Back in the saddle: Large-deviation statistics of the cosmic log-density field

TL;DR

This paper develops an analytical method based on large deviation principles and spherical collapse models to accurately predict cosmic density distributions in the mildly non-linear regime, surpassing standard perturbation theory.

Contribution

It introduces a novel large deviation approach combined with logarithmic density transformations to derive explicit, accurate density PDFs applicable across a wide density range.

Findings

Predictions match N-body simulations within a few percent.

Method provides accurate PDFs for all density values.

Applicable to various primordial power spectra.

Abstract

We present a first principle approach to obtain analytical predictions for spherically-averaged cosmic densities in the mildly non-linear regime that go well beyond what is usually achieved by standard perturbation theory. A large deviation principle allows us to compute the leading-order cumulants of average densities in concentric cells. In this symmetry, the spherical collapse model leads to cumulant generating functions that are robust for finite variances and free of critical points when logarithmic density transformations are implemented. They yield in turn accurate density probability distribution functions (PDFs) from a straightforward saddle-point approximation valid for all density values. Based on this easy-to-implement modification, explicit analytic formulas for the evaluation of the one- and two-cell PDF are provided. The theoretical predictions obtained for the PDFs are accurate to a few percent compared to the numerical integration, regardless of the density under consideration and in excellent agreement with N-body simulations for a wide range of densities. This formalism should prove valuable for accurately probing the quasi-linear scales of low redshift surveys for arbitrary primordial power spectra.