Generalized covariant prescriptions for averaging cosmological observables

TL;DR

This paper introduces two covariant averaging methods for scalar cosmological observables, demonstrating significant numerical differences in energy flux calculations within a perturbed ΛCDM universe.

Contribution

It proposes two new covariant prescriptions for averaging scalar observables on spatial regions relevant to observations, applicable to different source location characterizations.

Findings

Significant numerical differences (~10%) in averaged energy flux at various redshifts.

Both prescriptions are applicable in perturbed ΛCDM geometries.

Differences are notable even at leading perturbative order.

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 $\Lambda$CDM 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.