Light-cone averaging in cosmology: formalism and applications

TL;DR

This paper develops a gauge-invariant formalism for averaging cosmological observables along light-like signals, enabling more accurate analysis of inhomogeneous universes and observational data such as redshift and luminosity distance.

Contribution

It introduces a novel gauge-invariant framework for light-cone averaging in cosmology, including explicit formulas and commutation rules for inhomogeneous universes.

Findings

Derived explicit expressions for light-cone averages of redshift and luminosity distance.

Established generalized Buchert-Ehlers commutation rules for light-cone averages.

Provided a practical coordinate system for calculations in inhomogeneous cosmologies.

Abstract

We present a general gauge invariant formalism for defining cosmological averages that are relevant for observations based on light-like signals. Such averages involve either null hypersurfaces corresponding to a family of past light-cones or compact surfaces given by their intersection with timelike hypersurfaces. Generalized Buchert-Ehlers commutation rules for derivatives of these light-cone averages are given. After introducing some adapted "geodesic light-cone" coordinates, we give explicit expressions for averaging the redshift to luminosity-distance relation and the so-called "redshift drift" in a generic inhomogeneous Universe.