Calculation of distances in cosmological models with small-scale inhomogeneities and their use in observational cosmology: a review

TL;DR

This review discusses how small-scale inhomogeneities in the universe affect light propagation and distance measurements, exploring models, solutions, and applications relevant to observational cosmology.

Contribution

It provides a comprehensive overview of models and solutions accounting for inhomogeneities in cosmological distance calculations, including analytic, numerical, and approximation methods.

Findings

Inhomogeneities influence light propagation and distance-redshift relations.

Simple models can effectively approximate complex inhomogeneous universes.

The 'Swiss-cheese' model offers insights into inhomogeneity effects on cosmological observations.

Abstract

The Universe is not completely homogeneous. Even if it is sufficiently so on large scales, it is very inhomogeneous at small scales, and this has an effect on light propagation, so that the distance as a function of redshift, which in many cases is defined via light propagation, can differ from the homogeneous case. Simple models can take this into account. I review the history of this idea, its generalization to a wide variety of cosmological models, analytic solutions of simple models, comparison of such solutions with exact solutions and numerical simulations, applications, simpler analytic approximations to the distance equations, and (for all of these aspects) the related concept of a "Swiss-cheese" universe.