Evolution of the cosmological mass function in a moving barrier model

Abstract

I calculate the mass function evolution in a $\Lambda$CDM model by means of the excursion set model and an improved version of the barrier shape obtained in Del Popolo & Gambera (1998), which implicitly takes account of the total angular momentum acquired by the proto-structure during evolution and of a non-zero cosmological constant. I compare the result with Reed et al. (2003), who used a high resolution $\Lambda$CDM numerical simulation to calculate the mass function of dark matter haloes down to the scale of dwarf galaxies, back to a redshift of fifteen. I show that the mass function obtained in the present paper, gives similar predictions to the Sheth & Tormen mass function but it does not show the overprediction of extremely rare objects shown by the Sheth and Tormen mass function. 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.