Non-Gaussian Mode Coupling and the Statistical Cosmological Principle

TL;DR

This paper investigates how primordial non-Gaussianity causes biases in local measurements of cosmological statistics, potentially leading to discrepancies between observations in our Hubble volume and the larger universe.

Contribution

It provides a detailed analysis of bias effects due to non-Gaussian mode coupling for various models, highlighting how local measurements can be misleading.

Findings

Local non-Gaussianity induces biases in measured statistics.

Bias depends on the background curvature perturbation .

Weakly Gaussian local statistics can coexist with strongly non-Gaussian larger universe.

Abstract

Local-type primordial non-Gaussianity couples statistics of the curvature perturbation \zeta on vastly different physical scales. Because of this coupling, statistics (i.e. the polyspectra) of \zeta in our Hubble volume may not be representative of those in the larger universe -- that is, they may be biased. The bias depends on the local background value of \zeta, which includes contributions from all modes with wavelength k ~< H_0 and is therefore enhanced if the entire post-inflationary patch is large compared with our Hubble volume. We study the bias to locally-measured statistics for general local-type non-Gaussianity. We consider three examples in detail: (i) the usual fNL, gNL model, (ii) a strongly non-Gaussian model with \zeta ~ \zeta_G^p, and (iii) two-field non-Gaussian initial conditions. In each scenario one may generate statistics in a Hubble-size patch that are weakly Gaussian and consistent with observations despite the fact that the statistics in the larger, post-inflationary patch look very different.