The joint statistics of mildly non-linear cosmological densities and slopes in count-in-cells

TL;DR

This paper predicts the joint probability distribution of densities in concentric spheres in mildly non-linear cosmology, validates it with simulations, and explores its use for constraining cosmological parameters.

Contribution

It provides a first-principles prediction of joint density and slope distributions in count-in-cells, with applications to dark energy constraints.

Findings

Excellent agreement with simulations for joint distributions.

Conditional distributions of slopes and densities are robust for cosmological inference.

Potential for improved dark energy constraints using these statistics.

Abstract

In the context of count-in-cells statistics, the joint probability distribution of the density in two concentric spherical shells is predicted from first first principle for sigmas of the order of one. The agreement with simulation is found to be excellent. This statistics allows us to deduce the conditional one dimensional probability distribution function of the slope within under dense (resp. overdense) regions, or of the density for positive or negative slopes. The former conditional distribution is likely to be more robust in constraining the cosmological parameters as the underlying dynamics is less evolved in such regions. A fiducial dark energy experiment is implemented on such counts derived from Lambda-CDM simulations.