Averaging Robertson-Walker Cosmologies
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 Omegaeff~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 weff<-1/3 can be found for strongly phantom models.