Nonlinear cosmological power spectra in Einstein's gravity

TL;DR

This paper analytically derives the second-order density and velocity power spectra within Einstein's gravity, revealing relativistic corrections that are smaller than Newtonian ones but potentially more significant than higher-order nonlinear Newtonian effects.

Contribution

It provides the complete second-order power spectra in Einstein's gravity, including relativistic corrections, advancing the understanding of nonlinear cosmic structure evolution.

Findings

Relativistic corrections are smaller than Newtonian ones at second order.

Relativistic effects could surpass higher-order Newtonian nonlinearities.

Power transfer among scales is quantitatively estimated.

Abstract

Is Newton's gravity sufficient to handle the weakly nonlinear evolution stages of the cosmic large-scale structures? Here we resolve the issue by analytically deriving the density and velocity power spectra to the second order in the context of Einstein's gravity. The recently found pure general relativistic corrections appearing in the third-order perturbation contribute to power spectra to the second order. In this work the complete density and velocity power spectra to the second order are derived. The power transfers among different scales in the density power spectrum are estimated in the context of Einstein's gravity. The relativistic corrections in the density power spectrum are estimated to be smaller than the Newtonian one to the second order, but these could be larger than higher-order nonlinear Newtonian terms.