© CAMBRIDGE UNIVERSITY PRESS 1999

1.1 Introduction

The standard theory of cosmology is the Hot Big Bang, according to which the early universe was hot, dense, very nearly homogeneous, and expanding adiabatically according to the laws of general relativity (GR). This theory nicely accounts for the cosmic background radiation, and is at least roughly consistent with the abundances of the lightest nuclides. It is probably even true, as far as it goes; at least, I will assume so here. But as a fundamental theory of cosmology, the standard theory is seriously incomplete. One way of putting this is to say that it describes the middle of the story, but leaves us guessing about both the beginning and the end.

Galaxies and clusters of galaxies are the largest bound systems, and the filamentary or wall-like superclusters and the voids between them are the largest scale structures visible in the universe, but their origins are not yet entirely understood. Moreover, within the framework of the standard theory of gravity, there is compelling observational evidence that most of the mass detected gravitationally in galaxies and clusters, and especially on larger scales, is ``dark'' - that is, visible neither in absorption nor emission of any frequency of electromagnetic radiation. But we still do not know what this dark matter is.

Explaining the rich variety and correlations of galaxy and cluster morphology will require filling in much more of the history of the universe:

• Beginnings, in order to understand the origin of the fluctuations that eventually collapse gravitationally to form galaxies and large scale structure. This is a mystery in the standard hot big bang universe, because the matter that comprises a typical galaxy, for example, first came into causal contact about a year after the Big Bang. It is hard to see how galaxy-size fluctuations could have formed after that, but even harder to see how they could have formed earlier. The best solution to this problem yet discovered, and the one emphasized here, is cosmic inflation. The main alternative, discussed in less detail here, is cosmic topological defects.

• Denouement, since even given appropriate initial fluctuations, we are far from understanding the evolution of galaxies, clusters, and large scale structure - or even the origins of stars and the stellar initial mass function.

• And the dark matter is probably the key to unravelling the plot since it appears to be gravitationally dominant on all scales larger than the cores of galaxies. The dark matter is therefore crucial for understanding the evolution and present structure of galaxies, clusters, superclusters and voids.

The present chapter (updating Primack 1987-88, 1993, 1995-97) concentrates on the period after the first three minutes, during which the universe expands by a factor of ~ 10⁸ to its present size, and all the observed structures form. This is now an area undergoing intense development in astrophysics, both observationally and theoretically. It is likely that the present decade will see the construction at last of a fundamental theory of cosmology, with perhaps profound implications for particle physics - and possibly even for broader areas of modern culture.

The current controversy over the amount of matter in the universe will be emphasized, discussing especially the two leading alternatives: a critical-density universe, i.e. with _{0 0} / _c = 1 (see Table 1.1), vs. a low-density universe having ₀ 0.3 with a positive cosmological constant > 0 such that / (3H₀²) = 1 - ₀ supplying the additional density required for the flatness predicted by the simplest inflationary models. (The significance of the cosmological parameters ₀, H₀, t₀, and is discussed in Section 1.2.) = 1 requires that the expansion rate of the universe, the Hubble parameter H₀ 100h km s^-1 Mpc^-1 50 h₅₀ km s^-1 Mpc^-1, be relatively low, h 0.6, in order that the age of the universe t₀ be as large as the minimum estimate of the age of the stars in the oldest globular clusters. If the expansion rate turns out to be larger than this, we will see that GR then requires that ₀ < 1, with a positive cosmological constant giving a larger age for any value of ₀.

Although this chapter will concentrate on the implications of CDM and alternative theories of dark matter for the development of galaxies and large scale structure in the relatively ``recent'' universe, we can hardly avoid recalling some of the earlier parts of the story. Inflation or cosmic defects will be important in this context for the nearly constant curvature (near-``Zel'dovich'') spectrum of primordial fluctuations and as plausible solutions to the problem of generating these large scale fluctuations without violating causality; and primordial nucleosynthesis will be important as a source of information on the amount of ordinary (``baryonic'') matter in the universe. The fact that the observational lower bound on ₀ - namely 0.3 ₀ - exceeds the most conservative upper limit on baryonic mass _b 0.03 h^-2 from Big Bang Nucleosynthesis (Copi, Schramm, & Turner 1995; cf. Hata et al. 1995) is the main evidence that there must be such nonbaryonic dark matter particles.

