It takes two to know one: Computing accurate one-point PDF covariances from effective two-point PDF models

TL;DR

This paper develops a method to accurately compute the covariance of one-point PDFs of cosmic matter density using effective two-point PDF models, validated against simulations, aiding future galaxy survey analyses.

Contribution

It introduces a novel approach to derive one-point PDF covariances from effective two-point PDF models, including super-sample covariance effects, for cosmological applications.

Findings

Effective shifted lognormal two-point PDF models accurately predict covariances.

Super-sample covariance effects are captured by a large-separation expansion.

Method can be extended to 3D spectroscopic fields and supplemented with theoretical predictions.

Abstract

One-point probability distribution functions (PDFs) of the cosmic matter density are powerful cosmological probes that extract non-Gaussian properties of the matter distribution and complement two-point statistics. Computing the covariance of one-point PDFs is key for building a robust galaxy survey analysis for upcoming surveys like Euclid and the Rubin Observatory LSST and requires good models for the two-point PDFs characterising spatial correlations. In this work, we obtain accurate PDF covariances using effective shifted lognormal two-point PDF models for the mildly non-Gaussian weak lensing convergence and validate our predictions against large sets of Gaussian and non-Gaussian maps. We show how the dominant effects in the covariance matrix capturing super-sample covariance arise from a large-separation expansion of the two-point PDF and discuss differences between the covariances obtained from small patches and full sky maps. Finally, we describe how our formalism can be extended to characterise the PDF covariance for 3D-dimensional spectroscopic fields using the 3D matter PDF as an example. We describe how covariances from simulated boxes with fixed overall density can be supplemented with the missing super-sample covariance effect by relying on theoretical predictions validated against separate-universe style simulations.