Evolution of Structure in Cold Dark Matter Universes

We present an analysis of the clustering evolution of dark matter in four cold dark matter (CDM) cosmologies. We use a suite of high-resolution, 17 million particle, N-body simulations that sample volumes large enough to give clustering statistics with unprecedented accuracy. We investigate a flat model with Ω0 = 0.3, an open model also with Ω0 = 0.3, and two models with Ω = 1, one with the standard CDM power spectrum and the other with the same power spectrum as the Ω0 = 0.3 models. In all cases, the amplitude of primordial fluctuations is set so that the models reproduce the observed abundance of rich galaxy clusters by the present day. We compute mass two-point correlation functions and power spectra over 3 orders of magnitude in spatial scale and find that in all of our simulations they differ significantly from those of the observed galaxy distribution, in both shape and amplitude. Thus, for any of these models to provide an acceptable representation of reality, the distribution of galaxies must be biased relative to the mass in a nontrivial, scale-dependent fashion. In the Ω = 1 models, the required bias is always greater than unity, but in the Ω0 = 0.3 models, an "antibias" is required on scales smaller than ~5 h-1 Mpc. The mass correlation functions in the simulations are well fit by recently published analytic models. The velocity fields are remarkably similar in all the models, whether they are characterized as bulk flows, single-particle, or pairwise velocity dispersions. This similarity is a direct consequence of our adopted normalization and runs contrary to the common belief that the amplitude of the observed galaxy velocity fields can be used to constrain the value of Ω0. The small-scale pairwise velocity dispersion of the dark matter is somewhat larger than recent determinations from galaxy redshift surveys, but the bulk flows predicted by our models are broadly in agreement with most available data.