Generalized covariant prescriptions for averaging cosmological observables

Abstract

We present two new covariant and general prescriptions for averaging scalar observables on spatial regions typical of the observed sources and intersecting the past light-cone of a given observer. One of these prescriptions is adapted to sources exactly located on a given space-like hypersurface, the other applies instead to situations where the physical location of the sources is characterized by the experimental "spread" of a given observational variable. The geometrical and physical differences between the two procedures are illustrated by computing the averaged energy flux received by distant sources located on (or between) constant redshift surfaces, and by working in the context of a perturbed ΛCDM geometry. We find significant numerical differences (of about ten percent or more, in a large range of redshift) even limiting our model to scalar metric perturbations, and stopping our computations to the leading non-trivial perturbative order.

On average properties of inhomogeneous fluids in general relativity III: general fluid cosmologies

“…This would require the study of light cone averages, not considered in this work (however, see e.g. [54,50] for proposals of light cone averaging formalisms).…”

Construction of the cosmological model with periodically distributed inhomogeneities with growing amplitude

“…However, these approaches are often criticized as incomplete or inconclusive because of restrictive assumptions made [33][34][35][36]. There are also works which do not confirm the irrelevance of inhomogeneities despite similar methods and techniques used in studies [37][38][39]. Moreover, it is argued that the phenomena of virialization of clusters and volume dominance of voids significantly affect the Hubble diagram and may even explain dark energy [40][41][42][43][44].…”

Backreaction in Cosmology

“…Flanagan (2005), for example, used these ideas to compute the deceleration parameter as measured by comoving observers. Gasperini et al (2011) define a covariant light-cone average for the backreaction problem, see also (Fanizza et al, 2020) for a more recent generalized proposal. Räsänen (2009) and Räsänen (2010) derives a relationship of the redshift and the angular diameter distance to the average expansion rate for statistically homogeneous and isotropic universes, based on Buchert's approach, and and evaluate the distance-redshift relation and the luminosity distance in a perturbative framework.…”