Constraining Primordial Non-Gaussianity with Moments of the Large Scale
  Density Field
  We use cosmological N-body simulations to investigate whether measurements of
the moments of large-scale structure can yield constraints on primordial
non-Gaussianity. We measure the variance, skewness, and kurtosis of the evolved
density field from simulations with Gaussian and three different non-Gaussian
initial conditions: a local model with f_NL=100, an equilateral model with
f_NL=-400, and an orthogonal model with f_NL=-400. We show that the moments of
the dark matter density field differ significantly between Gaussian and
non-Gaussian models. We also make the measurements on mock galaxy catalogs that
contain galaxies with clustering properties similar to those of luminous red
galaxies (LRGs). We find that, in the case of skewness and kurtosis, galaxy
bias reduces the detectability of non-Gaussianity, though we can still clearly
discriminate between different models in our simulation volume. However, in the
case of the variance, galaxy bias greatly amplifies the detectability of
non-Gaussianity. In all cases we find that redshift distortions do not
significantly affect the detectability. When we restrict our measurements to
volumes equivalent to the Sloan Digital Sky Survey II (SDSS-II) or Baryon
Oscillation Spectroscopic Survey (BOSS) samples, the probability of detecting a
departure from the Gaussian model is high by using measurements of the
variance, but very low by using only skewness and kurtosis measurements. We
find that skewness and kurtosis measurements are never likely to yield useful
constraints on primordial non-Gaussianity, but future surveys should be large
enough to place meaningful constraints using measurements of the galaxy
variance.(Abridged)
