Light propagation in statistically homogeneous and isotropic universes with general matter content

TL;DR

This paper derives how redshift and angular diameter distance relate to the average expansion rate in universes with statistical homogeneity and isotropy, considering arbitrary geometry and matter, and discusses light deflection, shear, and dust approximation validity.

Contribution

It provides a general framework linking observable cosmological quantities to the average expansion rate in complex universe models with minimal assumptions.

Findings

Light deflection and shear remain small under the assumptions.

Derived evolution equations for the average expansion rate.

Discussed conditions under which the dust approximation is valid.

Abstract

We derive the relationship of the redshift and the angular diameter distance to the average expansion rate for universes which are statistically homogeneous and isotropic and where the distribution evolves slowly, but which have otherwise arbitrary geometry and matter content. The relevant average expansion rate is selected by the observable redshift and the assumed symmetry properties of the spacetime. We show why light deflection and shear remain small. We write down the evolution equations for the average expansion rate and discuss the validity of the dust approximation.