the Milky Way must be considered independent star clusters. Hubble soon identified two more independent galaxies, which finally confirmed the “island universes” hypothesis.
To be fair, it is worth noting that two years before Hubble, the distance to Andromeda was calculated by the Estonian astronomer Ernst Opik, whose result - 450,000 parsecs - was closer to the correct one. However, he used a number of theoretical considerations that were not as convincing as Hubble's direct observations.
By 1926, Hubble had conducted statistical analysis observations of four hundred “extragalactic nebulae” (he used this term for a long time, avoiding calling them galaxies) and proposed a formula to relate the distance to a nebula with its apparent brightness. Despite the enormous errors of this method, new data confirmed that nebulae are distributed more or less evenly in space and are located far beyond the boundaries of the Milky Way. Now there was no longer any doubt that space is not limited to our Galaxy and its closest neighbors.
Space fashion designers
Eddington became interested in Slipher's results even before the nature of spiral nebulae was finally clarified. By this time, a cosmological model already existed, which in a certain sense predicted the effect identified by Slipher. Eddington thought a lot about it and, naturally, did not miss the opportunity to give the observations of the Arizona astronomer a cosmological sound.
Modern theoretical cosmology began in 1917 with two revolutionary papers presenting models of the universe based on general relativity. One of them was written by Einstein himself, the other by the Dutch astronomer Willem de Sitter.
Hubble's laws
Edwin Hubble empirically discovered the approximate proportionality of redshifts and galactic distances, which he turned into a proportionality between velocities and distances using the Doppler-Fizeau formula. So we are dealing with two different patterns here.
Hubble didn't know how they were related to each other, but what does today's science say about it?
As Lemaître also showed, the linear correlation between cosmological (caused by the expansion of the Universe) redshifts and distances is by no means absolute. In practice, it is well observed only for displacements less than 0.1. So the empirical Hubble law is not exact, but approximate, and the Doppler-Fizeau formula is valid only for small shifts of the spectrum.
And here theoretical law, which connects the radial velocity of distant objects with the distance to them (with a proportionality coefficient in the form of the Hubble parameter V=Hd), is valid for any redshift. However, the speed V that appears in it is not at all the speed of physical signals or real bodies in physical space. This is the rate of increase in distances between galaxies and galaxy clusters, which is caused by the expansion of the Universe. We would be able to measure it only if we were able to stop the expansion of the Universe, instantly stretch measuring tapes between galaxies, read the distances between them and divide them into time intervals between measurements. Naturally, the laws of physics do not allow this. Therefore, cosmologists prefer to use the Hubble parameter H in another formula, which includes the scale factor of the Universe, which precisely describes the degree of its expansion in different cosmic epochs (since this parameter changes with time, its modern meaning denote H0). The Universe is now expanding at an accelerating rate, so the value of the Hubble parameter is increasing.
By measuring cosmological redshifts, we obtain information about the extent of expansion of space. The light of the galaxy, which came to us with a cosmological redshift z, left it when all cosmological distances were 1+z times smaller than in our era. Additional information about this galaxy, such as its current distance or speed of removal from the Milky Way, can only be obtained using a specific cosmological model. For example, in the Einstein-de Sitter model, a galaxy with z = 5 is moving away from us at a speed equal to 1.1 s (the speed of light). But if you make a common mistake and simply equalize V/c and z, then this speed will turn out to be five times greater than light speed. The discrepancy, as we see, is serious.
Dependence of the speed of distant objects on redshift according to STR, GTR (depends on the model and time, the curve shows the present time and the current model). At small displacements the dependence is linear.
Einstein, in the spirit of the times, believed that the Universe as a whole was static (he also tried to make it infinite in space, but could not find the correct border conditions for your equations). As a result, he built a model of a closed Universe, the space of which has a constant positive curvature (and therefore it has a constant finite radius). Time in this Universe, on the contrary, flows like Newton, in one direction and at the same speed. The space-time of this model is curved due to the spatial component, while the time component is not deformed in any way. The static nature of this world provides a special “insert” into the main equation, which prevents gravitational collapse and thereby acts as an omnipresent anti-gravity field. Its intensity is proportional to a special constant, which Einstein called universal (now called the cosmological constant).
Lemaître's cosmological model of the expansion of the Universe was far ahead of its time. Lemaître's universe begins with the Big Bang, after which the expansion first slows down and then begins to accelerate.
Einstein's model made it possible to calculate the size of the Universe, the total amount of matter, and even the value of the cosmological constant. To do this, you only need an average density cosmic matter, which, in principle, can be determined from observations. It is no coincidence that Eddington admired this model and used it in practice by Hubble. However, it is destroyed by instability, which Einstein simply did not notice: at the slightest deviation of the radius from the equilibrium value, Einstein’s world either expands or undergoes gravitational collapse. Therefore, this model has no relation to the real Universe.
Empty world
De Sitter also built, as he himself believed, a static world of constant curvature, but not positive, but negative. It contains Einstein's cosmological constant, but completely lacks matter. When test particles of arbitrarily small mass are introduced, they scatter and go to infinity. In addition, time flows more slowly at the periphery of the de Sitter universe than at its center. Because of this, light waves from large distances arrive with a red shift, even if their source is stationary relative to the observer. So in the 1920s, Eddington and other astronomers wondered whether de Sitter's model had anything in common with the reality reflected in Slipher's observations.
These suspicions were confirmed, albeit in a different way. The static nature of the de Sitter universe turned out to be imaginary, since it was associated with an unsuccessful choice of the coordinate system. After correcting this error, de Sitter space turned out to be flat, Euclidean, but non-static. Thanks to the antigravitational cosmological constant, it expands while maintaining zero curvature. Because of this expansion, the wavelengths of photons increase, which entails the shift of spectral lines predicted by de Sitter. It is worth noting that this is how the cosmological redshift of distant galaxies is explained today.
From statistics to dynamics
The history of openly non-static cosmological theories begins with two works Soviet physicist Alexander Friedman, published in German magazine Zeitschrift fur Physik in 1922 and 1924. Friedman calculated models of universes with time-varying positive and negative curvature, which became the golden fund of theoretical cosmology. However, contemporaries hardly noticed these works (Einstein at first even considered Friedman’s first paper to be mathematically erroneous). Friedman himself believed that astronomy does not yet have an arsenal of observations that would allow one to decide which of the cosmological models is more consistent with reality, and therefore limited himself to pure mathematics. Perhaps he would have acted differently if he had read Slifer's results, but this did not happen.
The largest cosmologist of the first half of the 20th century, Georges Lemaitre, thought differently. At home, in Belgium, he defended his dissertation in mathematics, and then in the mid-1920s he studied astronomy - at Cambridge under the direction of Eddington and at the Harvard Observatory under Harlow Shapley (while in the USA, where he prepared a second dissertation at MIT, he met Slifer and Hubble). Back in 1925, Lemaître was the first to show that the static nature of de Sitter’s model was imaginary. Upon his return to his homeland as a professor at the University of Louvain, Lemaitre built the first model of an expanding universe with a clear astronomical basis. Without exaggeration, this work was a revolutionary breakthrough in space science.
Universal revolution
In his model, Lemaitre retained a cosmological constant with an Einsteinian numerical value. So his universe begins static state, but over time, due to fluctuations, it enters a path of constant expansion at an increasing speed. At this stage it maintains a positive curvature, which decreases as the radius increases. Lemaitre included in the composition of his universe not only matter, but also electromagnetic radiation. Neither Einstein nor de Sitter, whose work was known to Lemaitre, nor Friedman, about whom he knew anything at that time, did this.
Associated coordinates
In cosmological calculations it is convenient to use accompanying coordinate systems, which expand in unison with the expansion of the Universe. In an idealized model, where galaxies and galaxy clusters do not participate in any proper motions, their accompanying coordinates do not change. But the distance between two objects at a given moment in time is equal to their constant distance in accompanying coordinates, multiplied by the value of the scale factor for this moment. This situation can be easily illustrated on an inflatable globe: the latitude and longitude of each point do not change, and the distance between any pair of points increases with increasing radius.
Using comoving coordinates helps us understand the profound differences between expanding universe cosmology, special relativity, and Newtonian physics. Thus, in Newtonian mechanics all movements are relative, and absolute immobility has no physical meaning. On the contrary, in cosmology, immobility in comoving coordinates is absolute and, in principle, can be confirmed by observations. The special theory of relativity describes processes in space-time, from which we can use Lorentz transformations infinite number ways to isolate spatial and temporal components. Cosmological space-time, on the contrary, naturally breaks up into a curved expanding space and a single cosmic time. In this case, the speed of retreat of distant galaxies can be many times higher than the speed of light.
