The Effect of Non-Gaussian Statistics on the Mass Multiplicity of Cosmic Structures

The mass function of cosmic structures is computed in the framework of the hierarchical clustering picture for a general statistics of density perturbations. 'Hierarchical' distributions are extensively analyzed; it is found that the multiplicity function preserves the Press-Schechter functional form with enhanced power on large scales compared to the Gaussian case. A class of scale-invariant non-Gaussian statistics, among which are a model due to Peebles and the lognormal distribution, are also analyzed. All these predict a mass function which is a decreasing power law at low mass followed by an exponential decay at high mass; none of them, however, yields a mass function of the Press-Schechter type. The effect of a statistical bias on the origin of condensations is also discussed. The comparison of these theoretical formulae with the observed mass multiplicity of galaxies, groups, and clusters may represent a powerful tool to test the statistics of cosmological perturbations.