Light-cone averaging in cosmology: formalism and applications

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.

Light-cone observables and gauge-invariance in the geodesic light-cone formalism

“…Such measure can be used to average scalar quantities on the constant redshift two-sphere embedded in the observer past light-cone, according to the prescription introduced in [8]:…”

“…In order to simplify the task of making theoretical predictions in the context of general relativity, the geodesic light-cone (GLC) coordinates were introduced in [8]. The GLC coordinates belong to a larger class of adapted coordinates that goes back to the pioneering works [9][10][11][12].…”

Geodesic-light-cone coordinates and the Bianchi I spacetime

“…Examples of such coordinate systems were proposed in the literature since the late 1930s with Temple's optical coordinates [2], followed in the 1970s by Maartens' observational coordinates [3][4][5], and more recently the geodesic-light-cone (GLC) coordinates [6]. Such a method was used in refs.…”

Impact of cosmic variance on the local measurement of $H_0$

“…We denote the light-cone average [17] over a surface at fixed redshift by · · · , and a statistical average by · · ·. Using the results of [18,19,20] (see also [21]) the fluctuation of the…”