NONSPHERICAL COLLAPSE AND THE ANALYTICAL MASS FUNCTION

Non-spherical dynamical approximations and models for gravitational co llapse are used to extend the well-known Press & Schechter (PS) approa ch, in order to determine analytical expressions for the mass function of cosmic structures. The problem is rigorously set up by considering the intrinsic Lagrangian nature of the mass function. The Zel'dovich approximation (ZEL), a ZEL-based model and the homogeneous ellipsodail collapse model are used to predict the collapse time of a mass elemen t. It results that more large-mass objects are expected to form than t he usual PS relation. In particular, it can be dynamically explained w hy lower delta(c) values are found to fit the results of several N-bod y simulations.