Lemaitre, back in the USA, suggested that the redshifts of distant galaxies arise due to the expansion of space, which “stretches” light waves. Now he has proven it mathematically. He also demonstrated that small (much smaller units) redshifts are proportional to the distances to the light source, and the proportionality coefficient depends only on time and carries information about the current rate of expansion of the Universe. Since the Doppler-Fizeau formula implied that the radial speed of a galaxy is proportional to its redshift, Lemaître came to the conclusion that this speed is also proportional to its distance. After analyzing the speeds and distances of 42 galaxies from Hubble's list and taking into account the intragalactic speed of the Sun, he established the values of the proportionality coefficients.
Unsung work
Lemaitre published his work in 1927 on French in the little-read magazine “Annals of the Brussels scientific society" It is believed that this was the main reason why she initially went virtually unnoticed (even by his teacher Eddington). True, in the fall of the same year, Lemaitre was able to discuss his findings with Einstein and learned from him about Friedman’s results. The creator of General Relativity had no technical objections, but he resolutely did not believe in the physical reality of Lemetre’s model (just as he had previously not accepted Friedman’s conclusions).
Hubble graphs
Meanwhile, in the late 1920s, Hubble and Humason discovered a linear correlation between the distances of 24 galaxies and their radial velocities, calculated (mostly by Slipher) from redshifts. Hubble concluded from this that the radial speed of a galaxy is directly proportional to its distance. The coefficient of this proportionality is now denoted by H0 and is called the Hubble parameter (according to the latest data, it slightly exceeds 70 (km/s)/megaparsec).
Hubble's paper plotting the linear relationship between galactic velocities and distances was published in early 1929. A year earlier, the young American mathematician Howard Robertson, following Lemaitre, derived this dependence from the model of an expanding Universe, which Hubble may have known about. However, his famous article did not mention this model either directly or indirectly. Hubble later expressed doubts that the velocities appearing in his formula actually describe the movements of galaxies in outer space, but he always refrained from their specific interpretation. He saw the meaning of his discovery in demonstrating the proportionality of galactic distances and redshifts, leaving the rest to theorists. Therefore, with all due respect to Hubble, there is no reason to consider him the discoverer of the expansion of the Universe.
And yet it is expanding!
Nevertheless, Hubble paved the way for the recognition of the expansion of the Universe and Lemaître's model. Already in 1930, such masters of cosmology as Eddington and de Sitter paid tribute to her; A little later, scientists noticed and appreciated Friedman’s work. In 1931, at the instigation of Eddington, Lemaitre translated his article into English (with small cuts) for the Monthly News of the Royal Astronomical Society. In the same year, Einstein agreed with Lemaître’s conclusions, and a year later, together with de Sitter, he built a model of an expanding Universe with flat space and curved time. This model, due to its simplicity, has been very popular among cosmologists for a long time.
In the same 1931, Lemaitre published a brief (and without any mathematics) description of another model of the Universe, which combined cosmology and quantum mechanics. In this model, the initial moment is the explosion of the primary atom (Lemaitre also called it a quantum), which gave rise to both space and time. Since gravity slows down the expansion of the newborn Universe, its speed decreases - perhaps almost to zero. Lemaitre later introduced a cosmological constant into his model, which forced the Universe to eventually enter a stable regime of accelerating expansion. So he anticipated both the idea of the Big Bang and modern cosmological models that take into account the presence of dark energy. And in 1933, he identified the cosmological constant with the energy density of the vacuum, which no one had ever thought of before. It’s simply amazing how ahead of his time this scientist, certainly worthy of the title of discoverer of the expansion of the Universe, was!
Our Sun and the stars closest to it form part of a vast star cluster called our Galaxy, or Milky Way. For a long time it was believed that this was the entire Universe. And only in 1924, the American astronomer Edwin Hubble showed that our Galaxy is not the only one. There are many other galaxies, separated by giant stretches of empty space. To prove this, Hubble had to measure distances to other galaxies. We can determine the distances to the nearest stars by recording changes in their position in the firmament as the Earth revolves around the Sun. But, unlike nearby stars, other galaxies are so far away that they appear motionless. Therefore, Hubble was forced to use indirect methods for measuring distances.
Currently, the apparent brightness of stars depends on two factors - actual luminosity and distance from Earth. For the closest stars, we can measure both the apparent brightness and distance, which allows us to calculate their luminosity. Conversely, knowing the luminosity of stars in other galaxies, we can calculate their distance by measuring their brightness. Hubble argued that certain types of stars always have the same luminosity when they are located at distances close enough to us to allow measurements. Having discovered similar stars in another galaxy, we can assume that they have the same luminosity. This will allow us to calculate the distances to another galaxy. If we do this for several stars in a galaxy and the resulting values coincide, then we can be quite confident in our results. In a similar way Edwin Hubble was able to calculate the distances to nine different galaxies.
Today we know that our Galaxy is only one of several hundred billion galaxies observed with modern telescopes, each of which may contain hundreds of billions of stars. We live in a Galaxy whose diameter is about one hundred thousand light years. It rotates slowly, and the stars in its spiral arms make about one revolution around its center every hundred million years. Our Sun is the most ordinary, medium-sized yellow star near the outer edge of one of the spiral arms. Undoubtedly, we have come a long way since the times of Aristotle and Ptolemy, when the Earth was considered the center of the Universe.
The stars are so far away from us that they appear to be just tiny points of light. We cannot distinguish their size or shape. How do scientists classify them? For the vast majority of stars, only one parameter that can be observed is reliably determined - their color.
radiation. Newton discovered that sunlight passed through a prism splits into its constituent set of colors (spectrum), the same as that of a rainbow. By focusing a telescope on a specific star or galaxy, you can observe the spectrum of light from that object. Different stars have different spectra, but the relative brightness of individual colors in the spectrum almost always corresponds to that which can be detected in the glow of very hot objects. This allows one to calculate its temperature from the spectrum of a star. Moreover, in the spectrum of a star one can detect the absence of some specific colors, and these colors are different for each star. It is known that each chemical element absorbs a set of colors characteristic of it. Thus, by identifying lines that are missing in the star's emission spectrum, we can accurately determine which chemical elements are contained in its outer layer.
Started in the 1920s. to study the spectra of stars in other galaxies, astronomers discovered amazing fact: They lacked the same set of color lines as the stars in our Galaxy, but all the lines were shifted by the same amount towards the red part of the spectrum. The only reasonable explanation was that galaxies are moving away from us and this causes a decrease in the frequency of light waves (the so-called red shift) due to the Doppler effect.
Listen to the noise of cars on the highway. As the car gets closer to you, the sound of its engine becomes higher in accordance with the frequency of the sound waves and becomes lower as the car moves away. The same thing happens with light or radio waves. Indeed, the Doppler effect is used by traffic police, determining the speed of a car by changing the frequency of the sent and received radio signal (the frequency shift depends on the speed of the reflecting object, that is, the car).
After Hubble discovered the existence of other galaxies, he began compiling a catalog of their distances and observing their spectra. At that time, many believed that galaxies moved completely chaotically and, therefore, in the same number of them, spectra should be found that had both a red shift and a blue shift. Imagine the general surprise when it was discovered that all galaxies exhibit a red shift. Each of them moves away from us. Even more striking were the results published by Hubble in 1929: even the redshift value of each galaxy is not random, but is proportional to the distance between the galaxy and the Solar system. In other words, the farther a galaxy is from us, the faster it is moving away.
This meant that the Universe could not possibly be stationary, as was previously thought; in fact, it was expanding. The distances between galaxies are constantly growing. The discovery that the Universe is expanding became one of the main intellectual revolutions of the 20th century. Looking back, it's easy to wonder why no one thought of this before. Newton and others should have realized that a stationary Universe would quickly collapse under the influence of gravity. But imagine that the Universe is not stationary, but expanding. At low expansion rates, the force of gravity would sooner or later stop it and begin compression. However, if the expansion rate exceeded a certain critical value, then the gravitational force would not be enough to stop it and the Universe would expand forever. Something similar happens when a rocket is launched.
from the surface of the Earth. If the rocket does not reach the required speed, gravity will stop it and it will begin to fall back. On the other hand, at a speed above a certain critical value (about 11.2 km/s), gravitational forces will not be able to hold the rocket near the Earth, and it will forever move away from our planet.
