Light propagation in statistically homogeneous and isotropic dust universes

TL;DR

This paper derives how light propagates in statistically homogeneous and isotropic dust universes with arbitrary geometry, showing that the Dyer-Roeder approximation is inadequate and that redshift and distance depend on average expansion, matter density, and shear.

Contribution

It provides a first-principles derivation of redshift and distance in such universes, highlighting the limitations of the Dyer-Roeder approximation and clarifying conditions for CMB peak positions.

Findings

Redshift and distance depend on average expansion rate, matter density, and shear.

Dyer-Roeder approximation does not accurately describe effects of clumping.

CMB peak positions are consistent with significant spatial curvature if expansion history matches flat LambdaCDM.

Abstract

We derive the redshift and the angular diameter distance in rotationless dust universes which are statistically homogeneous and isotropic, but have otherwise arbitrary geometry. The calculation from first principles shows that the Dyer-Roeder approximation does not correctly describe the effect of clumping. Instead, the redshift and the distance are determined by the average expansion rate, the matter density today and the null geodesic shear. In particular, the position of the CMB peaks is consistent with significant spatial curvature provided the expansion history is sufficiently close to the spatially flat LambdaCDM model.