Multi-variate joint PDF for non-Gaussianities: exact formulation and generic approximations

TL;DR

This paper derives an exact multi-variate joint PDF for non-Gaussian fields from Gaussian fields, with applications to cosmology, providing analytical expressions and approximations for non-Gaussianity estimation in CMB data and halo mass functions.

Contribution

It introduces an exact formulation for the joint PDF of non-Gaussian fields from Gaussian fields and develops analytical approximations applicable to cosmological data analysis.

Findings

Exact multi-variate joint PDF derived for non-Gaussian fields

Analytical expressions for non-Gaussianity estimation in CMB maps

Fast computation method valid up to 7σ for fNL values

Abstract

We provide an exact expression for the multi-variate joint probability distribution function of non-Gaussian fields primordially arising from local transformations of a Gaussian field. This kind of non-Gaussianity is generated in many models of inflation. We apply our expression to the non- Gaussianity estimation from Cosmic Microwave Background maps and the halo mass function where we obtain analytical expressions. We also provide analytic approximations and their range of validity. For the Cosmic Microwave Background we give a fast way to compute the PDF which is valid up to 7{\sigma} for fNL values (both true and sampled) not ruled out by current observations, which consists of expressing the PDF as a combination of bispectrum and trispectrum of the temperature maps. The resulting expression is valid for any kind of non-Gaussianity and is not limited to the local type. The above results may serve as the basis for a fully Bayesian analysis of the non-Gaussianity parameter.