Statistical Naturalness and non-Gaussianity in a Finite Universe

TL;DR

This paper investigates how the statistical properties of the primordial curvature perturbations in a finite universe are influenced by larger-scale non-Gaussian features, affecting observed n-point functions and bispectrum shapes.

Contribution

It introduces a framework for understanding how local non-Gaussian statistics in a larger universe influence the observed non-Gaussianity in smaller biased regions.

Findings

Sufficiently biased small volumes exhibit weakly non-Gaussian, ordered moments.

The bias affects the shape of the bispectrum in observable regions.

The analysis applies to a broad class of local non-Gaussian statistics.

Abstract

We study the behavior of n-point functions of the primordial curvature perturbations, assuming our observed Universe is only a subset of a larger space with statistically homogeneous and isotropic perturbations. If the larger space has arbitrary n-point functions in a family of local type non-Gaussian statistics, sufficiently biased smaller volumes will have statistics from a `natural' version of that family with moments that are weakly non-Gaussian and ordered, regardless of the statistics of the original field. We also describe the effect of this bias on the shape of the bispectrum.