PRESS–SCHECHTER MASS FUNCTION AND THE NORMALIZATION PROBLEM

摘要

The Press–Schechter (PS) formalism yields the number density of bound objects formed during the evolution of the Universe, which should be compared to the great clusters of galaxies now observed. This basic approach has an intrinsic problem of normalization (the so-called missing factor 2). We argue here that such a problem is related to specific choices of the statistical distribution describing the initial density fluctuations. The fudge factor 2 occurs even in the context of the q-nonextensive statistics which is the simplest one-parametric extension of the Gaussian distribution. In general, other distributions require different corrections, such as the log-normal distribution. However, by assuming that the perturbations can be described by the Burr distribution, we prove that the PS approach in this case is not plagued with the normalization problem.