COSMOLOGY, GALAXY FORMATION BARBARA RYDEN Cosmology, the study of the evolution of the universe as a whole, is closely linked with the study of the evolution and formation of galaxies. The properties of galaxies today depend, in part, on the physical conditions in the very early universe. Various cosmological models for the evolution of the universe make definite predictions of the masses, binding energies, angular momenta, spatial distribution, and other properties of galaxies. Comparison of the predicted with the observed values for galaxies can act as a discriminant among competing cosmological models. The general cosmological framework in which the formation of galaxies must be explained is the standard Hot Big Bang model. Edwin P. Hubble's discovery of a distance-redshift relation for galaxies is evidence for a uniformly expanding universe. Four decades after Hubble's discovery of the expansion of the universe, Arno Penzias and Robert Wilson discovered the cosmic microwave background (CMB), evidence for the Hot Big Bang; the universe, initially very hot, is cooling as it expands. To create galaxies in an expanding universe, there must be some force, working against the universal expansion, which pulls the mass of a galaxy together into a bound lump. In most theories of galaxy formation, this force is taken to be gravity, working on an initial density perturbation. Limits on the early height of the perturbations are imposed by the observed smoothness of the CMB. Observations of the CMB show that its temperature fluctuations **/T are smaller than a few times ****** over all angular scales smaller than the dipole. To achieve such a smooth microwave background, the universe must have been quite homogeneous at the time of recombination (at a redshift ********), when the universe became transparent to radiation. A successful theory of galaxy formation must thus explain the transition between the smooth universe at the time of recombination and the lumpy universe (where the lumps are galaxies) seen today. GRAVITATIONAL THEORY Suppose that the universe has a density * which varies throughout space, but which has a mean value **ł The gravitational instability scenario for galaxy formation states that galaxies form in regions where * is larger than **; that is, where the overdensity *** (********) is sufficiently greater than zero. These regions will collapse under their own Self-gravity; if they are then dense and hot enough for the gas within them to dissipate energy by bremsstrahlung and radiative recombination, the gas will fall to the center of the collapsed region, fragmenting to form stars, and thus forming the visible portions of galaxies that we see today. The rate at which the density perturbations * grow with time under the influence of gravity was first computed by James Jeans. He found that in a static, nearly uniform universe, perturbations longer than a critical length, known as the Jeans length, grow exponentially with time. Perturbations smaller than this size are stabilized by the pressure gradients which build up during the attempted collapse. Jeans assumed a static universe; in an expanding universe, the growth of the perturbations is slowed by the universal expansion. If the universe expands, perturbations grow at most as a power of the time t, instead of exponentially. In a flat (*****) matter-dominated universe, for instance, ********. The growth of the perturbations can thus be followed from their initially small values to the time when ****, when they collapse to form galaxies. The question remains, however: What was the cause of the initial small density perturbations? GAUSSIAN PERTURBATIONS In one promising theory, the density perturbations are formed during an inflationary era in the early universe, and take the form of an isotropic homogeneous Gaussian density field. Inflation was originally proposed as a means of making the universe flat (i.e., setting the density parameter ** extremely close to one) and of making the universe homogeneous on large scales. Although inflation flattens out previously existing perturbations, during the process of expansion, it stamps a new set of perturbations on the universe. Inflation occurs when a field * undergoes a phase transition from a false vacuum to a true vacuum of lower energy; during the transition, the universe expands exponentially. As a result, microscopic quantum fluctuations in * are expanded, along with the general expansion of the universe, to cosmological length scales. The perturbations in the field * lead, via distortions of the space-time metric, to perturbations * in the mass-energy density of the universe. As a necessary consequence of the quantum origins of the perturbations, the density is a Gaussian random field; that is, the probability distribution function for * takes the form **************. The simplest inflationary