O ct 2 00 1 Quasi - Self - Similar Evolution of the Two - Point Correlation Function : Strongly Nonlinear Regime in Ω 0 < 1 Universes

The well-known self-similar solution for the two-point correlation function of the density field is valid only in an Einstein – de Sitter universe. We attempt to extend the solution for non – Einstein – de Sitter universes. For this purpose we introduce an idea of quasi-self-similar evolution; this approach is based on the assumption that the evolution of the two-point correlation is a succession of stages of evolution, each of which spans a short enough period to be considered approximately self-similar. In addition we assume that clustering is stable on scales where a physically motivated ‘virialization condition’ is satisfied. These assumptions lead to a definite prediction for the behavior of the two-point correlation function in the strongly nonlinear regime. We show that the prediction agrees well with N-body simulations in non – Einstein – de Sitter cases, and discuss some remaining problems. Subject headings: cosmology: theory — large-scale structure of universe — gravitation — methods: N-body simulations