It has recently been shown that the correct halo mass function high mass behaviour may be obtained by an appropriate treatment of the all-mass-at-center problem. Here we show that the treatment of this problem leads to an accumulated mass fraction, F, which is not a universal function of the linear variance of the density contrast, but depends also on the shape of the power spectrum. For relevant power spectra F is a universal function of two quantities: the linear variance and a quantity related to the local shape (at the given mass scale) of the power spectrum. This implies, for a given shape of the power spectrum, a redshift dependence of the mass function, which is quite important for a cold dark matter power spectrum. Our results are in good agreement with numerical simulations.
@article{arxiv.astro-ph/0608291,
title = {The Halo Mass Function Redshift Dependence},
author = {Juan E. Betancort-Rijo and Antonio D. Montero-Dorta},
journal= {arXiv preprint arXiv:astro-ph/0608291},
year = {2009}
}