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Understanding the universal accretion history of dark matter halos is thefirst step towards determining the origin of their structure. We use theextended Press-Schechter formalism to derive the halo mass accretion historyfrom the growth rate of initial density perturbations. We show that the halomass history is well described by an exponential function of redshift in thehigh-redshift regime. However, in the low-redshift regime the mass historyfollows a power law because the growth of density perturbations is halted inthe dark energy dominated era due to the accelerated expansion of the Universe.We provide an analytic model that follows the expression $M(z) =M_{0}(1+z)^{af(M_{0})}e^{-f(M_{0})z}$, where $M_{0} = M(z=0)$, $a$ depends oncosmology and $f(M_{0})$ depends only on the linear matter power spectrum. Theanalytic model does not rely on calibration against numerical simulations andis suitable for any cosmology. We compare our model with the latest empiricalmodels for the mass accretion history in the literature and find very goodagreement. We provide numerical routines for the model online.

The accretion history of dark matter halos I: The physical origin of the universal function