Such behavior of the Universe could be predicted based on Newton's law universal gravity back in the 19th century, and in the 18th century, even at the end of the 17th century. However, the belief in a stationary Universe was so unshakable that it lasted until the beginning of the 20th century. Einstein himself, in 1915, when he formulated the general theory of relativity, remained convinced of the stationary nature of the Universe. Unable to part with this idea, he even modified his theory by introducing the so-called cosmological constant into the equations. This value characterized a certain antigravity force, which, unlike all other physical forces, did not come from a specific source, but was “built-in” into the very fabric of space-time. The cosmological constant gave space-time an inherent tendency to expand, and this could be done to balance the mutual attraction of all matter present in the Universe, that is, for the sake of stationarity of the Universe. It seems that in those years only one person was ready to accept the general theory of relativity at face value. While Einstein and other physicists were looking for a way to circumvent the non-stationary nature of the Universe, which followed from the general theory of relativity, Russian physicist Alexander Friedman instead offered his own explanation.
FRIEDMAN'S MODELS
The equations of general relativity that describe the evolution of the Universe are too complex to solve in detail.
So Friedman suggested making two simple assumptions instead:
(1) The universe looks exactly the same in all directions;
(2) this condition is valid for all its points.
Based on general relativity and these two simple assumptions, Friedman was able to show that we should not expect the universe to be stationary. In fact, he accurately predicted in 1922 what Edwin Hubble discovered several years later.
The assumption that the Universe looks the same in all directions is, of course, not entirely true to reality. For example, the stars of our Galaxy form a clearly visible band of light in the night sky called the Milky Way. But if we turn our gaze to distant galaxies, the number of them observed in different directions turns out to be approximately the same. So the Universe appears to be relatively uniform in all directions when viewed on cosmic scales comparable to the distances between galaxies.
For a long time this was considered a sufficient justification for Friedman's assumption - a rough approximation to the real Universe. However, relatively recently Lucky case proved that Friedman's assumption describes our world with remarkable accuracy. In 1965, American physicists Arno Penzias and Robert Wilson worked at the Bell laboratory in New Jersey on an ultrasensitive microwave radiation receiver for communication with orbital satellites. artificial satellites. They were very concerned that the receiver was picking up more noise than it should, and that the noise was not coming from any particular direction. They began searching for the cause of the noise by clearing their large horn antenna of bird droppings that had accumulated inside it and ruling out possible malfunctions. They knew that any atmospheric noise is amplified when the antenna is not pointed straight up, because the atmosphere appears thicker when viewed at an angle from the vertical.
The additional noise remained the same no matter which direction the antenna was turned, so the source of the noise had to be outside the atmosphere. The noise remained unchanged day and night throughout the year, despite the rotation of the Earth around its axis and revolution around the Sun. This indicated that the source of the radiation was outside the solar system and even outside our galaxy, otherwise the signal intensity would change as the antenna turned out to be facing in different directions in accordance with the movement of the Earth.
Indeed, we now know that the radiation on its way to us had to cross the entire observable Universe. Since it is the same in different directions, then the Universe must be homogeneous in all directions (at least on a large scale). We know that no matter which direction we turn our gaze, the fluctuations in the "background noise" cosmic radiation do not exceed 1/10,000. So Penzias and Wilson accidentally stumbled upon a strikingly accurate confirmation of Friedman's first hypothesis.
Around the same time, two other American physicists from nearby Princeton University in New Jersey, Bob Dick and Jim Peebles, also became interested in cosmic microwave radiation. They worked on the hypothesis of George (George) Gamow, who had once been a student of Alexander Friedman, that in its earliest stages of development the Universe was extremely dense and hot, heated to “white heat”. Dick and Peebles concluded that we can still observe its past glow because light from the most distant parts of the early Universe is just reaching Earth. However, due to the expansion of the Universe, this light has apparently undergone such a large red shift that it should now be perceived by us in the form of microwave radiation. Dick and Peebles were just searching for such radiation when Penzias and Wilson, hearing about their work, realized that they had already found what they were looking for. For this discovery Penzias and Wilson were awarded Nobel Prize in Physics in 1978, which seems a bit unfair to Dick and Peebles.
At first glance, this evidence that the Universe looks the same in all directions suggests that the Earth occupies some kind of special place in the Universe. For example, one can imagine that since all the galaxies are moving away from us, we are in the very center of space. There is, however, an alternative explanation: the Universe may look the same in all directions and from any other galaxy. This, as already mentioned, was Friedman's second assumption.
We have no evidence to support or refute this assumption. We accept it on faith only out of modesty. It would be in highest degree it would be surprising if the universe looked the same in all directions around us, but not around any other point. In Friedmann's model, all galaxies are moving away from each other. Imagine balloon, on the surface of which specks are drawn. When the balloon is inflated, the distance between any two spots increases, but neither of them can be called the center of expansion. Moreover, the further apart the spots are, the faster they move away from each other. Similarly, in Friedman's model, the speed of retreat of any two galaxies is proportional to the distance between them. It follows that the redshift of galaxies should be directly proportional to their distance from Earth, which is what Hubble discovered.
Despite the fact that Friedman's model was successful and turned out to be consistent with the results of Hubble's observations, it remained almost unknown in the West for a long time. They learned about it only after in 1935, the American physicist Howard Robertson and the English mathematician Arthur Walker developed similar models to explain the homogeneous expansion of the Universe discovered by Hubble.
Although Friedman only proposed one model, three different models can be constructed based on his two fundamental assumptions. In the first of them (which is what Friedman formulated), the expansion occurs so slowly that the gravitational attraction between galaxies gradually slows it down even more, and then stops it. The galaxies then begin to move towards each other, and the Universe contracts. The distance between two neighboring galaxies first increases from zero to a certain maximum, and then decreases again to zero.
In the second solution, the expansion rate is so high that gravity can never stop it, although it does slow it down somewhat. The separation of neighboring galaxies in this model begins at zero distance, and then they disperse at a constant speed. Finally, there is a third solution, in which the rate of expansion of the Universe is sufficient only to prevent reverse compression, or collapse. In this case, the division also starts from zero and increases indefinitely. However, the expansion speed is constantly decreasing, although it never reaches zero.
A remarkable feature of the first type of Friedmann model is that the Universe is not infinite in space, but space has no boundaries. Gravity in this case is so strong that space bends, closing on itself like the surface of the Earth. A person traveling along the earth's surface in one direction never encounters an insurmountable obstacle and does not risk falling off the “edge of the Earth”, but simply returns to the starting point. This is the space in Friedman’s first model, but instead of the two dimensions inherent in the earth’s surface, it has three. The fourth dimension - time - has a finite extent, but it can be likened to a line with two edges or boundaries, a beginning and an end. Next, we will show that the combination of the provisions of the general theory of relativity and the uncertainty principle of quantum mechanics allows for the finiteness of space and time while at the same time they have no limits or boundaries. The idea of a space traveler circling the Universe and returning to his starting point is good for science fiction stories, but does not have practical value, because - and this can be proven - the Universe will shrink to zero dimensions before the traveler returns to the start. In order to return to the starting point before the Universe ceases to exist, this poor fellow must move faster than light, which, alas, the laws of nature known to us do not allow.
Which Friedman model corresponds to our Universe? Will the expansion of the Universe stop, giving way to compression, or will it continue forever? To answer this question, we need to know the rate of expansion of the Universe and its average density at present. If this density is less than a certain critical value determined by the expansion rate, the gravitational attraction will be too weak to stop the retreat of galaxies. If the density is greater than the critical value, gravity will sooner or later stop the expansion and reverse compression will begin.
We can determine the current rate of expansion by measuring the speeds at which other galaxies are moving away from us, using the Doppler effect. This can be done with high precision. However, the distances to galaxies are not very well known, since we measure them using indirect methods. We know one thing: the Universe is expanding by about 5-10% every billion years. However, our estimates of the current density of matter in the Universe are subject to even greater uncertainty.
If we add up the mass of all the stars in our and other galaxies visible to us, the total will be less than one hundredth of the value that is necessary to stop the expansion of the Universe even at its slowest speed. However, we know that our and other galaxies contain large amounts of dark matter, which we cannot observe directly, the influence of which, however, is detected through its gravitational effect on the orbits of stars and galactic gas. Moreover, most galaxies form giant clusters, and the presence of even more dark matter between galaxies in these clusters can be predicted by the effect it has on the motion of galaxies. But even adding all this dark matter, we still get one tenth of what is needed to stop the expansion. However, it is possible that there are other forms of matter that have not yet been identified by us, which could raise the average density of the Universe to a critical value that could stop the expansion.
Thus, existing evidence suggests that the Universe will apparently expand forever. But don't bet on it. We can only be sure that if the Universe is destined to collapse, this will not happen earlier than tens of billions of years from now, since it has been expanding for at least the same time period. So no need to worry ahead of schedule. If we fail to settle outside the solar system, humanity will perish long before that, along with our star, the Sun.
