Backreaction Effects on the Luminosity-Redshift Relation in Inhomogeneous Cosmology

Abstract

We recall a general gauge invariant formalism for defining cosmological averages that are relevant for observations based on light-like signals. Using such formalism, together with adapted “geodesic light-cone” coordinates, the effect of a stochastic background of cosmological perturbations on the luminosity-redshift relation is computed to second order. The resulting expressions are free from both ultraviolet and infrared divergences, implying that such perturbations cannot mimic a sizable fraction of dark energy. Different averages are estimated and depend on the particular function of the luminosity distance being averaged. The energy flux, being minimally affected by perturbations at large \(z\), is proposed as the best choice for precision estimates of dark-energy parameters. Nonetheless, its irreducible (stochastic) variance induces statistical errors on \(\varOmega _{\varLambda }(z)\) typically lying in the few-percent range.