Modification of the halo mass function by kurtosis associated with primordial non-Gaussianity

TL;DR

This paper investigates how primordial kurtosis-related non-Gaussianity influences the halo mass function and cosmic structures, providing methods to distinguish it from skewness effects and analyzing its impact on early universe phenomena.

Contribution

It derives a non-Gaussian halo mass function incorporating kurtosis parameters and explores their effects on cosmic structures and early star formation.

Findings

Kurtosis affects the abundance of cosmic voids and massive clusters.

Comparison with skewness helps distinguish types of primordial non-Gaussianity.

Kurtosis has limited impact on overall reionization but influences early stages at high redshift.

Abstract

We study the halo mass function in the presence of the kurtosis type of primordial non-Gaussianity. The kurtosis corresponds to the trispectrum as defined in Fourier space. The primordial trispectrum is commonly characterized by two parameters, $\tau_{\rm NL}$ and $g_{\rm NL}$. As applications of the derived non-Gaussian mass function, we consider the effect on the abundance of void structure, the effect on early star formation and on formation of the most massive object at high redshift. We show that by comparing the effects of primordial non-Gaussianity on cluster abundance with that on void abundance, we can distinguish between the skewness and the kurtosis types of primordial non-Gaussianity. As for early star formation, we show that the kurtosis type of primordial non-Gaussianity seems not to affect the reionization history of the Universe on average. However, at high redshifts (up to $z\simeq 20$) such non-Gaussianity does somewhat affect the early stages of reionization.