Computation of the Halo Mass Function Using Physical Collapse
  Parameters: Application to Non-Standard Cosmologies
  In this article we compare the halo mass function predicted by the excursion
set theory with a drifting diffusive barrier against the results of N-body
simulations for several cosmological models. This includes the standard LCDM
case for a large range of halo masses, models with different types of
primordial non-Gaussianity, and the Ratra-Peebles quintessence model of Dark
Energy. We show that in all those cosmological scenarios, the abundance of dark
matter halos can be described by a drifting diffusive barrier, where the two
parameters describing the barrier have physical content. In the case of the
Gaussian LCDM, the statistics are precise enough to actually predict those
parameters at different redshifts from the initial conditions. Furthermore, we
found that the stochasticity in the barrier is nonnegligible making the simple
deterministic spherical collapse model a bad approximation even at very high
halo masses. We also show that using the standard excursion set approach with a
barrier inspired by peak patches leads to inconsistent predictions of the halo
mass function.
