A MODEL FOR THE EVOLUTION OF LARGE DENSITY PERTURBATIONS - NORMALIZATION AND PREDICTIONS

We study the nonlinear evolution of matter density fluctuations in the universe. We apply the Zeldovich solution to the quasi-linear regime and consider a model to stop the fluctuations from growing in the very nonlinear regime. The model is based in the virialization of collapsing pancakes. The density contrast of a typical pancake at the time it starts to relax is given for universes with different Ω. With this model we are able to calculate the probability density of the final density fluctuations. Results on the normalization of the power spectrum of the initial density fluctuations are given as a function of Ω. Predictions of the model on the filling factor of superclusters and voids are compared with observations.