Einstein's signature in cosmological large-scale structure

TL;DR

This paper demonstrates how Einstein's general relativity introduces a specific non-Gaussian signal in the large-scale structure of the universe, highlighting the importance of relativistic effects in cosmological modeling.

Contribution

It provides a perturbative calculation of the non-Gaussian signature in large-scale structure arising from Einstein's gravity, linking curvature and initial matter density.

Findings

Identifies a non-Gaussian contribution from Einstein's gravity to initial conditions.

Shows the relation between spatial curvature and matter density perturbations.

Highlights the necessity of relativistic approaches for initial condition modeling.

Abstract

We show how the non-linearity of general relativity generates a characteristic non-Gaussian signal in cosmological large-scale structure that we calculate at all perturbative orders in a large scale limit. Newtonian gravity and general relativity provide complementary theoretical frameworks for modelling large-scale structure in $\Lambda$CDM cosmology; a relativistic approach is essential to determine initial conditions which can then be used in Newtonian simulations studying the non-linear evolution of the matter density. Most inflationary models in the very early universe predict an almost Gaussian distribution for the primordial metric perturbation, $\zeta$. However, we argue that it is the Ricci curvature of comoving-orthogonal spatial hypersurfaces, $R$, that drives structure formation at large scales. We show how the non-linear relation between the spatial curvature, $R$, and the metric perturbation, $\zeta$, translates into a specific non-Gaussian contribution to the initial comoving matter density that we calculate for the simple case of an initially Gaussian $\zeta$. Our analysis shows the non-linear signature of Einstein's gravity in large-scale structure.