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Modern Cosmological Theories
The Steady-State Theory
The Big-Bang Theory
According to big-bang theories, at the beginning of time, all of the matter and energy in the universe was concentrated in a very dense state, from which it “exploded,” with the resulting expansion continuing until the present. This big bang is dated between 10 and 20 billion years ago, most likely c.13.799 billion years ago. In this initial state, the universe was very hot and contained a thermal soup of quarks, electrons, photons, and other elementary particles. The temperature rapidly decreased, falling from 1013 degrees Kelvin after the first microsecond to about one billion degrees after three minutes. As the universe cooled, the quarks condensed into protons and neutrons, the building blocks of atomic nuclei. Some of these were converted into helium nuclei by fusion; the relative abundance of hydrogen and helium is used as a test of the theory. After many millions of years the expanding universe, at first a very hot gas, thinned and cooled enough to condense into individual galaxies and then stars.
Several spectacular discoveries since 1950 have shed new light on the problem. Optical and radio astronomy complemented each other in the discovery of the quasars and the radio galaxies. It is believed that the energy reaching us now from some of these objects was emitted not long after the creation of the universe. Further evidence for the big-bang theory was the discovery in 1965 that a cosmic background noise is received from every part of the sky. This background radiation has the same intensity and distribution of frequencies in all directions and is not associated with any individual celestial object. It has a blackbody temperature of 2.7K (−270℃) and is interpreted as the electromagnetic remnant of the primordial fireball, stretched to long wavelengths by the expansion of the universe. More recently, the analysis of radiation from distant celestial objects detected by artificial satellites and orbiting observatories has given additional evidence for the big-bang theory.
Development of Modern Cosmology
The earliest pre-Ptolemaic theories assumed that the earth was the center of the universe (see Ptolemaic system). With the acceptance of the heliocentric, or sun-centered, theory (see Copernican system), the nature and extent of the solar system began to be realized. The Milky Way, a vast collection of stars separated by enormous distances, came to be called a galaxy and was thought to constitute the entire universe with the sun at or near its center. By studying the distribution of globular star clusters the American astronomer Harlow Shapley was able to give the first reliable indication of the size of the galaxy and the position of the sun within it. Modern estimates show it to have a diameter of about 100,000 light-years with the sun toward the edge of the disk, about 28,000 light-years from the center.
During the first two decades of the 20th cent. astronomers came to realize that some of the faint hazy patches in the sky, called nebulae, are not within our own galaxy, but are separate galaxies at great distances from the Milky Way. Willem de Sitter of Leyden suggested that the universe began as a single point and expands without end. After studying the red shift (see Doppler effect) in the spectral lines of the distant galaxies, the American astronomers Edwin Hubble and M. L. Humason concluded that the universe is expanding, with the galaxies appearing to fly away from each other at great speeds. According to Hubble's law, the expansion of the universe is approximately uniform. The greater the distance between any two galaxies, the greater their relative speed of separation.
At the end of the 20th cent. the study of very distant supernovas led to the belief that the cosmic expansion was accelerating. To explain this cosmologists postulated a repulsive force, dark energy, that counteracts gravity and pushes galaxies apart. It also appears that the universe has been expanding at different rates over its cosmic history. This led to a variation of the big-bang theory in which, under the influence of gravity, the expansion slowed initially and then, under the influence of dark energy, suddenly accelerated. It is estimated that this “cosmic jerk” occurred five billion years ago, about the time the solar system was formed. This theory postulates a flat, expanding universe with a composition of c.68% dark energy, c.27% dark matter, and c.5% normal energy and matter.
A number of questions must be answered, however, before cosmologists can establish a single, comprehensive theory. The expansion rate and age of the universe must be established. The nature and density of the missing mass, the dark matter and dark energy that is far more abundant than ordinary, visible matter, must be identified. The total mass of the universe must be determined to establish whether it is sufficient to support an equilibrium condition—a state in which the universe will neither collapse of its own weight nor expand into diminishing infinity. Such an equilibrium is called “omega equals one,” where omega is the ratio between the actual density of the universe and the critical density required to support equilibrium. If omega is greater than one, the universe would have too much mass and its gravity would cause a cosmic collapse. If omega is less than one, the low-density universe would expand forever. Today the most widely accepted picture of the universe is an omega-equals-one system of hundreds of billions of galaxies, many of them clustered in groups of hundreds or thousands, spread over a volume with a diameter of at least 10 billion light-years and all receding from each other, with the speeds of the most widely separated galaxies approaching the speed of light. On a more detailed level there is great diversity of opinion, and cosmology remains a highly speculative and controversial science.
