MCMC generation of cosmological fields far beyond Gaussianity

TL;DR

This paper develops a Markov Chain Monte Carlo method to generate highly non-Gaussian cosmological fields, enabling better analysis of complex structures observed in the universe.

Contribution

It introduces a non-Gaussian sampling distribution for cosmological fields that handles strong non-Gaussianity and enforces key statistical properties, surpassing perturbative methods.

Findings

Generated fields show strong non-Gaussianity not visible to the naked eye.

Sampled pixel pair marginals appear Gaussian despite overall non-Gaussianity.

High-dimensionality causes non-Gaussian information to be hidden in seemingly Gaussian fields.

Abstract

Structure formation in our Universe creates non-Gaussian random fields that will soon be observed over almost the entire sky by the Euclid satellite, the Vera-Rubin observatory, and the Square Kilometre Array. An unsolved problem is how to analyze best such non-Gaussian fields, e.g. to infer the physical laws that created them. This problem could be solved if a parametric non-Gaussian sampling distribution for such fields were known, as this distribution could serve as likelihood during inference. We therefore create a sampling distribution for non-Gaussian random fields. Our approach is capable of handling strong non-Gaussianity, while perturbative approaches such as the Edgeworth expansion cannot. To imitate cosmological structure formation, we enforce our fields to be (i) statistically isotropic, (ii) statistically homogeneous, and (iii) statistically independent at large distances. We generate such fields via a Monte Carlo Markov Chain technique and find that even strong non-Gaussianity is not necessarily visible to the human eye. We also find that sampled marginals for pixel pairs have an almost generic Gauss-like appearance, even if the joint distribution of all pixels is markedly non-Gaussian. This apparent Gaussianity is a consequence of the high dimensionality of random fields. We conclude that vast amounts of non-Gaussian information can be hidden in random fields that appear nearly Gaussian in simple tests, and that it would be short-sighted not to try and extract it.