Of special concern will be evidence and arguments bearing on the astrophysical properties of the dark matter, which can also help to constrain possible particle physics candidates. The most popular of these are few-eV neutrinos (the ``hot'' dark matter candidate), heavy stable particles such as ~ 100 GeV photinos (or whatever neutralino is the lightest supersymmetric partner particle) or 10<sup>-6</sup>-10<sup>-3</sup> eV ``invisible'' axions (these remain the favorite ``cold'' dark matter candidates), and various more exotic ideas such as keV gravitinos (``warm'' dark matter) or primordial black holes (BH).

The usual astrophysical classification of the dark matter candidates is into hot, warm, or cold, depending on their thermal velocity in the early universe. Hot dark matter, such as few-eV neutrinos, is still relativistic when galaxy-size masses (~ 10¹² M) are first encompassed within the horizon. Warm dark matter is just becoming nonrelativistic then. Cold dark matter, such as axions or massive photinos, is nonrelativistic when even globular cluster masses (~ 10⁶ M) come within the horizon. As a consequence, fluctuations on galaxy scales are wiped out by the ``free streaming'' of the hot dark matter particles which are moving at nearly the speed of light. But galaxy-size fluctuations are preserved with warm dark matter, and all cosmologically relevant fluctuations survive in a universe dominated by the sluggishly moving cold dark matter.

The first possibility for nonbaryonic dark matter that was examined in detail was massive neutrinos, assumed to have mass ~ 25 eV - both because that mass corresponds to closure density for h 0.5, and because in the late 1970s the Moscow tritium -decay experiment provided evidence (subsequently contradicted by other experiments) that the electron neutrino has that mass. Although this picture leads to superclusters and voids of roughly the size seen, superclusters are the first structures to collapse in this theory since smaller size fluctuations do not survive. The theory foundered on this point, however, since galaxies are almost certainly older than superclusters. The standard (adiabatic) form of this theory has recently been ruled out by the COBE data: if the amplitude of the fluctuation spectrum is small enough for consistency with the COBE fluctuations, superclusters would just be beginning to form at the present epoch, and hardly any smaller-scale structures, including galaxies, could have formed by the present epoch.

A currently popular possibility is that the dark matter is cold. After Peebles (1982), we were among those who first proposed and worked out the consequences of the Cold Dark Matter (CDM) model (Primack & Blumenthal 1983, 1984; Blumenthal et al. 1984). Its virtues include an account of galaxy and cluster formation that at first sight appeared to be very attractive. Its defects took longer to uncover, partly because uncertainty about how to normalize the CDM fluctuation amplitude allowed for a certain amount of fudging, at least until COBE measured the fluctuation amplitude. The most serious problem with CDM is probably the mismatch between supercluster-scale and galaxy-scale structures and velocities, which suggests that the CDM fluctuation spectrum is not quite the right shape - which can perhaps be remedied if the dark matter content is a mixture of hot and cold, or if there is less than a critical density of cold dark matter.

The basic theoretical framework for cosmology is reviewed first, followed by a discussion of the current knowledge about the fundamental cosmological parameters.

Table 1.1 lists the values of the most important physical constants used in this chapter (cf. Barnett et al. 1996). The distance to distant galaxies is deduced from their redshifts; consequently, the parameter h appears in many formulas where the distance matters.

Table 1.1. Physical Constants for Cosmology

parsec	pc	= 3.09 x 1018 cm = 3.26 light years (lyr)
Newton's const.	G	= 6.67 x 10-8 dyne cm2 g-2
Hubble parameter	H0	= 100h km s-1 Mpc-1 , 1/2 h 1
Hubble time	H0-1	= h-1 9.78 Gyr
Hubble radius	RH	= cH-1 = 3.00h-1 Gpc
critical density	c	= 3H2 / 8 G = 1.88 x 10-29 h2 g cm-3
		= 10.5h2 keV cm-3 = 2.78 x 1011 h2 M Mpc-3
speed of light	c	= 3.00 x 1010 cm s-1 = 306 Mpc Gyr-1
solar mass	M	= 1.99 x 1033 g
solar luminosity	L	= 3.85 x 1033 erg s-1
Planck's const.		= 1.05 x 10-27 erg s = 6.58 x 10-16 eV s
Planck mass	mPl	= ( c/G)1/2 = 2.18 x 10-5 g = 1.22 x 1019 GeV