A model for the evolution of large density perturbations - Normalization and predictions

The nonlinear evolution of matter density fluctuations in the universe is studied. The Zeldovich solution is applied to the quasi-linear regime, and a model to stop the fluctuations from growing in the very nonlinear regime is considered. 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 values of Omega. With this model, it is possible 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 Omega. Predictions of the model on the filling factor of superclusters and voids are compared with observations. 37 refs