scenarios predict a scale-invariant distribution of perturbation sires. An alternate way of expressing this result is to say that the power spectrum P(k) of the Gaussian field * has the Harrison-Zel'dovich form P(k) * k. When the universe stops inflating (when it is ******** old, in most inflationary scenarios), it enters a period when the majority of the energy of the universe is in the form of radiation. During this radiation-dominated period, density fluctuations with wavelengths smaller than the cosmological horizon size remain nearly constant in amplitude. Fluctuations which are larger than the horizon, however, are able to grow at the rate *****. As the radiation-dominated epoch continues, perturbations of longer and longer wavelength fall within the horizon and have their growth frozen. Thus, during this epoch, the shape of the power spectrum P(k) is continuously modified. As the radiation redshifts away its energy, the massive particles in the universe contribute a larger and larger fraction of the mass-energy density of the universe. Finally, at a redshift *** = 2.5x********(h is Hubble's constant in units of 100 km *******), the contributions of radiation and matter are equal, and the universe enters a matter-dominated phase, when all density perturbations inside and outside the horizon are free to grow. At ***, the power spectrum of the inflation-born perturbations, as modified during the radiation-dominated era, remains P(k) * k at the smallest wave numbers (corresponding to long wavelengths), but falls off at the rate P(k) *********** as k goes to infinity. The turnover in the power spectrum occurs gradually around wave number ************ Mpc, corresponding to the horizon size at the redshift ***. In standard cosmological models, the universe has been matter dominated from *** until the present. If ** is presently nearly equal to one, a natural result of inflation, then most of the mass must be in the form of dark matter. The fate of density perturbations after **** depends on whether the dark matter is cold, having negligibly small streaming velocities, or is hot, having relativistic streaming velocities at the time when galactic-sized masses first enter the horizon. Cold dark matter (or CDM) may consist of particles (e.g., photinos) which are massive enough to render their thermal velocities negligible, or of particles (e.g., axions) which are created with negligible velocities. In either case, the velocities are too small to smooth out density fluctuations, and the power spectrum P(k) is unmodified by smoothing at large k; see Fig. 1 for the shape of the CDM power spectrum. A CDM-dominated universe has density fluctuations on all length scales from subgalactic sizes upward. In the CDM scenario, then, galaxies form by a hierarchical process of collisions and mergers; the smallest and densest objects collapse first, then subsequent collisions gradually build up objects the size of galaxies. In recognition of this process, the CDM scenario is referred to as a "hierarchical clustering," or "bottom-up" model. The CDM model has been extensively studied with analytic calculations and n-body simulations. The main successes of CDM are that it produces objects with the proper masses, density profiles, and angular momenta to match observed galaxies. The principal failures of CDM are that it fails to produce sufficient large-scale structure; it cannot match the observed correlation function for clusters of galaxies or the streaming velocities reported on scales as large as ****** Mpc. Hot dark matter (HDM), by contrast with CDM, smooths out the smallest density fluctuations by its free streaming velocity. The leading candidate for the HDM particle is a massive neutrino. If the neutrino has a mass of 30 eV, thus providing enough mass to make ***, then cosmological neutrinos will not cool sufficiently to have nonrelativistic thermal velocities until the universe has a comoving horizon size of 4 Mpc, containing a mass ********, roughly that of a supercluster of galaxies. Perturbations smaller than this size will be smoothed away; the resulting HDM power spectrum is shown in Fig.1. In the HDM scenario, the first objects which form are superclusters; these collapse first along their short axes to form "pancakes," which then fragment to form galaxies. For this reason, the HDM scenario is referred to as a "pancaking" or "top-down" scenario. The main success of HDM is that a top-down scenario more easily explains the observed streaming velocities and correlations on large scale. The principal, perhaps fatal, failure of HDM is that it requires galaxies to have formed very recently, at *****; as astronomers look deeper into space, they find galaxies at considerably earlier redshifts than this. In order to evade the flaws of both the CDM and HDM scenarios, astrophysicists have speculated about universes filled with