BIG BANG
A characteristic feature of all solutions resulting from Friedman’s model is that, according to them, in the distant past, 10 or 20 billion years ago, the distance between neighboring galaxies in the Universe should have been zero. At this moment in time, called the Big Bang, the density of the Universe and the curvature of space-time were infinitely large. This means that the general theory of relativity, on which all solutions of the Friedmann model are based, predicts the existence of a special, singular point in the Universe.
All ours scientific theories are built on the assumption that spacetime is smooth and almost flat, so that they all crash into the specificity (singularity) of the Big Bang, where the curvature of spacetime is infinite. This means that even if some events happened before the Big Bang, they cannot be used to determine what happened after, because all predictability at the moment of the Big Bang was broken. Accordingly, knowing only what happened after the Big Bang, we cannot establish what happened before it. As applied to us, all events before the Big Bang have no consequences, and therefore cannot be part of the scientific model of the Universe. We must exclude them from the model and say that time began with the Big Bang.
Many people don't like the idea that time has a beginning, probably because it smacks of divine intervention. (On the other hand, the Catholic Church seized on the Big Bang model and, in 1951, officially declared that the model was consistent with the Bible.) Attempts have been made to avoid the conclusion that there was a Big Bang at all. The theory of a stationary universe received the widest support. It was proposed in 1948 by Hermann Bondi and Thomas Gold, who fled from Nazi-occupied Austria, together with the Briton Fred Hoyle, who worked with them during the war to improve radars. Their idea was that as galaxies move apart, new galaxies are constantly being formed from newly formed matter in the space between them. That is why the Universe looks approximately the same at all times, as well as from any point in space.
The theory of a stationary Universe required such a change in the general theory of relativity that would allow the constant formation of new matter, but the rate of its formation was so low - about one elementary particle per cubic kilometer per year - that the idea of Bondi, Gold and Hoyle did not conflict with experimental data. Their theory was “sound,” that is, it was simple enough and offered clear predictions that could be tested experimentally. One such prediction was that the number of galaxies or galaxy-like objects in any given volume of space would be the same wherever and whenever we looked in the Universe.
In the late 1950s - early 1960s. a group of astronomers from Cambridge, led by Martin Ryle, investigated sources of radio emission in outer space. It turned out that most of such sources must lie outside our Galaxy and that among them there are much more weak ones than strong ones. Weak sources were considered more distant, and strong sources were considered closer. Another thing became obvious: the number of close sources per unit volume is less than distant ones.
This could mean that we are located in the center of a vast region where the density of radio sources is much lower than in the rest of the Universe. Or the fact that in the past, when radio waves were just beginning their journey to us, there were much more sources of radiation than there are now. Both the first and second explanations contradicted the theory of a stationary Universe. Moreover, discovered by Penzias and Wilson in 1965 microwave radiation also indicated that at some time in the past the Universe must have had much higher density. So the theory of a stationary Universe was buried, albeit not without regret.
Another attempt to circumvent the conclusion that there was a Big Bang and time has a beginning was made in 1963 by Soviet scientists Evgeniy Lifshits and Isaac Khalatnikov. They suggested that the Big Bang may represent some kind of specific feature Friedmann's models, which, after all, are just an approximation of the real Universe. Perhaps, of all the models that approximately describe the real Universe, only Friedmann's models contain the Big Bang singularity. In these models, galaxies scatter in outer space in straight lines.
Therefore, it is not surprising that at some time in the past they were all located at the same point. In the real Universe, however, galaxies scatter not along straight lines, but along slightly curved trajectories. So at the initial position they were not located at the same geometric point, but simply very close to each other. It therefore seems likely that the current expanding Universe arose not from the Big Bang singularity, but from an earlier contraction phase; during the collapse of the Universe, not all particles had to collide with each other; some of them could avoid direct collision and fly apart, creating the picture of the expansion of the Universe that we observe today. Can we then say that the real Universe began with the Big Bang?
Lifshits and Khalatnikov studied models of the Universe that were approximately similar to Friedman’s, but took into account inhomogeneities and random distribution speeds of galaxies in the real Universe. They showed that such models can also begin with the Big Bang, even if the galaxies do not scatter in strictly straight lines. However, Lifshitz and Khalatnikov argued that this is only possible in certain specific models, where all galaxies move in a straight line.
Since there are far more models like Friedman's that do not contain the Big Bang singularity than those that do, the scientists reasoned, we must conclude that the probability of a Big Bang is extremely low. However, they later had to recognize that the class of models like Friedmann's, which contain singularities and in which galaxies should not move in any particular way, is much larger. And in 1970 they abandoned their hypothesis altogether.
The work done by Lifshitz and Khalatnikov was valuable because it showed that the universe could have a singularity—the Big Bang—if general relativity was correct. However, they did not allow vital important issue: Does general relativity predict that our universe must have had a Big Bang, the beginning of time? The answer to this was provided by a completely different approach, first proposed by the English physicist Roger Penrose in 1965. Penrose used the behavior of so-called light cones in the theory of relativity and the fact that gravity always causes attraction to show that stars that collapse under the influence of their own gravity , are contained within a region whose boundaries are compressed to zero dimensions. This means that all the matter of the star is compressed into one point of zero volume, so that the density of matter and the curvature of space-time become infinite. In other words, there is a singularity contained in a region of space-time known as a black hole.
At first glance, Penrose's conclusions said nothing about whether the Big Bang singularity existed in the past. However, at the same time that Penrose derived his theorem, I, then a graduate student, was desperately searching for math problem, which would allow me to complete my dissertation. I realized that if we reversed the direction of time in Penrose's theorem so that collapse was replaced by expansion, the conditions of the theorem would remain the same, as long as the present Universe approximately corresponded to Friedmann's model on a large scale. It followed from Penrose's theorem that the collapse of any star ends in a singularity, and my example with time reversal proved that any Friedmann expanding Universe must arise from a singularity. For purely technical reasons, Penrose's theorem required that the universe be infinite in space. I could use this to prove that singularities arise only in one case: if a high expansion rate excludes the reverse contraction of the Universe, because only the Friedmann model is infinite in space.
Some next years I developed new mathematical techniques that would eliminate this and others technical specifications from theorems proving that singularities must exist. The result was a joint paper published in 1970 by Penrose and myself, which argued that the Big Bang singularity must have existed provided that general relativity was correct and the amount of matter in the universe matched that which we observed.
A host of objections followed, partly from Soviet scientists who adhered to the “party line” proclaimed by Lifshitz and Khalatnikov, and partly from those who had an aversion to the very idea of a singularity, which offended the beauty of Einstein’s theory. However, it is difficult to argue with the mathematical theorem. Therefore, it is now widely accepted that the universe must have had a beginning.
Just a hundred years ago, scientists discovered that our Universe is rapidly increasing in size.
In 1870, the English mathematician William Clifford came to a very profound idea that space can be curved, and unequally at different points, and that over time its curvature can change. He even admitted that such changes were somehow related to the movement of matter. Both of these ideas, many years later, formed the basis of the general theory of relativity. Clifford himself did not live to see this - he died of tuberculosis at the age of 34, 11 days before Albert Einstein was born.
Redshift
The first information about the expansion of the Universe was provided by astrospectrography. In 1886, English astronomer William Huggins noticed that the wavelengths of starlight were slightly shifted compared to the terrestrial spectra of the same elements. Based on the formula for the optical version of the Doppler effect, derived in 1848 by the French physicist Armand Fizeau, the radial velocity of a star can be calculated. Such observations make it possible to track the movement of a space object.
A quarter of a century later, this opportunity was used in a new way by Vesto Slifer, an employee of the observatory in Flagstaff, Arizona, who, since 1912, had been studying the spectra of spiral nebulae with a 24-inch telescope with a good spectrograph. To obtain a high-quality image, the same photographic plate was exposed for several nights, so the project moved slowly. From September to December 1913, Slipher studied the Andromeda nebula and, using the Doppler-Fizeau formula, came to the conclusion that it was approaching the Earth by 300 km every second.
In 1917, he published data on the radial velocities of 25 nebulae, which showed significant asymmetries in their directions. Only four nebulae approached the Sun, the rest ran away (and some very quickly).
Slifer did not seek fame and did not promote his results. Therefore, they became known in astronomical circles only when the famous British astrophysicist Arthur Eddington drew attention to them.
In 1924, he published a monograph on the theory of relativity, which included a list of the radial velocities of 41 nebulae found by Slipher. The same four blue-shifted nebulae were present there, while the remaining 37 had spectral lines red-shifted. Their radial velocities ranged from 150 to 1800 km/s and were on average 25 times higher than the known velocities of the Milky Way stars at that time. This suggested that nebulae participate in different movements than “classical” luminaries.
