Non-Gaussian Halo Mass Function and Non-Spherical Halo Collapse: Theory
  vs. Simulations
  The mass distribution of dark matter halos is a sensitive probe of primordial
non-Gaussianity (NG). We derive an analytical formula of the halo mass function
by perturbatively computing excursion set path-integrals for a non-Gaussian
density field with non-vanishing skewness, fnl. We assume a stochastic barrier
model which captures the main features of the ellipsoidal collapse of halos.
Contrary to previous results based on extensions of the Press-Schechter
formalism to NG initial conditions, we find that the non-spherical collapse of
halos directly alter the signature of primordial NG. This points toward a
potential degeneracy between the effect of primordial non-Gaussianity and that
of non-linear halo collapse. The inferred mass function is found to be in
remarkable agreement with N-body simulations of NG local type. Deviations are
well within numerical uncertainties for all values of -80 < fNL^loc < 300 in
the range of validity of the perturbative calculation. Moreover, the comparison
with simulation results suggests that for fNL > 150 or fNL < -50 the non-linear
collapse of halos, as described by our barrier model, strongly deviates from
that of Gaussian initial conditions. This is not surprising since the effect of
non-linear gravitational processes may be altered by initially large NG. Hence,
in the lack of prior theoretical knowledge, halo collapse model parameters
should be included in statistical halo mass function data analysis which aim to
constrain the signature of primordial NG
