The large-scale correlations of multi-cell densities and profiles, implications for cosmic variance estimates

TL;DR

This paper investigates the two-point statistics of cosmic densities in concentric spheres to accurately estimate cosmic variance, introducing bias functions and large deviation principles for improved precision in large-scale structure analysis.

Contribution

It introduces a novel approach using large deviation principles to compute bias functions and provides a rapid convergence method for large-separation limits in cosmic density correlations.

Findings

Large-separation limit converges rapidly, enabling sub-percent precision.

Bias functions accurately describe spatial correlations of cell densities.

Asymptotic estimates effectively quantify cosmic variance in finite surveys.

Abstract

In order to quantify the error budget in the measured probability distribution functions of cell densities, the two-point statistics of cosmic densities in concentric spheres is investigated. Bias functions are introduced as the ratio of their two-point correlation function to the two-point correlation of the underlying dark matter distribution. They describe how cell densities are spatially correlated. They are computed here via the so-called large deviation principle in the quasi-linear regime. Their large-separation limit is presented and successfully compared to simulations for density and density slopes: this regime is shown to be rapidly reached allowing to get sub-percent precision for a wide range of densities and variances. The corresponding asymptotic limit provides an estimate of the cosmic variance of standard concentric cell statistics applied to finite surveys. More generally, no assumption on the separation is required for some specific moments of the two-point statistics, for instance when predicting the generating function of cumulants containing any powers of concentric densities in one location and one power of density at some arbitrary distance from the rest. This exact "one external leg" cumulant generating function is used in particular to probe the rate of convergence of the large-separation approximation.