Space Islands
In the early 1920s, most astronomers believed that spiral nebulae were located on the periphery of the Milky Way, and beyond there was nothing but empty, dark space. True, back in the 18th century, some scientists saw giant star clusters in nebulae (Immanuel Kant called them island universes). However, this hypothesis was not popular, since it was impossible to reliably determine the distances to the nebulae.
This problem was solved by Edwin Hubble, working on the 100-inch reflecting telescope at California's Mount Wilson Observatory. In 1923–1924, he discovered that the Andromeda nebula consists of many luminous objects, including Cepheid variable stars. It was already known then that the period of change in their apparent brightness is related to absolute luminosity, and therefore Cepheids are suitable for calibrating cosmic distances. With their help, Hubble estimated the distance to Andromeda at 285,000 parsecs (according to modern data, it is 800,000 parsecs). The diameter of the Milky Way was then believed to be approximately 100,000 parsecs (in reality it is three times less). It followed that Andromeda and the Milky Way must be considered independent star clusters. Hubble soon identified two more independent galaxies, which finally confirmed the “island universes” hypothesis.
Hubble's laws
Edwin Hubble empirically discovered the approximate proportionality of redshifts and galactic distances, which he turned into a proportionality between velocities and distances using the Doppler-Fizeau formula. So we are dealing with two different patterns here.
Hubble didn't know how these patterns were related to each other, but what does today's science say about it?
As Lemaître also showed, the linear correlation between cosmological (caused by the expansion of the Universe) redshifts and distances is by no means absolute. In practice, it is well observed only for displacements less than 0.1. So the empirical Hubble law is not exact, but approximate, and the Doppler–Fizeau formula is valid only for small shifts of the spectrum.
But here is a theoretical law connecting the radial speed of distant objects with the distance to them (with a proportionality coefficient in the form of the Hubble parameter V = HD), is valid for any redshift. However, the speed appearing in it V- not at all the speed of physical signals or real bodies in physical space. This is the rate of increase in distances between galaxies and galaxy clusters, which is caused by the expansion of the Universe. We could measure it only if we were able to stop the expansion of the Universe, instantly stretch measuring tapes between galaxies, read the distances between them and divide them into the time intervals between measurements. Naturally, the laws of physics do not allow this. Therefore, cosmologists prefer to use the Hubble parameter H in another formula, where the scale factor of the Universe appears, which precisely describes the degree of its expansion in various cosmic eras (since this parameter changes over time, its modern value is denoted H 0). The Universe is now expanding at an accelerating rate, so the value of the Hubble parameter is increasing.
By measuring cosmological redshifts, we obtain information about the extent of expansion of space. Galaxy light coming to us at cosmological redshift z, left it when all cosmological distances were 1 + z times less than in our era. Additional information about this galaxy, such as its current distance or speed of removal from the Milky Way, can only be obtained using a specific cosmological model. For example, in the Einstein-de Sitter model, a galaxy with z= 5 is moving away from us at a speed equal to 1.1 With(speed of light). What if you make a common mistake and just call V/c And z, then this speed will be five times greater than light speed. The discrepancy, as we see, is serious.
In fairness, it is worth noting that two years before Hubble, the distance to Andromeda was calculated by the Estonian astronomer Ernst Opik, whose result - 450,000 parsecs - was closer to the correct one. However, he used a number of theoretical considerations that were not as convincing as Hubble's direct observations.
By 1926, Hubble had conducted a statistical analysis of observations of four hundred “extragalactic nebulae” (a term he used for a long time, avoiding calling them galaxies) and proposed a formula for relating the distance to a nebula to its apparent brightness. Despite the enormous errors of this method, new data confirmed that nebulae are distributed more or less evenly in space and are located far beyond the boundaries of the Milky Way. Now there was no longer any doubt that space is not limited to our Galaxy and its closest neighbors.
Space fashion designers
Eddington became interested in Slipher's results even before the nature of spiral nebulae was finally clarified. By this time, a cosmological model already existed, which in a certain sense predicted the effect identified by Slipher. Eddington thought a lot about it and, naturally, did not miss the opportunity to give the observations of the Arizona astronomer a cosmological sound.
Modern theoretical cosmology began in 1917 with two revolutionary papers presenting models of the universe based on general relativity. One of them was written by Einstein himself, the other by the Dutch astronomer Willem de Sitter.
Einstein, in the spirit of the times, believed that the Universe as a whole was static (he tried to make it also infinite in space, but could not find the correct boundary conditions for his equations). As a result, he built a model of a closed Universe, the space of which has a constant positive curvature (and therefore it has a constant finite radius). Time in this Universe, on the contrary, flows like Newton, in one direction and at the same speed. The space-time of this model is curved due to the spatial component, while the time component is not deformed in any way. The static nature of this world provides a special “insert” into the main equation, which prevents gravitational collapse and thereby acts as an omnipresent anti-gravity field. Its intensity is proportional to a special constant, which Einstein called universal (now called the cosmological constant).
Einstein's model made it possible to calculate the size of the Universe, the total amount of matter, and even the value of the cosmological constant. To do this, we only need the average density of cosmic matter, which, in principle, can be determined from observations. It is no coincidence that Eddington admired this model and used it in practice by Hubble. However, it is destroyed by instability, which Einstein simply did not notice: at the slightest deviation of the radius from the equilibrium value, Einstein’s world either expands or undergoes gravitational collapse. Therefore, this model has no relation to the real Universe.
Empty world
De Sitter also built, as he himself believed, a static world of constant positive curvature. It contains Einstein's cosmological constant, but completely lacks matter. When test particles of arbitrarily small mass are introduced, they scatter and go to infinity. In addition, time flows more slowly at the periphery of the de Sitter universe than at its center. Because of this, light waves from large distances arrive with a red shift, even if their source is stationary relative to the observer. So in the 1920s, Eddington and other astronomers wondered whether de Sitter's model had anything in common with the reality reflected in Slipher's observations.
These suspicions were confirmed, albeit in a different way. The static nature of the de Sitter universe turned out to be imaginary, since it was associated with an unsuccessful choice of the coordinate system. After correcting this error, de Sitter space turned out to be flat, Euclidean, but non-static. Thanks to the antigravitational cosmological constant, it expands while maintaining zero curvature. Because of this expansion, the wavelengths of photons increase, which entails the shift of spectral lines predicted by de Sitter. It is worth noting that this is how the cosmological redshift of distant galaxies is explained today.
Associated coordinates
In cosmological calculations it is convenient to use accompanying coordinate systems, which expand in unison with the expansion of the Universe.
In an idealized model, where galaxies and galaxy clusters do not participate in any proper motions, their accompanying coordinates do not change. But the distance between two objects at a given moment in time is equal to their constant distance in accompanying coordinates, multiplied by the value of the scale factor for this moment. This situation can be easily illustrated on an inflatable globe: the latitude and longitude of each point do not change, and the distance between any pair of points increases with increasing radius.
Using comoving coordinates helps us understand the profound differences between expanding universe cosmology, special relativity, and Newtonian physics. Thus, in Newtonian mechanics all movements are relative, and absolute immobility has no physical meaning. On the contrary, in cosmology, immobility in comoving coordinates is absolute and, in principle, can be confirmed by observations.
The special theory of relativity describes processes in space-time, from which spatial and temporal components can be isolated in an infinite number of ways using Lorentz transformations. Cosmological space-time, on the contrary, naturally breaks down into a curved expanding space and a single cosmic time. In this case, the speed of retreat of distant galaxies can be many times higher than the speed of light.
From statistics to dynamics
The history of openly non-static cosmological theories begins with two works by Soviet physicist Alexander Friedman, published in a German journal Zeitschrift für Physik in 1922 and 1924. Friedman calculated models of universes with time-varying positive and negative curvature, which became the golden fund of theoretical cosmology. However, contemporaries hardly noticed these works (Einstein at first even considered Friedman’s first paper to be mathematically erroneous). Friedman himself believed that astronomy does not yet have an arsenal of observations that would allow one to decide which of the cosmological models is more consistent with reality, and therefore limited himself to pure mathematics. Perhaps he would have acted differently if he had read Slifer's results, but this did not happen.
The largest cosmologist of the first half of the 20th century, Georges Lemaitre, thought differently. At home, in Belgium, he defended his dissertation in mathematics, and then in the mid-1920s he studied astronomy - at Cambridge under the direction of Eddington and at the Harvard Observatory under Harlow Shapley (while in the USA, where he prepared a second dissertation at MIT, he met Slifer and Hubble). Back in 1925, Lemaître was the first to show that the static nature of de Sitter’s model was imaginary. Upon his return to his homeland as a professor at the University of Louvain, Lemaitre built the first model of an expanding universe with a clear astronomical basis. Without exaggeration, this work was a revolutionary breakthrough in space science.
