A relativistic signature in large-scale structure

TL;DR

This paper discusses how General Relativity introduces an inherent non-Gaussianity in large-scale dark matter density, but this does not translate into galaxy bias, raising questions about observable signatures in mass proxies.

Contribution

It clarifies the physical origin of non-Gaussianity in GR and explores the conditions under which relativistic signatures could be observed in large-scale structure.

Findings

Intrinsic non-Gaussianity in GR is real and physical.

No relativistic signature in galaxy bias under simple models.

Potential observables may encode relativistic signatures if mass proxies differ from physical mass.

Abstract

In General Relativity, the constraint equation relating metric and density perturbations is inherently nonlinear, leading to an effective non-Gaussianity in the dark matter density field on large scales - even if the primordial metric perturbation is Gaussian. Intrinsic non-Gaussianity in the large-scale dark matter overdensity in GR is real and physical. However, the variance smoothed on a local physical scale is not correlated with the large-scale curvature perturbation, so that there is no relativistic signature in the galaxy bias when using the simplest model of bias. It is an open question whether the observable mass proxies such as luminosity or weak lensing correspond directly to the physical mass in the simple halo bias model. If not, there may be observables that encode this relativistic signature.