A Large Deviation Principle at play in Large-Scale Structure cosmology

TL;DR

This paper applies Large Deviation Theory to large-scale structure cosmology, deriving a principle that describes the evolution of densities in spherical shells and enabling computation of their cumulant generating functions.

Contribution

It introduces a Large Deviation Principle for non-linear densities in cosmology, providing new formulas for cumulant generating functions under gravitational evolution.

Findings

Large Deviation Principle holds for shell densities without shell-crossing.

Derived cumulant generating functions for non-linear densities.

Formulas applicable to general window functions.

Abstract

We present an application of Large Deviation Theory to the problem of structure growth on large-scale structure cosmology. Starting from gaussian distributed overdensities on concentric spherical shells, we show that a Large Deviation Principle holds for the densities on the corresponding shells after gravitational evolution if no shell-crossing happens. As consequences of the Large Deviation Principle we obtain the cumulant generating function for the non-linear densities, and present formulae to compute the cumulant generating function for general window functions.