The averaging problem on the past null cone in inhomogeneous dust cosmologies

TL;DR

This paper develops a covariant averaging formalism on the past null cone in inhomogeneous dust cosmologies, enabling analysis of backreaction effects on observable quantities like distance and redshift in a more general setting than standard models.

Contribution

It introduces a novel covariant averaging approach on light fronts that accounts for inhomogeneities without assuming local homogeneity or isotropy, extending the analysis of cosmic backreaction effects.

Findings

Formalism quantifies deviations from FLRW models due to inhomogeneities.

Averages of observable quantities like angular diameter distance are formulated.

Backreaction effects on redshift drift are discussed.

Abstract

Cosmological models typically neglect the complicated nature of the spacetime manifold at small scales in order to hypothesize idealized general relativistic solutions for describing the average dynamics of the Universe. Although these solutions are remarkably successful in accounting for data, they introduce a number of puzzles in cosmology, and their foundational assumptions are therefore important to test. In this paper, we go beyond the usual assumptions in cosmology and propose a formalism for averaging the local general relativistic spacetime on an observer's past null cone: we formulate average properties of light fronts as they propagate from a cosmological emitter to an observer. The energy-momentum tensor is composed of an irrotational dust source and a cosmological constant -- the same components as in the $\Lambda$CDM model for late cosmic times -- but the metric solution is not \emph{a priori}constrained to be locally homogeneous or isotropic. This generally makes the large-scale dynamics depart from that of a simple Friedmann--Lema\^\i tre--Robertson--Walker solution through \emph{backreaction} effects. Our formalism quantifies such departures through a fully covariant system of area-averaged equations on the light fronts propagating towards an observer, which can be directly applied to analytical and numerical investigations of cosmic observables. For this purpose, we formulate light front averages of observable quantities, including the effective angular diameter distance and the cosmological redshift drift and we also discuss the backreaction effects for these observables.