Quasi-self-similar evolution of the two-point correlation function: strongly nonlinear regime in Omega_0 < 1 universes

Abstract

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.