A gradient expansion for cosmological backreaction

TL;DR

This paper develops a gradient expansion method to model the non-linear evolution of the universe's metric, providing insights into the impact of backreaction effects on cosmic expansion and their potential significance for precision cosmology.

Contribution

It introduces a new approximation technique based on gradient expansion to model non-linear structure formation and backreaction in a dust-dominated universe.

Findings

Backreaction effects can be as large as 10% of the background expansion.

The model suggests backreaction could significantly influence cosmic evolution.

The approach offers a more realistic framework than previous models for studying backreaction.

Abstract

We address the issue of cosmological backreaction from non-linear structure formation by constructing an approximation for the time evolved metric of a dust dominated universe based on a gradient expansion. Our metric begins as a perturbation of a flat Friedmann-Robertson-Walker state described by a nearly scale invariant, Gaussian, power-law distribution, and evolves in time until non-linear structures have formed. After describing and attempting to control for certain complications in the implementation of this approach, this metric then forms a working model of the universe. We numerically calculate the evolution of the average scale factor in this model and hence the backreaction. We argue that, despite its limitations, this model is more realistic than previous models that have confronted the issue of backreaction. We find that the \emph{instantaneous} effects of backreaction in this model could be as large as $\sim10%$ of the background. This suggests that a proper understanding of the \emph{cumulative} effects of backreaction could be crucial for precision cosmology and any future exploration of the dark sector.