  Understanding the universal accretion history of dark matter halos 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 $M(z) =
M_{0}(1+z)^{af(M_{0})}e^{-f(M_{0})z}$, where $M_{0} = M(z=0)$, $a$ depends on
cosmology and $f(M_{0})$ depends only on the linear matter power spectrum. The
analytic model does not rely on calibration against numerical simulations and
is suitable for any cosmology. We compare our model with the latest empirical
models for the mass accretion history in the literature and find very good
agreement. We provide numerical routines for the model online.
