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In the previous Sections we have described several possible scenarios for galaxy formation. It is reasonable to ask whether any aspects of these theories will survive for a significant length of time, or whether our knowledge of galaxy formation is still so patchy that even basic ideas might be completely overturned by new observations. Of course, any judgement on the relative merits of current theories is bound to be subjective, so we would caution the reader that the views expressed below are unlikely to be shared by all research workers.

In this article, we have taken the approach that the cosmological density parameter Omega and the initial shape of the fluctuation spectrum are effectively free parameters for theories of galaxy formation, to be constrained by observations. Dynamical arguments (Section 2.4) suggest that Omega lies somewhere between the limits 0.1 ltapprox Omega ltapprox 1, but the large. uncertainty means that we can attempt to make theories with any value of Omega within this range.

However, there is an alternative view that the only natural value for the cosmological density is Omega = 1. Suppose that the present cosmological density parameter were Omega = 0.1. At early times, for example at the GUT epoch when T ~ 1015 GeV, the density parameter would have been equal to unity except for one part in ~ 1050. Any larger deviation would lead to a universe which either has a negligible present density or to a closed universe which would have recollapsed before stars and galaxies could have formed. Rather than appeal to such finely tuned conditions (perhaps motivated by anthropic arguments, e.g. Barrow, 1982) in the early universe, it seems preferable to find a fundamental principle which requires Omega = 1. One idea, due to Gunn (1981) utilizes phase transitions in grand unified theories (see Guth, 1982, for an introductory review). In Guth's inflationary scenario (see also Linde, 1982; Albrecht and Steinhardt, 1982) the embryo universe expands exponentially by many orders of magnitude as it supercools below the critical temperature of a GUT phase transition. The flatness of the universe may be explained because the energy density remains constant during the expansion phase while the curvature term k / R2 decreases exponentially. By the time the exponential phase is over, the curvature term is likely to be negligible so the present value of Omega should be extremely close to unity. In addition, inflationary scenarios may help to explain why the density of GUT monopoles is much less than the density of nucleons (Guth, 1982; see also Preskill, 1979) and may provide an explanation of scale-free (n = + 1) primordial fluctuations, though recent work indicates a spectrum with an excessively large amplitude (Hawking, 1982; Guth and Pi, 1982; Bardeen et al., 1983). Despite the difficulties with the inflationary model, it is impressive that we can now contemplate quantitative calculations to answer such fundamental questions.

Grand unification theories favour adiabatic perturbations, although as described in Section 9.1 entropy perturbations may arise from primordial shear or vorticity. The most natural hypothesis, however, is that only the adiabatic mode is present. We would argue that the Zel'dovich scale-free spectrum is the only spectrum that is likely to arise naturally in the early universe (see Press, 1980; Zel'dovich, 1980; Kibble, 1976; and the papers on inflationary models referred to above). This is because we require an amplitude of delta rho / rho ~ 10-4 on galactic scales to produce galaxies by gravitational instability. Any other power-law spectrum must be truncated to avoid divergent curvature fluctuations and requires that a theory for the origin of fluctuations involves a characteristic mass scale comparable to that of a galaxy. The Zel'dovich spectrum neatly avoids this difficulty.

If we take these arguments at all seriously, we are required to build a theory of galaxy formation using a scale-free adiabatic spectrum with the cosmological density parameter set to unity. This provides a severe constraint. The pancake theory, assuming massless neutrinos, is ruled out since it predicts order unity fluctuations in the mass density on scales much larger than the coherence-length of the galaxy distribution. The pancake theory, including massive neutrinos, also faces a problem in accounting for galaxy clustering (cf. Eq. 5.24b) unless galaxies form at very recent epochs (z ltapprox 1) which would seem to be unreasonable (White, Frenk and Davis, 1983; and Kaiser, 1983b). The remaining possibility is that "cold" weakly interacting particles (e.g. gravitinos or axions) provide the dominant contribution to the mass density. As reviewed in Section 9.3, this leads to a non-power law fluctuation spectrum. The details of galaxy formation and clustering within this theory are only just beginning to be worked out (e.g. Peebles, 1983) but we would expect that many of the features of hierarchical clustering models discussed in previous sections, such as radiative cooling processes, angular momentum and dissipative collapse are applicable in this context. If, ultimately, the theory is found not to work, we will have to revise our opinions as to the "naturalness" of the initial conditions.

Understanding the formation of galaxies and clusters requires an understanding of the physics of the very early universe. Particle physicists are likely to provide galaxy formers with a variety of new ideas in the next few years. We expect that galaxy formers will come up with a few surprises for particle physicists as well.


G.E. acknowledges the hospitality of the Astronomy Department at Berkeley where part of this review was written and to King's College, Cambridge, for financial support. We thank Rebecca Elson, Nick Kaiser, Nigel Sharp and Brent Tully for their comments on parts of the manuscript. We are especially grateful to Carol Loretz for her skillful job in typing the manuscript and to Richard Sword for preparing the Figures. We would like to thank our various colleagues who have helped shape our ideas on galaxy formation. Dick Bond, Mike Fall, Craig Hogan, Colin Norman and Mike Wilson deserve a special mention. This work was supported in part by DOE contract ATO3-82ER40069 and by a NASA grant, NGR 05-003-578.

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