Perturbative treatment of the luminosity distance

TL;DR

This paper derives a generalized luminosity distance-redshift relation for perturbed FLRW universes using two methods, with applications to simple models and potential relevance for realistic cosmology.

Contribution

It introduces a new perturbative approach to compute luminosity distances in linearly perturbed FLRW models using Jacobi map and van Vleck determinant methods.

Findings

Derived a generalized luminosity distance formula for perturbed FLRW metrics.

Applied the formula to exact and approximate FLRW models with scalar perturbations.

Provided cosmographic expansions for luminosity distance in these models.

Abstract

We derive a generalized luminosity distance versus redshift relation for a linearly perturbed FLRW (Friedmann-Lemaitre-Robertson-Walker) metric with two scalar mode excitations. We use two equivalent approaches, based on the Jacobi map and the van Vleck determinant respectively. We apply the resultant formula to two simple models - an exact FLRW universe and an approximate FLRW universe perturbed by a single scalar mode sinusoidally varying with time. For both models we derive a cosmographic expansion for d_L in terms of z. We comment on the interpretation of our results and their possible application to more realistic cosmological models.