See D. W. Sciama, Modern Cosmology and the Dark Matter Problem (1993); J. D. Barrow, The Origin of the Universe (1994); P. Coles and F. Lucchin, Cosmology: The Origin and Evolution of Cosmic Structure (1995); M. S. Longair, Our Evolving Universe (1996); B. Green, The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory (2000); S. Hawking, The Universe in a Nutshell (2001); R. P. Kirshner, The Extravagant Universe: Exploding Stars, Dark Energy, and Accelerating Cosmos (2002); S. Singh, Big Bang: The Origin of the Universe (2005).
cosmology(koz-mol -ŏ-jee) The study of the origin, evolution, and large-scale structure of the Universe. Cosmological models describing the behavior of the cosmic scale factor with time are constructed from gravitational theory. These are then tested by comparison with, for example, source counts, the Hubble diagram, and the cosmic helium abundance. The angular size of cosmic objects does not necessarily vary linearly with redshift and can be used as a further test – the angular-size redshift test. The nonlinearity arises because such objects were closer to us in the past and because radiation is bent by the gravitational attraction of intervening matter.
a branch of astronomy that treats the universe as a unified whole and the various parts of the universe, studied through astronomical observations, as parts of the whole. The conclusions of cosmology (models of the universe) are based on the laws of physics and on data from observational astronomy as well as on the philosophical principles of a given epoch (in the final analysis—on the entire body of knowledge). The most important philosophical postulate of cosmology is the proposition according to which the laws of nature (the laws of physics), established from the study of an extremely limited part of the universe (most frequently from experiments on the planet earth), may be extrapolated to significantly larger regions and in the final analysis, to the entire universe. Cosmology as a science is not possible without this postulate.
Cosmological theories of various periods (and frequently of the same period) differ markedly, depending on which physical principles and laws are accepted as sufficiently universal and are used as a basis for cosmology. The degree of universality of principles and laws cannot be verified directly, but models based on them must allow for verification. Conclusions drawn from a global model of an observed part of the universe (”astronomical universe”) must be confirmed by observations (in any case, they must not contradict them) and should also predict new phenomena that previously had not been observed. Of the vast number of models that can be constructed, only a few are able to satisfy these criteria. In the 1970’s these requirements were best met by homogeneous isotropic models of a nonstationary hot universe developed on the basis of the overall theory of relativity (in relativistic cosmology).
History. Naϊve cosmological ideas were conceived in remote antiquity as a result of man’s attempts to understand his place in the universe. These ideas were a characteristic and integral part of various myths and beliefs. The cosmological ideas of the ancient philosophical schools of Democritus, Pythagoras, and Aristotle (fifth and fourth centuries B.C.) satisfied stricter logical criteria. Aristotle’s influence on cosmology continued for nearly two millennia.
The first mathematical model of the universe, based on all available information from astronomical observations, was presented in the Almagest (second century A.D.). This geocentric system of the world explained all astronomical phenomena known at the time and prevailed for about 1,500 years. During this period there were essentially no new astronomical discoveries, but the manner of thinking changed dramatically. Despite the opposition of Christian dogmatism, the heliocentric system of the world proposed by N. Copernicus (16th century) was gradually accorded greater recognition, particularly after Galileo, using a telescope for astronomical observations (first half of the 17th century), made discoveries that were highly incompatible with the geocentric system. Even prior to this, G. Bruno, following the teachings of Copernicus, deduced the infinite nature of the universe and the absence in it of a specific center. This conclusion exerted a profound influence on the successive development of cosmology.
The revolution in cosmology, based on the teachings of Copernicus, was a point of departure for the revolution in astronomy and natural science as a whole. The law of universal gravitation (I. Newton, 1685), the very name of which emphasizes its cosmological universality, made it possible to view the universe as a system of masses, the interactions and motions of which are governed by this unified law. However, cosmological paradoxes were discovered in the application of Newtonian physics to the infinite system of masses.
The emergence of modern cosmology is associated with the creation of the relativistic theory of gravitation (A. Einstein, 1916) and the birth of extragalactic astronomy (1920’s). During the first stage of development of relativistic cosmology, attention was focused on the geometry of the universe (space-time curvature and the possible closed nature of space). The beginning of the second stage may be dated to the works of A. A. Fridman (1922–24), in which it was shown that curved space cannot be stationary but must expand or contract. However, these fundamentally new results received recognition only after the discovery of the law of red shifts (E. Hubble, 1929).
The problems of the mechanics and age (duration of expansion) of the universe now assumed primary importance. The third stage began with models of a hot universe (G. Gamow, second half of the 1940’s). Interest shifted to the physics of the universe—the state of matter and the physical processes occurring at various stages of expansion of the universe, including the earliest stages, when the state of matter was quite unusual. The laws of thermodynamics, the data of nuclear physics, and the physics of elementary particles, along with the law of gravitation, acquired great importance. Relativistic astrophysics, which filled the existing gap between cosmology and astrophysics, emerged.
