Nonlinear density evolution from an improved spherical collapse model

We investigate the evolution of nonlinear density perturbations by taking into account the effects of shear and angular momentum of the system. Starting from the standard spherical top hat model in which these terms are ignored, we introduce a physically motivated closure condition which specifies the dependence of these terms on δ. The modified equation can be used to model the behavior of an overdense region over a sufficiently large range of δ. The key new idea is a Taylor series expansion in (1/δ) to model the nonlinear epoch. We show that the modified equations quite generically lead to the formation of stable structures in which the gravitational collapse is halted at around the virial radius. The analysis also allows us to connect up the behavior of individual overdense regions with the nonlinear scaling relations satisfied by the two point correlation function. Subject headings: Cosmology : theory – dark matter, large scale structure of the Universe