The accretion history of dark matter haloes - I. The physical origin of the universal function

Abstract

Understanding the universal accretion history of dark matter haloes is the first step towards determining the origin of their structure. We use the extended Press-Schechter formalism to derive the halo mass accretion history from the growth rate of initial density perturbations. We show that the halo mass history is well described by an exponential function of redshift in the high-redshift regime. However, in the low-redshift regime the mass history follows a power law because the growth of density perturbations is halted in the dark energy dominated era due to the accelerated expansion of the Universe. We provide an analytic model that follows the expression M(z) = M0(1 + z)af (M0)e-f (M0)z..