Annu. Rev. Astron. Astrophys. 1998. 36: 599-654 Copyright © 1998 by Annual Reviews. All rights reserved

4. TESTING OF COSMOLOGICAL MODELS

During the 1980s the dominant use of cosmological simulations was to test models of structure formation, particularly the CDM model. While simulations have proven to be much more versatile in recent years, model testing remains an important application.

Perhaps the first test of a cosmogonical model should be whether it is sufficiently well posed to enable meaningful simulation in the first place. Phenomenological models must be formulated precisely within a consistent physical framework (e.g. explosive galaxy formation models). Sometimes the fundamental physics is known but is too complex to allow for fully satisfactory simulation, given the limitations of current computers and numerical algorithms (e.g. superconducting cosmic strings). It is possible that even the best current simulations vastly oversimplify the physics needed for reliable structure formation models. However, the detailed comparison of these models with data suggests that such a view is overly pessimistic. Recent high-resolution simulations compare remarkably well with many aspects of the observed galaxy distribution.

4.1. Cold Dark Matter

The CDM model became the platform on which simulations of cosmic structure formation matured into a powerful theoretical tool during the 1980s. It is not reviewed extensively here, as accounts have been given already by Frenk (1991), Davis et al (1992a), Liddle & Lyth (1993), Ostriker (1993). However, a brief discussion of the CDM model and its shortcomings is worthwhile to motivate study of the currently popular alternatives.

The CDM model adopts parameter values H₀ 50 km s^-1 Mpc^-1 and _c = 1 - _b 0.95, where _c and _b give the present mean mass density of CDM and baryons, respectively, normalized to the critical density 8 G / 3H₀². Prior to the COBE measurement of temperature anisotropy (Smoot et al 1992), the only significant free parameter in the CDM model was the normalization of the power spectrum, conventionally specified by the rms relative mass density fluctuation in a sphere of radius R₈ = 8 h^-1 Mpc, ₈ = (R₈), computed using Equation 9 with the power spectrum extrapolated to the present day assuming linear theory. When set to the observed value based on galaxy counts, ₈ = 1, the CDM model predicts excessive peculiar velocities for galaxies (Davis et al 1985). A similar conclusion follows from the cosmic virial theorem, which implies 0.3 if galaxies are a fair tracer of the clustering and dynamics of the mass (Peebles 1986). However, Carlberg et al (1990), Couchman & Carlberg (1992) found in their high-resolution simulations that dark matter halos have substantially smaller velocities than the mass, an effect they termed velocity bias. During this same period, evidence accumulated that the b = 1 / ₈ = 2.5 "standard biased" CDM model favored by Davis et al (1985) lacked sufficient power on large (~ 50 h^-1 Mpc) scales to explain the observed clustering (Maddox et al 1990, Saunders et al 1991) or velocity fields (Lynden-Bell et al 1988) of galaxies.

Without exotic physics such as gravitational radiation produced in "tilted" inflationary models, the large-angular-scale microwave background anisotropy measurements pinned down the normalization of CDM models to ₈ 1.2 (Wright et al 1992, Bunn & White 1997). With a strong velocity bias, interest revived in "unbiased" (b 1) CDM models. Several groups explored the constraints imposed by small-scale clustering, pairwise velocities, the circular velocity and mass distributions of galaxies, galaxy cluster masses, etc (e.g. Bahcall & Cen 1993, Cen & Ostriker 1993c, Brainerd & Villumsen 1994a, b, Gelb & Bertschinger 1994a, b, Zurek et al 1994). From this and additional work, the consensus has emerged that the unbiased CDM model is ruled out because it has too much power on small scales.