The Halo Mass Function from Excursion Set Theory with a Non-Gaussian Trispectrum

TL;DR

This paper investigates how a primordial non-Gaussian trispectrum influences the halo mass function using an advanced excursion set theory that accounts for non-Markovian stochastic processes, providing more precise results than traditional methods.

Contribution

It develops a formalism to compute the non-Gaussian trispectrum's effect on the halo mass function, including subleading terms often neglected in previous approaches.

Findings

Leading-order results agree with previous heuristic approaches.

Subleading terms depend on derivatives of the four-point correlator.

Explicit computation up to next-to-leading order is performed.

Abstract

A sizeable level of non-Gaussianity in the primordial cosmological perturbations may be induced by a large trispectrum, i.e. by a large connected four-point correlation function. We compute the effect of a primordial non-Gaussian trispectrum on the halo mass function, within excursion set theory. We use the formalism that we have developed in a previous series of papers and which allows us to take into account the fact that, in the presence of non-Gaussianity, the stochastic evolution of the smoothed density field, as a function of the smoothing scale, is non-markovian. In the large mass limit, the leading-order term that we find agrees with the leading-order term of the results found in the literature using a more heuristic Press-Schecther (PS)-type approach. Our approach however also allows us to evaluate consistently the subleading terms, which depend not only on the four-point cumulant but also on derivatives of the four-point correlator, and which cannot be obtained within non-Gaussian extensions of PS theory. We perform explicitly the computation up to next-to-leading order.