The kinetic evolution and velocity distribution of gravitational galaxy clustering

Abstract

The spatial statistical distribution function for quasi-equilibrium gravitational clustering in an expanding universe is derived from more general assumptions than before, without needing an earlier Ansatz. Then, it is shown how this statistical distribution is related to the kinetic development of the BBGKY hierarchy and how to obtain an analytic descriptioin for the time evolution of an initial Poisson distribution. From general principles, an analytic velocity distribution function for quasi-equilibrium gravitational clustering is also derived. It has no free parameters. Comparison with N-body experiments shows excellent agreement.