Universal revolution
In his model, Lemaitre retained a cosmological constant with an Einsteinian numerical value. Therefore, his universe begins in a static state, but over time, due to fluctuations, it embarks on a path of constant expansion at an increasing rate. At this stage it maintains a positive curvature, which decreases as the radius increases. Lemaitre included in his universe not only matter, but also electromagnetic radiation. Neither Einstein nor de Sitter, whose work was known to Lemaitre, nor Friedman, about whom he knew anything at that time, did this.
Lemaitre, back in the USA, suggested that the redshifts of distant galaxies arise due to the expansion of space, which “stretches” light waves. Now he has proven it mathematically. He also demonstrated that small (much smaller units) redshifts are proportional to the distances to the light source, and the proportionality coefficient depends only on time and carries information about the current rate of expansion of the Universe. Since the Doppler–Fizeau formula implied that the radial velocity of a galaxy is proportional to its redshift, Lemaître came to the conclusion that this velocity is also proportional to its distance. After analyzing the speeds and distances of 42 galaxies from Hubble's list and taking into account the intragalactic speed of the Sun, he established the values of the proportionality coefficients.
Unsung work
Lemaitre published his work in 1927 in French in the little-read journal Annals of the Brussels Scientific Society. It is believed that this was the main reason why she initially went virtually unnoticed (even by his teacher Eddington). True, in the fall of the same year, Lemaitre was able to discuss his findings with Einstein and learned from him about Friedman’s results. The creator of General Relativity had no technical objections, but he resolutely did not believe in the physical reality of Lemetre’s model (just as he had previously not accepted Friedman’s conclusions).
Hubble graphs
Meanwhile, in the late 1920s, Hubble and Humason discovered a linear correlation between the distances of 24 galaxies and their radial velocities, calculated (mostly by Slipher) from redshifts. Hubble concluded from this that the radial speed of a galaxy is directly proportional to its distance. The coefficient of this proportionality is now denoted H 0 and is called the Hubble parameter (according to the latest data, it is slightly higher than 70 (km/s)/megaparsec).
Hubble's paper plotting the linear relationship between galactic velocities and distances was published in early 1929. A year earlier, the young American mathematician Howard Robertson, following Lemaitre, derived this dependence from the model of an expanding Universe, which Hubble may have known about. However, his famous article did not mention this model either directly or indirectly. Hubble later expressed doubts that the velocities appearing in his formula actually describe the movements of galaxies in outer space, but he always refrained from their specific interpretation. He saw the meaning of his discovery in demonstrating the proportionality of galactic distances and redshifts, leaving the rest to theorists. Therefore, with all due respect to Hubble, there is no reason to consider him the discoverer of the expansion of the Universe.
And yet it is expanding!
Nevertheless, Hubble paved the way for the recognition of the expansion of the Universe and Lemaître's model. Already in 1930, such masters of cosmology as Eddington and de Sitter paid tribute to her; A little later, scientists noticed and appreciated Friedman’s work. In 1931, at the instigation of Eddington, Lemaitre translated his article into English (with small cuts) for the Monthly News of the Royal Astronomical Society. In the same year, Einstein agreed with Lemaître’s conclusions, and a year later, together with de Sitter, he built a model of an expanding Universe with flat space and curved time. This model, due to its simplicity, has been very popular among cosmologists for a long time.
In the same 1931, Lemaitre published a brief (and without any mathematics) description of another model of the Universe, which combined cosmology and quantum mechanics. In this model, the initial moment is the explosion of the primary atom (Lemaitre also called it a quantum), which gave rise to both space and time. Since gravity slows down the expansion of the newborn Universe, its speed decreases - it is possible that almost to zero. Lemaitre later introduced a cosmological constant into his model, which forced the Universe to eventually enter a stable regime of accelerating expansion. So he anticipated both the idea of the Big Bang and modern cosmological models that take into account the presence of dark energy. And in 1933, he identified the cosmological constant with the energy density of the vacuum, which no one had ever thought of before. It’s simply amazing how ahead of his time this scientist, certainly worthy of the title of discoverer of the expansion of the Universe, was!
If you look at the sky on a clear moonless night, the most bright objects, most likely, the planets will be Venus, Mars, Jupiter and Saturn. And you will also see a whole scattering of stars similar to our Sun, but located much further from us. Some of these fixed stars actually move slightly relative to each other as the Earth moves around the Sun. They are not motionless at all! This happens because such stars are relatively close to us. Due to the movement of the Earth around the Sun, we see these closer stars against the background of more distant ones from various positions. The same effect is observed when you are driving a car, and the trees along the road seem to change their position against the background of the landscape stretching towards the horizon (Fig. 14). The closer the trees are, the more noticeable their apparent movement is. This change in relative position is called parallax. In the case of stars, this is a real success for humanity, because parallax allows us to directly measure the distance to them.
Rice. 14. Stellar parallax.
Whether you're moving on a road or in space, the relative positions of near and far bodies change as you move. The magnitude of these changes can be used to determine the distance between bodies.
The closest star, Proxima Centauri, is about four light years away, or forty million million kilometers. Most other stars visible to the naked eye are within a few hundred light years of us. For comparison, there are only eight light minutes from the Earth to the Sun! Stars are scattered throughout the night sky, but they are especially dense in the band we call the Milky Way. As early as 1750, some astronomers suggested that the appearance of the Milky Way could be explained by thinking that most of the visible stars were collected in a disk-shaped configuration, like what we now call spiral galaxies. Only a few decades later, the English astronomer William Herschel confirmed the validity of this idea, painstakingly counting the number of stars visible through a telescope on different areas sky. However, this idea received full recognition only in the twentieth century. We now know that the Milky Way, our Galaxy, spans approximately one hundred thousand light years from end to end and rotates slowly; the stars in its spiral arms complete one revolution around the center of the Galaxy every few hundred million years. Our Sun, an ordinary yellow star of medium size, is located at the inner edge of one of the spiral arms. We have certainly come a long way since the days of Aristotle and Ptolemy, when people considered the Earth to be the center of the Universe.
The modern picture of the Universe began to emerge in 1924, when American astronomer Edwin Hubble proved that the Milky Way is not the only galaxy. He discovered that there were many other star systems separated by vast empty spaces. To confirm this, Hubble had to determine the distance from Earth to other galaxies. But galaxies are so far away that, unlike nearby stars, they actually appear motionless. Unable to use parallax to measure distances to galaxies, Hubble was forced to use indirect methods to estimate distances. An obvious measure of a star's distance is its brightness. But apparent brightness depends not only on the distance to the star, but also on the star's luminosity - the amount of light it emits. A dim star close to us will outshine the brightest star from a distant galaxy. Therefore, to use apparent brightness as a measure of distance, we must know the luminosity of the star.
The luminosity of nearby stars can be calculated from their apparent brightness because, thanks to parallax, we know their distance. Hubble noted that nearby stars can be classified by the nature of the light they emit. Stars of the same class always have the same luminosity. He further suggested that if we discover stars of these classes in a distant galaxy, then they can be assigned the same luminosity as similar stars near us. With this information, it is easy to calculate the distance to the galaxy. If calculations made for many stars in the same galaxy give the same distance, then we can be confident that our estimate is correct. In this way, Edwin Hubble calculated the distances to nine different galaxies.
Today we know that stars visible to the naked eye make up a tiny fraction of all stars. We see about 5,000 stars in the sky - only about 0.0001% of all the stars in our Galaxy, the Milky Way. And the Milky Way is just one of more than a hundred billion galaxies that can be observed with modern telescopes. And each galaxy contains about a hundred billion stars. If a star were a grain of salt, all the stars visible to the naked eye would fit in a teaspoon, but the stars of the entire Universe would form a ball with a diameter of more than thirteen kilometers.
The stars are so far away from us that they appear to be points of light. We cannot distinguish their size or shape. But, as Hubble noted, there are many various types stars, and we can distinguish them by the color of the radiation they emit. Newton discovered that if sunlight was passed through a three-sided glass prism, it would split into its component colors, like a rainbow (Fig. 15). The relative intensity of the different colors in the radiation emitted by a light source is called its spectrum. By focusing a telescope on a single star or galaxy, you can study the spectrum of light it emits.
Rice. 15. Stellar spectrum.
By analyzing the emission spectrum of a star, we can determine both its temperature and the composition of its atmosphere.
