A Study of High-Order Non-Gaussianity with Applications to Massive Clusters and Large Voids

TL;DR

This paper explores the statistical properties of local non-Gaussianity parameters and their impact on cosmic structures, providing methods to reconstruct probability distributions and analyzing effects on galaxy clusters and voids.

Contribution

It introduces fitting formulae relating f_NL and g_NL to skewness and kurtosis, and demonstrates how to use a truncated Edgeworth series for modeling non-Gaussian distributions.

Findings

Edgeworth series cannot model nonzero f_NL without g_NL

Void abundance is more sensitive to high-order non-Gaussianities than clusters

Reconstruction of density fluctuation distributions is feasible with weakened non-Gaussianity parameters

Abstract

The statistical meaning of the local non-Gaussianity parameters f_NL and g_NL is examined in detail. Their relations to the skewness and the kurtosis of the probability distribution of density fluctuations are shown to obey simple fitting formulae, accurate on galaxy-cluster scales. We argue that the knowledge of f_NL and g_NL is insufficient for reconstructing a well-defined distribution of density fluctuations. However, by weakening the statistical significance of f_NL and g_NL, it is possible to reconstruct a well-defined pdf by using a truncated Edgeworth series. We give some general guidelines on the use of such a series, noting in particular that 1) the Edgeworth series cannot represent models with nonzero f_NL, unless g_NL is nonzero also, 2) the series cannot represent models with g_NL<0, unless some higher-order non-Gaussianities are known. Finally, we apply the Edgeworth series to calculate the effects of g_NL on the abundances of massive clusters and large voids. We show that the abundance of voids may generally be more sensitive to high-order non-Gaussianities than the cluster abundance.