Cosmological backreaction in the presence of radiation and a cosmological constant

TL;DR

This paper develops high-precision cosmological models with radiation, a cosmological constant, and inhomogeneous matter, quantifying how small-scale structures influence large-scale expansion, revealing radiation reduces back-reaction effects.

Contribution

The paper introduces a generalized post-Newtonian framework to model inhomogeneous cosmologies with radiation and a cosmological constant, providing explicit formulas for back-reaction effects.

Findings

Radiation reduces the magnitude of back-reaction effects.

A cosmological constant has negligible impact on back-reaction.

Derived simple Friedmann-like equations for inhomogeneous models.

Abstract

We construct high-precision models of the Universe that contain radiation, a cosmological constant, and periodically distributed inhomogeneous matter. The density contrasts in these models are allowed to be highly non-linear, and the cosmological expansion is treated as an emergent phenomenon. This is achieved by employing a generalised version of the post-Newtonian formalism, and by joining together inhomogeneous regions of space-time at reflection symmetric junctions. Using these models, we find general expressions that precisely and unambiguously quantify the effect of small-scale inhomogeneity on the large-scale expansion of space (an effect referred to as "back-reaction", in the literature). We then proceed to specialize our models to the case where the matter fields are given by a regular array of point-like particles. This allows us to derive extremely simple expressions for the emergent Friedmann-like equations that govern the large-scale expansion of space. It is found that the presence of radiation tends to reduce the magnitude of back-reaction effects, while the existence of a cosmological constant has only a negligible effect.