Among other things, the radiation of a body makes it possible to judge its temperature. In 1860 German physicist Gustav Kirchhoff established that any material body, for example, a star, when heated, emits light or other radiation, just as hot coals glow. The glow of heated bodies is due to the thermal movement of the atoms inside them. This is called black body radiation (even though the heated bodies themselves are not black). The spectrum of blackbody radiation is difficult to confuse with anything: it has a characteristic appearance that changes with body temperature (Fig. 16). Therefore, the radiation of a heated body is similar to the readings of a thermometer. The emission spectrum we observe various stars always similar to black body radiation, it is a kind of notification about the temperature of the star.
Rice. 16. Black body radiation spectrum.
All bodies - not just stars - emit radiation due to the thermal motion of their constituent microscopic particles. The frequency distribution of radiation characterizes body temperature.
If we study starlight closely, it will tell us even more information. We will discover the absence of some strictly certain colors, and they will be different for different stars. And since we know that each chemical element absorbs its own characteristic set of colors, by comparing these colors with those that are absent in the star's spectrum, we can accurately determine which elements are present in its atmosphere.
In the 1920s, when astronomers began studying the spectra of stars in other galaxies, they discovered something very interesting: they turned out to have the same characteristic patterns of missing colors as stars in our own galaxy, but they were all shifted to the red end of the spectrum , and in the same proportion. Physicists know a shift in color or frequency as the Doppler effect.
We are all familiar with how this phenomenon affects sound. Listen to the sound of a car passing by. When it approaches, the sound of its engine or horn seems higher, and when the car has already passed by and began to move away, the sound decreases. A police car driving towards us at a speed of one hundred kilometers per hour develops about a tenth of the speed of sound. The sound of his siren is a wave, alternating crests and troughs. Recall that the distance between the nearest crests (or troughs) is called the wavelength. The shorter the wavelength, the more vibrations reach our ear every second and the higher the tone, or frequency, of the sound.
The Doppler effect is caused by the fact that an approaching car, emitting each successive sound wave crest, will be closer to us, and as a result, the distances between the crests will be less than if the car were standing still. This means that the lengths of the waves coming to us become shorter, and their frequency becomes higher (Fig. 17). Conversely, if the car moves away, the length of the waves we pick up becomes longer and their frequency lower. And the faster the car moves, the stronger the Doppler effect appears, which makes it possible to use it to measure speed.
Rice. 17. Doppler effect.
When the source emitting waves moves towards the observer, the wavelength decreases. As the source moves away, on the contrary, it increases. This is called the Doppler effect.
Light and radio waves behave in a similar way. Police use the Doppler effect to determine the speed of cars by measuring the wavelength of the radio signal reflected from them. Light is vibrations, or waves, of an electromagnetic field. As we noted in Chap. 5, the wavelength of visible light is extremely small - from forty to eighty millionths of a meter.
The human eye perceives light waves of different lengths as various colors, with the longest wavelengths corresponding to the red end of the spectrum, and the shortest - those corresponding to the blue end. Now imagine a light source located at a constant distance from us, such as a star, emitting light waves of a certain wavelength. The length of the recorded waves will be the same as those emitted. But suppose now that the light source begins to move away from us. As with sound, this will cause the wavelength of light to increase, meaning the spectrum will shift towards the red end.
Having proved the existence of other galaxies, Hubble in subsequent years worked on determining the distances to them and observing their spectra. At the time, many assumed that galaxies moved randomly and expected that the number of blue-shifted spectra would be about the same as the number of red-shifted ones. Therefore, it was a complete surprise to discover that the spectra of most galaxies show a red shift - almost all star systems are moving away from us! Even more surprising was the fact discovered by Hubble and made public in 1929: the redshift of galaxies is not random, but is directly proportional to their distance from us. In other words, the farther a galaxy is from us, the faster it is moving away! It followed from this that the Universe cannot be static, unchanged in size, as previously thought. In reality, it is expanding: the distance between galaxies is constantly growing.
The realization that the Universe is expanding produced a real revolution in the mind, one of the greatest in the twentieth century. In retrospect, it may seem surprising that no one thought of this before. Newton and other great minds must have realized that a static universe would be unstable. Even if at some moment it were motionless, the mutual attraction of stars and galaxies would quickly lead to its compression. Even if the Universe were to expand relatively slowly, gravity would eventually put an end to its expansion and cause it to contract. However, if the expansion rate of the Universe is greater than a certain critical point, gravity will never be able to stop it and the Universe will continue to expand forever.
Here there is a vague resemblance to a rocket rising from the surface of the Earth. At a relatively low speed, gravity will eventually stop the rocket and it will begin to fall toward Earth. On the other hand, if the rocket's speed is higher than critical (more than 11.2 kilometers per second), gravity cannot hold it and it leaves the Earth forever.
Based on Newton's theory of gravity, this behavior of the Universe could have been predicted at any time in the nineteenth or eighteenth century and even at the end of the seventeenth century. However, the belief in a static Universe was so strong that the delusion retained its power over minds until the beginning of the twentieth century. Even Einstein was so confident in the static nature of the Universe that in 1915 he made a special amendment to the general theory of relativity, artificially adding a special term to the equations, called the cosmological constant, which ensured the static nature of the Universe.
The cosmological constant manifested itself as the action of a certain new strength- “antigravity”, which, unlike other forces, did not have any specific source, but was simply an integral property inherent in the fabric of space-time itself. Under the influence of this force, space-time revealed an innate tendency to expand. By choosing the value of the cosmological constant, Einstein could vary the strength of this tendency. With its help, he was able to precisely balance the mutual attraction of all existing matter and obtain a static Universe as a result.
Einstein later rejected the idea of a cosmological constant, admitting it to be his “biggest mistake.” As we will soon see, there are reasons today to believe that Einstein may have been right after all in introducing the cosmological constant. But what must have saddened Einstein most of all was that he allowed his faith to motionless Universe to negate the conclusion that the Universe must expand, predicted by his own theory. Only one person seems to have seen this consequence of general relativity and taken it seriously. While Einstein and other physicists were looking for how to avoid the non-static nature of the Universe, Russian physicist and mathematician Alexander Friedman, on the contrary, insisted that it was expanding.
Friedman made two very simple assumptions about the Universe: that it looks the same no matter which direction we look, and that this assumption is true no matter where in the Universe we look from. Based on these two ideas and solving the equations of general relativity, he proved that the Universe cannot be static. Thus, in 1922, several years before Edwin Hubble's discovery, Friedman accurately predicted the expansion of the Universe!
The assumption that the Universe looks the same in every direction is not entirely true. For example, as we already know, the stars of our Galaxy form a distinct light stripe in the night sky - the Milky Way. But if we look at distant galaxies, their number seems to be more or less equal in all parts of the sky. So the Universe looks about the same in any direction when observed on a large scale compared to the distances between galaxies and ignore differences on small scales.
Imagine that you are in a forest where trees grow randomly. Looking in one direction, you will see the nearest tree a meter away from you. In the other direction, the closest tree will be three meters away. In the third, you will see several trees at once, one, two and three meters away from you. The forest doesn't seem to look the same in any direction. But if you take into account all the trees within a kilometer radius, these kinds of differences average out and you will see that the forest is the same in all directions (Fig. 18).
Rice. 18. Isotropic forest.
Even if the distribution of trees in a forest is generally even, upon closer inspection they may appear to be denser in some areas. Likewise, the Universe does not look the same in the space closest to us, whereas when we zoom in, we see the same picture, no matter in which direction we observe.
For a long time, the uniform distribution of stars served as sufficient grounds for accepting the Friedmann model as a first approximation to the real picture of the Universe. But later, a happy accident revealed further evidence that Friedman's assumption was a surprisingly accurate description of the Universe. In 1965, two American physicists, Arno Penzias and Robert Wilson from Bell Telephone Laboratories in New Jersey, were debugging a very sensitive microwave receiver. (Microwaves are radiation with a wavelength of about a centimeter.) Penzias and Wilson were concerned that the receiver was detecting more noise than expected. They found bird droppings on the antenna and eliminated other potential causes of failure, but soon exhausted all possible sources of interference. The noise was different in that it was recorded around the clock throughout the year, regardless of the Earth’s rotation around its axis and its revolution around the Sun. Since the movement of the Earth directed the receiver into different sectors of space, Penzias and Wilson concluded that the noise was coming from outside the Solar System and even from outside the Galaxy. He seemed to be walking towards equally from all directions of space. We now know that, no matter where the receiver is pointed, this noise remains constant, apart from negligible variations. So Penzias and Wilson accidentally stumbled upon a striking example that supported Friedman's first hypothesis that the Universe is the same in all directions.
