# Effects of structure formation on the expansion rate of the Universe: An estimate from numerical simulations

## TL;DR

This study uses numerical simulations to estimate relativistic corrections to the Universe's expansion rate due to inhomogeneities, finding they are too small to explain cosmic acceleration.

## Contribution

It introduces a new simulation-based scheme to accurately estimate relativistic effects on cosmic expansion in inhomogeneous universes.

## Key findings

- Corrections are slightly larger than 10^{-5} but not enough to cause acceleration.
- Inhomogeneities do not significantly alter the overall expansion rate.
- Further research needed for strong-field effects.

## Abstract

General relativistic corrections to the expansion rate of the Universe arise when the Einstein equations are averaged over a spatial volume in a locally inhomogeneous cosmology. It has been suggested that they may contribute to the observed cosmic acceleration. In this paper, we propose a new scheme that utilizes numerical simulations to make a realistic estimate of the magnitude of these corrections for general inhomogeneities in (3+1) spacetime. We then quantitatively calculate the volume averaged expansion rate using N-body large-scale structure simulations and compare it with the expansion rate in a standard FRW cosmology. We find that in the weak gravitational field limit, the converged corrections are slightly larger than the previous claimed 10^{-5} level, but not large enough nor even of the correct sign to drive the current cosmic acceleration. Nevertheless, the question of whether the cumulative effect can significantly change the expansion history of the Universe needs to be further investigated with strong-field relativity.