Cosmological $N$-body simulations including radiation perturbations

TL;DR

This paper introduces hybrid cosmological N-body simulations that incorporate leading-order relativistic radiation effects, revealing up to 3% corrections on large scales in the matter power spectrum, enhancing the understanding of structure formation.

Contribution

It develops a novel hybrid simulation method combining relativistic radiation effects with non-linear matter dynamics in Newtonian gravity.

Findings

Radiation causes up to 3% correction on large-scale matter power spectrum.

Simulation results agree with linear analytical predictions, indicating minimal non-linear mode-coupling.

The approach enables unified investigation of structure formation with relativistic effects.

Abstract

Cosmological $N$-body simulations are the standard tool to study the emergence of the observed large-scale structure of the Universe. Such simulations usually solve for the gravitational dynamics of matter within the Newtonian approximation, thus discarding general relativistic effects such as the coupling between matter and radiation ($\equiv$ photons and neutrinos). In this paper we investigate novel hybrid simulations which incorporate interactions between radiation and matter to the leading order in General Relativity, whilst evolving the matter dynamics in full non-linearity according to Newtonian theory. Our hybrid simulations come with a relativistic space-time and make it possible to investigate structure formation in a unified framework. In the present work we focus on simulations initialized at $z=99$, and show that the extracted matter power spectrum receives up to $3\%$ corrections on very large scales through radiation. Our numerical findings compare favourably with linear analytical results from Fidler et al. (2016), from which we deduce that there cannot be any significant non-linear mode-coupling induced through linear radiation corrections.