Geometry and mechanics of the universe. Two postulates are central to the theory of a homogeneous isotropic universe: (1) Einstein’s equations are the best known description of a gravitational field; from this follows the space-time curvature and the relationship between curvature and mass density (energy); (2) there are no singular points (homogeneity) or preferred directions (isotropy) in the universe, that is, all points and all directions are equal. The latter assertion is frequently referred to as the cosmological principle; it may also be called the generalized principle of Bruno. If we also assume that the cosmological constant is equal to zero and the mass density is created primarily by matter (photons and neutrinos may be disregarded), then the cosmological equations acquire a simple appearance and only two models are possible. In one model, the curvature of space is negative or, at most, equal to zero, and space is infinite (open model). In such a model, all distances increase without limit with time. In the second model, the curvature of space is positive and space is finite but as unbounded as in the open model. In such a (closed) model, expansion over time is replaced by contraction. In the course of evolution, curvature decreases during expansion and increases during contraction, but the sign of the curvature does not change, that is, the open model remains open, and the closed model, closed. The initial stages of evolution of both models are identical: there must have existed a specific initial state with infinite mass density and infinite curvature of space and an explosive expansion, which slowed down over time.
The nature of evolution is schematically illustrated in Figures 1 (closed model) and 2 (open model). Time is plotted along the axis of the abscissas. The start of explosive expansion is taken to be the beginning of the calculation of time ( t = 0). A particular scale factor R is plotted along the axis of the ordinates. R may represent, for example, the distance between any two distant objects (galaxies). In the figures, the solid line represents the relation R = R( t), and the dotted line, the change in curvature during the process of evolution (the curvature is proportional to l/ R2). We further note that the relative rate of change of distances (1/ R2)( dR/dt) = H is nothing more than Hubble’s constant (more precisely, parameter). At the initial moment ( t → 0), the factor R → 0 and Hubble’s parameter H → ∞. It follows from the cosmological equations that with the given H, zero curvature may occur only with the specific (critical) mass density pcr = 3 c2H2/ G, where c is the velocity of light and G is the gravitational constant. If ρ > ρcr, space is closed, and if p ≤ ρcr, it is open.
Physics of the universe. The postulates indicated above are sufficient to judge the general character of evolution and lead, specifically, to the conclusion that the initial density (given small values of t) was extremely great. However, density does not provide an exhaustive characteristic of the physical state. It is also necessary, for example, to know temperature. Specifying in one way or another the characteristics of the initial state is the task of the third postulate (hypothesis) of relativistic cosmology, which is independent of the first two. The postulate of a hot universe (a high initial temperature is assumed) has generally been accepted in the 1960’s and 1970’s. Having accepted this postulate, we can draw several important conclusions.
First, at very small values of t, not only molecules or atoms but even atomic nuclei could not have existed; all that existed was some sort of mixture of various elementary particles (including photons and neutrinos). On the basis of the physics of elementary particles, we can calculate the composition of such a mixture at various stages of evolution.
Second, knowing the law of expansion, it can be shown when certain conditions existed: the density of matter changes in in-verse proportion to R3 or t2 the radiation density changes even more rapidly—in inverse proportion to R4. Inasmuch as initially expansion also proceeded rapidly, it is apparent that high density and temperature could have existed only for a very short time. In fact, if at t = 0 the density ρ = ∞, then already at t ≈ 0.01 sec the density falls to ρ ∽ 1011 g/cm3. At this time, photons, electrons, positrons, neutrinos, and antineutrinos existed in the universe; there were few nucleons. Through successive transformations, a mixture of light nuclei was obtained (apparently two-thirds hydrogen and one-third helium). All other chemical elements formed from these, but much later, as a result of nuclear reactions in stellar interiors. The remaining photons and neutrinos at a very early stage of expansion ceased to interact with matter and should be able to be observed at the present time in the form of residual radiation, the properties of which may be predicted on the basis of the theory of a hot universe.
Third, although expansion initially proceeds rapidly, the processes of elementary particle conversion flow incomparably more rapidly, as a result of which a sequence of states of thermodynamic equilibrium is established. This is an extremely important circumstance, since such a state is fully described by macroscopic parameters (determined by the rate of expansion) and is not at all a function of preceding history. Therefore, a lack of knowledge of what happened at densities significantly exceeding nuclear density (that is, during the first 10−4sec of expansion) does not hinder us from making more or less reliable judgments about later states, beginning, for example, with t = 10−2 sec, when the state of the matter was “ordinary” as is known in modern microphysics.