warm dark matter (intermediate between hot and cold in its properties), or with a mixture of hot dark matter and cold dark matter, or with unstable dark matter, in which heavy cold particles decay into light hot particles. All of these speculations are variations on the theme of gravitational collapse of Gaussian density fields. COSMIC STRINGS Galaxies might form by the collapse of non-gaussian density perturbations. One possible source of such perturbations are the topological defects known as cosmic strings. As the universe cools from its initial high temperature, symmetry breaking can result in the formation of stable topological defects, which have high energy density and may act as seeds for galaxy formation. Depending on the form of the symmetry, thełtopological defects can be monopoles (pointlike defects), cosmic strings (linear defects), or domain walls (planar defects). Monopoles and domain walls have undesirable side effects, cosmologically speaking; thus, attention has been focused on cosmic strings as a possible source of seeds for galaxy formation. Analytic and numerical computations of the evolution of cosmic string networks indicate that at any given time after the strings form, there will be approximately one infinite string, reaching from horizon to horizon. In addition, the number of strings with radii in the interval ***** will be **************. These string loops of all sizes act as seeds for the gravitational accretion of matter. Computer simulations have been run of the accretion of mass onto cosmic strings embedded in a background of CDM, HDM, or simply ordinary gas. Of these models, the one which most closely resembles the observed universe is the model which combines strings with hot dark matter. The strings provide the seeds for galaxies; the HDM provides the longer wavelength fluctuations which are required to explain the large-scale structure (on scales greater than 10 Mpc). EXPLOSION THEORY The difficulty of simultaneously explaining the existence of galaxies and of large-scale structure in gravitational collapse models has led to the consideration of models in which the mass destined to become galaxies is shoved into place by forces other than gravity. One such model is the explosion theory. If a large amount of energy is injected into a small region of the early universe-by a powerful explosion, for instance-then a blast wave will expand outward from that region. The blast sweeps up a shell of matter; this shell is gravitationally unstable, and fragments into galaxies. Thus, if these explosions went off at random positions in the early universe, today galaxies would exist on thin shells surrounding the voids which were evacuated by the explosion. In fact, this is what is seen; redshift surveys show a "bubbly" or "spongy" distribution of galaxies, containing voids which are typically ****** Mpc across. Thus, the explosion theory provides a plausible explanation for the observed large-scale distribution of galaxies. A drawback of the theory, however, is the large energies which it requires. Creating a void 30 Mpc across requires an explosion with energy ***** erg. Procuring such a large energy requires exotic mechanisms, such as, for instance, a radiating superconducting cosmic string. PRESENT STATUS: FUTURE TRENDS None of the cosmological scenarios sketched above is completely satisfactory at describing the known properties of galaxies. The borderland between cosmology and the study of galaxy formation is, and will probably long remain, a fruitful realm for research. On one hand, further observations of galaxies will give us more clues about how they must have formed; on the other hand, theoretical advances in cosmology will hint at new mechanisms for making galaxies. In the end, a better knowledge of galaxy formation will improve our understanding of cosmology; a better knowledge of cosmology will improve our understanding of galaxy formation. Additional Reading Blumenthal, G.R., Faber, S.M., Primack, J.R., and Rees, M.J. (1984). Formation of galaxies and large-scale structure in the universe. Nature 311 517. Krauss, L.M.(1986). Dark matter in the Universe. Scientific American 255(No. 6)58. Ostriker, J.P.(1988). Explosive origins of large-scale structures. In Large Scale Structures of the Universe, J. Audouze et al., eds. Reidel, Dordrecht, p.321. Rees, M.J.(1987). The emergence of structure in the universe: Galaxy formation and dark matter. In Three Hundred Years of Gravitation, S.W. Hawking and W.Israel, eds. Cambridge University Press, Cambridge, p.459. Silk, J.(1987). Galaxy formation: Confrontation with observations. In Observational Cosmology, A. Hewitt et al., eds. Reidel, Dordrecht, p.391. See also Background Radiation, Microwave; Cosmology, Big Bang Theory; Cosmology, Cosmic Strings; Cosmology, Inflationary Universe; Dark Matter, Cosmological; Voids, Extragalactic.