The Halo Mass Function Redshift Dependence

It has recently been shown that the correct halo mass function high-mass behavior 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, that is not a universal function of the linear variance of the density contrast but depends 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.