The cosmological mass function

Abstract

This paper reviews the cosmological mass function from a theoretical point of view, starting from the seminal paper of Press and Shechter to the latest developments, and discusses some improvements on mass-function models in the literature. The numerical mass function given by Yahagi et al. YNY is compared with the theoretical mass function obtained in the present paper by means of an excursionset model and an improved version of the barrier shape obtained by Del Popolo and Gambera [30], which implicitly takes account of the total angularmomentum acquired by the proto-structure during its evolution and of a non-zero cosmological constant. The mass function obtained in the present paper is in better agreement with the simulations of Del Popolo than other previous models. The mass function considered provides as good a fit to the simulation results as the function proposed in Del Popolo, but, in contrast to this latter function, was derived from a sound theoretical basis. The evolution of the mass function is calculated in a ΛCDM model, and the results compared with those of Reed et al. [94], who used a high resolution ΛCDM numerical simulation to calculate the mass function of dark matter haloes down to the scale of dwarf galaxies and back to a redshift of fifteen. The mass function obtained in the present paper gives similar predictions as the Sheth-Tormen (ST) mass function, but does not overpredict the number of extremely rare objects. The results confirm previous findings that the simulated halo mass function can be described solely by the variance of the mass distribution, and thus has no explicit redshift dependence. It is show that a PS-like approach together with the ellipsoidal model introduced in Del Popolo provides a better description of the theoretical mass function.