Excursion Set Theory for generic moving barriers and non-Gaussian initial conditions

TL;DR

This paper advances excursion set theory by analytically solving the first-passage time problem for generic moving barriers, including ellipsoidal collapse, under both Gaussian and non-Gaussian initial conditions, providing a more consistent halo mass function.

Contribution

It introduces a path integral approach to solve the first-passage time problem for arbitrary moving barriers with non-Gaussian initial conditions, improving upon previous models.

Findings

Analytical expression for the halo mass function with ellipsoidal collapse barrier.

Extension of excursion set theory to non-Gaussian initial conditions.

No need for artificial form factors in mass function calculations.

Abstract

Excursion set theory, where density perturbations evolve stochastically with the smoothing scale, provides a method for computing the mass function of cosmological structures like dark matter halos, sheets and filaments. The computation of these mass functions is mapped into the so-called first-passage time problem in the presence of a moving barrier. In this paper we use the path integral formulation of the excursion set theory developed recently to analytically solve the first-passage time problem in the presence of a generic moving barrier, in particular the barrier corresponding to ellipsoidal collapse. We perform the computation for both Gaussian and non-Gaussian initial conditions. The expression of the halo mass function for the ellipsoidal collapse barrier and with non-Gaussianity is therefore obtained in a fully consistent way and it does not require the introduction of any form factor artificially derived from the Press-Schechter formalism based on the spherical collapse and usually adopted in the literature.