Observational verification. The conclusions of relativistic cosmology are radical and revolutionary, and the question of the degree of their reliability is of considerable scientific and philosophical interest. Greatest importance is attached to conclusions about the nonstationary nature (expansion) of the universe, high specific entropy (hot universe), and the curved nature of space. Problems of a more specific nature are those of the sign of the curvature and the degree of homogeneity and isotropy of the universe.
The conclusion about the nonstationary nature of the universe has been reliably confirmed: the cosmological red shift, observed up to z ≈ 2 and higher, is evidence that the part of the universe with linear dimensions on the order of several billion parsecs is expanding and that this expansion has been continuing for at least several billion years (objects located at a distance of 1 billion parsecs we see as they were approximately 3 billion years ago). The concept of a hot universe has received equal confirmation. Residual radio-frequency radiation was discovered in 1965, and its properties are extremely close to those predicted. Subsequent detailed study has established with accuracy down to fractions of a percent that residual radiation is also highly isotropic. This proves that for more than 99 percent of its history, the universe has been isotropic. This, naturally, increases the confidence in uniform isotropic models, which previously had been viewed as extremely crude approximations of reality.
The existence of space curvature has not been proved as yet, although it is highly probable if one takes into account the confirmed conclusions of relativistic cosmology. There is no way to measure curvature directly. It could be determined indirectly if the average mass density were known or if it were possible to determine more precisely the dependence of the red shift on distance (deviation from linear dependence). Astronomical observations lead to values of average density of luminous matter of approximately 10−31 g/cm3. It is much more difficult to determine the density of dark matter and particularly the energy density of neutrinos. Because of this, the uncertainty of the total density is extremely high (it may, in particular, be two orders higher than the average density of stellar matter). If one accepts the modern value of Hubble’s constant, H = 1.7 X 10−18 sec−1, then ρer = 6 X 10−30 g/cm3. Thus, on the basis of available observational data (10−31 < ρ < 10−29), it is impossible to make any choice between an open (expanding without limit) model and a closed (expansion in the distant future will be replaced by contraction) model. This uncertainty does not pertain to the overall nature of past and present expansion but rather influences the age of the universe (period of expansion), a value that is already sufficiently indefinite. If the expansion had occurred at a constant speed, then the time elapsed from the moment of initial explosion would equal T0 = 1/ H = 6 X 1017 sec =18 billion years. But expansion, as is seen in Figures 1 and 2, proceeds at a decelerating rate. Therefore, the time T that elapsed since the moment of the beginning of expansion is less than T0. Thus, at ρ = ρcr we have T = 2/3 T0 = 12 billion years. T is even less for ρ > ρcr, that is, for closed models. On the other hand, if the cosmological constant is not strictly equal to zero, then there exist other possibilities, for example, a lengthy (on the order of 10 or more billion years) delay in expansion in the past, and T could equal tens of billions of years.
Unsolved problems. Relativistic cosmology explains the observed modern state of the universe; it has predicted previously unknown phenomena. However, the development of cosmology has also posed a number of extremely difficult, as yet unsolved, problems. Thus, in order to study the state of matter with densities many orders higher than nuclear density, it is necessary to develop a completely new physical theory (presumably, some sort of synthesis between the existing theory of gravitation and quantum mechanics). As yet there exist no suitable mathematical tools for research on the state of matter at infinite density (and infinite space-time curvature). In addition, the continuity of time much be disrupted in such a situation, and the question of what there was “before” t = 0, applicable to the standard (metric) concept of time, is devoid of meaning. Some type of extended concept of time is needed. Only the first steps are being taken in the solution of this problem.
As theory and the techniques and methods of observations develop, the very concept of a cosmological universe will be refined. Within the framework of modern cosmology, it is rather natural to think of the metagalaxy as unique. But questions of space-time topology have not been sufficiently worked out so as to arrive at an understanding of all the possibilities that can be realized in nature. This should be remembered particularly in relation to the problem of the age of the universe.
It is not excluded that it will be just as difficult to explain charge asymmetry in the universe. In our cosmic environment (at any rate, within the solar system and probably within the entire galaxy) there is an overwhelming predominance of matter over antimatter. At the same time, according to modern theoretical conceptions, matter and antimatter are completely equal. Cosmology as yet does not offer a sufficiently convincing explanation of this contradiction.
There is still no convincing theory about the origin of the stars and galaxies (a shared problem of cosmology and cosmogony). This problem is at least as difficult as other fundamental problems of origin in modern science (origin of the planets, origin of life). A number of other unsolved problems of cosmology exist as well.
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