Inhomogeneous universes in observational coordinates

TL;DR

This paper develops a method to analyze isotropic inhomogeneous dust universes using observational coordinates, leading to exact solutions that are nearly homogeneous locally but inhomogeneous at larger scales, with new ways to characterize homogeneity.

Contribution

It introduces a novel observational coordinate approach that simplifies the field equations to a single ODE, enabling explicit solutions and new characterizations of homogeneity in cosmological models.

Findings

Derived an explicit exact solution nearly homogeneous locally

Developed a reduced first-order ODE in observational variables

Provided new observational criteria for homogeneity

Abstract

Isotropic inhomogeneous dust universes are analysed via observational coordinates based on the past light cones of the observer's galactic worldline. The field equations are reduced to a single first--order {\sc ode} in observational variables on the past light cone, completing the observational integration scheme. This leads naturally to an explicit exact solution which is locally nearly homogeneous (i.e. {\sc frw}), but at larger redshift develops inhomogeneity. New observational characterisations of homogeneity ({\sc frw} universes) are also given.