The second-order luminosity-redshift relation in a generic inhomogeneous cosmology

TL;DR

This paper derives a second-order luminosity-redshift relation in a generic inhomogeneous cosmology within the Poisson gauge, enabling better understanding of inhomogeneity effects on dark energy measurements.

Contribution

It provides a comprehensive second-order luminosity-redshift relation in the Poisson gauge for generic cosmologies, facilitating improved analysis of inhomogeneity impacts on dark energy observations.

Findings

Derived the second-order luminosity-redshift relation in the Poisson gauge.

Connected the relation to stochastic inhomogeneities affecting dark-energy cosmology.

Provided a tool for analyzing light signals in inhomogeneous universes.

Abstract

After recalling a general non-perturbative expression for the luminosity-redshift relation holding in a recently proposed "geodesic light-cone" gauge, we show how it can be transformed to phenomenologically more convenient gauges in which cosmological perturbation theory is better understood. We present, in particular, the complete result on the luminosity-redshift relation in the Poisson gauge up to second order for a fairly generic perturbed cosmology, assuming that appreciable vector and tensor perturbations are only generated at second order. This relation provides a basic ingredient for the computation of the effects of stochastic inhomogeneities on precision dark-energy cosmology whose results we have anticipated in a recent letter. More generally, it can be used in connection with any physical information carried by light-like signals traveling along our past light-cone.