Cumulative gravitational lensing in Newtonian perturbations of Friedman-Robertson-Walker cosmologies

TL;DR

This paper investigates whether the common assumption that gravitational lensing effects average out in cosmological observations holds true in Newtonian perturbations of FRW models, finding zero-mean corrections under certain conditions.

Contribution

It provides a detailed analysis of gravitational lensing corrections in perturbed FRW cosmologies using Newtonian perturbations and synchronous gauge, including specific models.

Findings

Zero mean first-order correction for dust-filled intergalactic matter with no mean density perturbation.

Analysis confirms the assumption holds in specific Newtonian perturbation scenarios.

Consideration of point particle and Swiss cheese models as case studies.

Abstract

It is a common assumption amongst astronomers that, in the determination of the distances of remote sources from their apparent brightness, the cumulative gravitational lensing due to the matter in all the galaxies is the same, on average, as if the matter were uniformly distributed throughout the cosmos. The validity of this assumption is considered here by way of general Newtonian perturbations of Friedman-Robertson-Walker (FRW) cosmologies. The analysis is carried out in synchronous gauge, with particular attention to an additional gauge condition that must be imposed. The mean correction to the apparent magnitude-redshift relation is obtained for an arbitrary mean density perturbation. In the case of a zero mean density perturbation, when the intergalactic matter has a dust equation of state, then there is indeed a zero-mean first order correction to the apparent magnitude-redshift relation for all redshifts. Point particle and Swiss cheese models are considered as particular cases.