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 which sample volumes large enough to give clustering statistics with unprecedented accuracy. We investigate both a flat and an open model with Omega_0=0.3, and two models with Omega=1, one with the standard CDM power spectrum and the other with the same power spectrum as the Omega_0=0.3 models. The amplitude of primordial fluctuations is set so that the models reproduce the observed abundance of rich galaxy clusters by the present day. The mass 2-point correlation function and power spectrum of all the simulations 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 non-trivial, scale-dependent, fashion. In the Omega=1 models the required bias is always greater than unity, but in the Omega_0=0.3 models an "antibias" is required on scales smaller than \sim 5\hmpc. 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 be characterised as bulk flows, 1-particle or pairwise velocity dispersions. This similarity is a direct consequence of our adopted normalisation. 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.