Relativistic and non-Gaussianity contributions to the one-loop power spectrum

TL;DR

This paper calculates the one-loop matter power spectrum including relativistic effects and primordial non-Gaussianities, revealing that certain non-Gaussian parameters can significantly impact observable scales in upcoming galaxy surveys.

Contribution

It provides new expressions for matter density perturbations incorporating relativistic and non-Gaussian effects at second and third order, extending previous Newtonian analyses.

Findings

Relativistic effects are sub-dominant at cosmic variance scales.

g_NL parameter can have a sizable impact within Planck constraints.

Primordial non-Gaussianities influence the matter bispectrum at tree level.

Abstract

We compute the one-loop density power spectrum including Newtonian and relativistic contributions, as well as the primordial non-Gaussianity contributions from $f_{\rm NL}$ and $g_{\rm NL}$ in the local configuration. To this end we take solutions to the Einstein equations in the long-wavelength approximation and provide expressions for the matter density perturbation at second and third order. These solutions have shown to be complementary to the usual Newtonian cosmological perturbations. We confirm a sub-dominant effect from pure relativistic terms, manifested at scales dominated by cosmic variance, but find that a sizable effect of order one comes from $g_{\rm NL}$ values allowed by Planck-2018 constraints, manifested at scales probed by forthcoming galaxy surveys like DESI and Euclid. As a complement, we present the matter bispectrum at the tree-level including the mentioned contributions.