Higher moments of primordial non-Gaussianity and constraints from X-ray clusters

We perform cosmological N-body simulations of dark matter structure formation using non-Gaussian initial conditions, with two different scaling of higher order moments (skewness, kurtosis etc). The scalings determine the relative strength of the total non-Gaussianity for a given value of skewness. We show that a current analytic prescription to compute the non-Gaussian mass function (number density of dark matter halos as a function of the halo mass) can describe the simulation results, after some calibration, in a useful parameter space when the strength of non-Gaussianity is small. We use our simulation results to produce semi-analytic fitting functions for the non-Gaussian mass function relative to the Gaussian mass function. These mass function results have already been used to generate constraints on the primordial non-Gaussianity parameter $f_{\rm NL}$ using X-ray cluster measurements. The constraints are consistent with Gaussian initial conditions, and demonstrate the potential of cluster mass function in constraining primordial non-Gaussianity.