From Finance to Cosmology: The Copula of Large-Scale Structure

TL;DR

This paper introduces the use of copulas to analyze correlations in large-scale structure, deriving an empirical 2-point copula for dark matter density and exploring its Gaussian approximation.

Contribution

It applies copula methodology to cosmology, deriving the empirical 2-point copula for dark matter density and examining the Gaussian copula hypothesis for higher-order correlations.

Findings

Empirical 2-point copula is well-approximated by a Gaussian copula.

The Gaussian copula hypothesis for the full n-point copula is considered plausible.

Future research directions are discussed.

Abstract

Any multivariate distribution can be uniquely decomposed into marginal (1-point) distributions, and a function called the copula, which contains all of the information on correlations between the distributions. The copula provides an important new methodology for analyzing the density field in large-scale structure. We derive the empirical 2-point copula for the evolved dark matter density field. We find that this empirical copula is well-approximated by a Gaussian copula. We consider the possibility that the full n-point copula is also Gaussian and describe some of the consequences of this hypothesis. Future directions for investigation are discussed.