Averaging Robertson-Walker Cosmologies

TL;DR

This paper investigates the effects of cosmological backreaction in averaged Robertson-Walker universes, quantifying deviations from standard models and their implications for dark energy and early universe conditions.

Contribution

It applies the Buchert averaging formalism to various cosmological models, providing numerical estimates of backreaction effects and their dependence on model parameters.

Findings

Largest deviations in Einstein-de Sitter universe (~0.01%)

Backreaction in LCDM model is around 4x10^-6

Effective equations of state are generally dust-like, with exceptions for phantom models

Abstract

The cosmological backreaction arises when one directly averages the Einstein equations to recover an effective Robertson-Walker cosmology, rather than assuming a background a priori. While usually discussed in the context of dark energy, strictly speaking any cosmological model should be recovered from such a procedure. We apply the Buchert averaging formalism to linear Robertson-Walker universes containing matter, radiation and dark energy and evaluate numerically the discrepancies between the assumed and the averaged behaviour, finding the largest deviations for an Einstein-de Sitter universe, increasing rapidly with Hubble rate to a 0.01% effect for h=0.701. For the LCDM concordance model, the backreaction is of the order of Omega_eff~4x10^-6, with those for dark energy models being within a factor of two or three. The impacts at recombination are of the order of 10^-8 and those in deep radiation domination asymptote to a constant value. While the effective equations of state of the backreactions in Einstein-de Sitter, concordance and quintessence models are generally dust-like, a backreaction with an equation of state w_eff<-1/3 can be found for strongly phantom models.