On the clustering of particles in an expanding Universe

Abstract

The clustering of particles in an expanding Friedmann universe is investigated through 1000- and 20,000-body numerical simulations. Results of the simulations are analyzed in terms of two- and three-point correlation functions, the mean relative peculiar velocity between particle pairs and the mean square peculiar velocity dispersion between pairs, and compared with the results of the numerical integration of the BBGKY hierarchy of kinetic equations of Davis and Peebles (1977). In the case of Einstein-de Sitter models, a nonpower law form for the two-point correlation function is obtained, in rough agreement with simple analytic treatments based on the homogeneous spherical cluster models for the collapse of protoclusters. The results, however, are observed to be in conflict with the calculations of Davis and Peebles, which suggest that clusters develop substantial nonradial motions while they are still small density fluctuations, so that when a cluster fragments out of the Hubble expansion it is already virialized. It is pointed out that more observational and theoretical work is required to determine whether the present approach is, in fact, reasonable.