The copula of the cosmological matter density field is non-Gaussian

TL;DR

This paper investigates the non-Gaussian nature of the cosmological matter density field's copula, revealing limitations of the Gaussian copula hypothesis and proposing methods to better diagnose residual non-Gaussianities.

Contribution

It identifies the limitations of the Gaussian copula hypothesis in diagnosing residual non-Gaussianities and proposes a refined approach using copula density analysis.

Findings

Gaussianization reduces non-Gaussianity at two-point level

Significant non-Gaussianities remain in Gaussianized fields

A new method using copula density better detects residual non-Gaussianity

Abstract

Non-Gaussianity of the cosmological matter density field can be largely reduced by a local Gaussianization transformation (and its approximations such as the logrithmic transformation). Such behavior can be recasted as the Gaussian copula hypothesis, and has been verified to very high accuracy at two-point level. On the other hand, statistically significant non-Gaussianities in the Gaussianized field have been detected in simulations. We point out that, this apparent inconsistency is caused by the very limited degrees of freedom in the copula function, which make it misleading as a diagnosis of residual non-Gaussianity in the Gaussianized field. Using the copula density, we highlight the departure from Gaussianity. We further quantify its impact in the predicted n-point correlation functions. We explore a remedy of the Gaussian copula hypothesis, which alleviates but not completely solves the above problems.