EINSTEIN'S SIGNATURE IN COSMOLOGICAL LARGE-SCALE STRUCTURE

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.