Alternatives to the Press–Schechter cosmological mass function

We investigate the validity of the Press–Schechter formalism for calculating the mass distribution function, |f(M)| of the bound objects which condense out of a primordial density perturbation field. We give a revised analysis, which automatically has the correct normalization and accounts explicitly for the mass in underdense regions. The resulting |f(M)| depends on the form of the filter function chosen; in general this method predicts more low-mass objects than the Press–Schechter formalism. We also consider the effects of identifying density maxima as the sites of proto-objects. This predicts an |f(M)| with a different shape, but again with a low-mass power-law tail which lies above the Press–Schechter result, unless a very large mass is assigned to each peak.