What is the origin of this cosmic background noise? Around the same time that Penzias and Wilson were investigating the mysterious noise in the receiver, two American physicists at Princeton University, Bob Dick and Jim Peebles, also became interested in microwaves. They studied the assumption of Georgy (George) Gamow (formerly a student of Alexander Friedman) that on early stages development, the Universe was very dense and white-hot. Dick and Peebles believed that if this was true, then we should be able to observe the glow of the early Universe, since light from very distant regions of our world is only now arriving at us. However, due to the expansion of the Universe, this light should be so strongly shifted to the red end of the spectrum that it will turn from visible radiation in the microwave. Dick and Peebles were just preparing to search for this radiation when Penzias and Wilson, hearing about their work, realized that they had already found it. For this discovery, Penzias and Wilson were awarded the Nobel Prize in 1978 (which seems somewhat unfair to Dick and Peebles, not to mention Gamow).
At first glance, the fact that the Universe looks the same in any direction indicates that we occupy some special place in it. In particular, it may seem that since all the galaxies are moving away from us, then we must be at the center of the Universe. There is, however, another explanation for this phenomenon: the Universe may look the same in all directions also when viewed from any other galaxy. If you remember, this was precisely Friedman’s second assumption.
We do not have any scientific arguments for or against Friedman's second hypothesis. Centuries ago Christian church would recognize it as heretical, since church doctrine postulated that we occupy a special place in the center of the universe. But today we accept Friedman's assumption for almost the opposite reason, out of a kind of modesty: it would seem absolutely amazing to us if the Universe looked the same in all directions only to us, but not to other observers in the Universe!
In the Friedmann model of the Universe, all galaxies are moving away from each other. This is reminiscent of the spreading of colored spots on the surface of an inflated balloon. As the size of the ball increases, the distances between any two spots increase, but none of the spots can be considered the center of expansion. Moreover, if the radius of the balloon is constantly growing, then the further apart the spots on its surface are, the faster they will move away as they expand. Let's say that the radius of the balloon doubles every second. Then two spots, initially separated by a distance of one centimeter, after a second will already be at a distance of two centimeters from each other (if measured along the surface of the balloon), so that their relative speed will be one centimeter per second. On the other hand, a pair of spots that were separated by ten centimeters will, a second after the start of expansion, move apart by twenty centimeters, so that their relative speed will be ten centimeters per second (Fig. 19). Similarly, in the Friedmann model, the speed at which any two galaxies move away from each other is proportional to the distance between them. Thus, the model predicts that the redshift of a galaxy should be directly proportional to its distance from us - this is the same dependence that Hubble later discovered. Although Friedman was able to propose a successful model and anticipate the results of Hubble's observations, his work remained almost unknown in the West until in 1935 a similar model was proposed by the American physicist Howard Robertson and the British mathematician Arthur Walker, following in the footsteps of Hubble's discovery of the expansion of the Universe.
Rice. 19. The Expanding Universe of a Balloon.
Due to the expansion of the Universe, galaxies are moving away from each other. Over time, the distance between distant stellar islands increases more than between nearby galaxies, just as the spots on an inflating balloon do. Therefore, to an observer from any galaxy, the speed at which another galaxy is moving away seems to be greater, the further away it is located.
Friedman proposed only one model of the Universe. But under the assumptions he made, Einstein’s equations admit three classes of solutions, that is, there are three different types of Friedmann models and three different scenarios for the development of the Universe.
The first class of solutions (the one Friedman found) assumes that the expansion of the universe is slow enough that the attraction between galaxies gradually slows down and eventually stops it. After this, the galaxies begin to move closer together, and the Universe begins to shrink. According to the second class of solutions, the Universe is expanding so quickly that gravity will only slightly slow down the retreat of galaxies, but will never be able to stop it. Finally, there is a third solution, according to which the Universe is expanding at just the right speed to avoid collapse. Over time, the speed of galaxy expansion becomes less and less, but never reaches zero.
An amazing feature of Friedman's first model is that in it the Universe is not infinite in space, but there are no boundaries anywhere in space. Gravity is so strong that space collapses and closes in on itself. This is to some extent similar to the surface of the Earth, which is also finite, but has no boundaries. If you move along the surface of the Earth in a certain direction, you will never come across an insurmountable barrier or the end of the world, but in the end you will return to where you started. In Friedman's first model, space is arranged in exactly the same way, but in three dimensions, rather than two, as in the case of the Earth's surface. The idea that you can go around the universe and return to starting point, good for science fiction, but has no practical significance, since, as can be proven, the Universe will shrink to a point before the traveler returns to the beginning of his journey. The universe is so large that you need to move faster than light in order to finish your journey where you started, and such speeds are prohibited (by the theory of relativity. - Transl.). In Friedman's second model, space is also curved, but in a different way. And only in the third model is the large-scale geometry of the Universe flat (although space is curved in the vicinity of massive bodies).
Which Friedman model describes our Universe? Will the expansion of the Universe ever stop and be replaced by compression, or will the Universe expand forever?
It turned out that answering this question is more difficult than scientists initially thought. Its solution depends mainly on two things - the currently observed rate of expansion of the Universe and its current average density (the amount of matter per unit volume of space). The higher the current expansion rate, the greater the gravity, and therefore the density of matter, required to stop the expansion. If the average density is above a certain critical value (determined by the rate of expansion), then the gravitational attraction of matter can stop the expansion of the Universe and cause it to contract. This behavior of the Universe corresponds to Friedman's first model. If the average density is less than a critical value, then gravitational attraction will not stop the expansion and the Universe will expand forever - as in the second Friedmann model. Finally, if the average density of the Universe is exactly equal to critical value, the expansion of the Universe will slow down forever, getting closer and closer to static state, but never reaching it. This scenario corresponds to Friedman's third model.
So which model is correct? We can determine the current rate of expansion of the Universe if we measure the speed at which other galaxies are moving away from us using the Doppler effect. This can be done very accurately. However, the distances to galaxies are not very well known, since we can only measure them indirectly. Therefore, we only know that the expansion rate of the Universe is from 5 to 10% per billion years. Our knowledge of the current average density of the Universe is even more vague. So, if we add up the masses of all the visible stars in our and other galaxies, the sum will be less than a hundredth of what is required to stop the expansion of the Universe, even at the lowest estimate of the expansion rate.
But that's not all. Our galaxy and others must contain large amounts of some kind of “dark matter” that we cannot observe directly, but whose existence we know due to its gravitational effect on the orbits of stars in the galaxies. Perhaps the best evidence for the existence of dark matter comes from the orbits of stars on the periphery of spiral galaxies like Milky Way. These stars orbit their galaxies too quickly to be held in orbit by the gravitational pull of the galaxy's visible stars alone. Additionally, most galaxies are part of clusters, and we can similarly infer the presence of dark matter between galaxies in these clusters from its effect on the motion of galaxies. In fact, the amount of dark matter in the Universe greatly exceeds the amount of ordinary matter. If we include all the dark matter, we get about a tenth of the mass needed to stop the expansion.
However, we cannot exclude the existence of other forms of matter, not yet known to us, distributed almost evenly throughout the Universe, which could increase its average density. For example, there are elementary particles, called neutrinos, which interact very weakly with matter and are extremely difficult to detect.
(One of the new neutrino experiments uses an underground tank filled with 50,000 tons of water.) Neutrinos are thought to be weightless and therefore have no gravitational pull.
However, studies from several recent years indicate that the neutrino still has a negligibly small mass, which could not be detected previously. If neutrinos have mass, they could be a form of dark matter. However, even with this dark matter, there appears to be far less matter in the Universe than is needed to stop its expansion. Until recently, most physicists agreed that Friedman’s second model was closest to reality.
But then new observations appeared. Over the past few years, different groups of researchers have been studying the tiny ripples in the microwave background that Penzias and Wilson discovered. The size of these ripples can serve as an indicator of the large-scale structure of the Universe. Its character seems to indicate that the Universe is flat after all (as in Friedmann's third model)! But since the total amount of ordinary and dark matter is not enough for this, physicists postulated the existence of another, not yet discovered, substance - dark energy.
And as if to further complicate the problem, recent observations have shown that the expansion of the Universe is not slowing down, but accelerating. Contrary to all Friedman's models! This is very strange, since the presence of matter in space - high or low density - can only slow down the expansion. After all, gravity always acts as an attractive force. Accelerating cosmological expansion is like a bomb that collects rather than dissipates energy after it explodes. What force is responsible for the accelerating expansion of space? No one has a reliable answer to this question. However, Einstein may have been right after all when he introduced the cosmological constant (and the corresponding antigravity effect) into his equations.
With the development of new technologies and the advent of excellent space telescopes, we are constantly learning amazing things about the Universe. And here's the good news: we now know that the Universe will continue to expand in the near future at an ever-increasing rate, and time promises to last forever, at least for those who are wise enough not to fall into a black hole. But what happened in the very first moments? How did the Universe begin, and what caused it to expand?