Non-Gaussian initial conditions in $\Lambda$CDM: Newtonian, relativistic and primordial contributions

TL;DR

This paper develops a relativistic framework for setting initial conditions in structure formation, incorporating primordial non-Gaussianity and relativistic effects, with implications for N-body simulations.

Contribution

It provides a second-order relativistic solution for the matter density contrast in a $ mf extLambda$CDM universe including primordial non-Gaussianity.

Findings

Relativistic corrections can mimic a non-zero $f_{NL}$ in simulations.

Extended previous Newtonian and matter-dominated results to a $ mf extLambda$CDM context.

Identified non-linear contributions from primordial and intrinsic non-Gaussianity.

Abstract

The goal of the present paper is to set initial conditions for structure formation at non-linear order, consistent with general relativity, while also allowing for primordial non-Gaussianity. We use the non-linear continuity and Raychauduri equations, which together with the non-linear energy constraint determine the evolution of the matter density fluctuation in general relativity. We solve this equations at first and second order in a perturbative expansion, recovering and extending previous results derived in the matter-dominated limit and in the Newtonian regime. We present a second-order solution for the comoving density contrast in a $\Lambda$CDM universe, identifying non-linear contributions coming from the Newtonian growing mode, primordial non-Gaussianity and intrinsic non-Gaussianity, due to the essential non-linearity of the relativistic constraint equations. We discuss the application of these results to initial conditions in N-body simulations, showing that relativistic corrections mimic a non-zero non-linear parameter $f_{\rm NL}$.