Shrinking II -- The Distortion of the Area Distance-Redshift Relation in Inhomogeneous Isotropic Universes

TL;DR

This paper demonstrates that inhomogeneities in the universe can significantly distort the area distance-redshift relation, challenging standard cosmological assumptions and highlighting potential errors in distance estimates.

Contribution

It provides an analysis of Lemaître-Tolman-Bondi models showing how lensing distorts distance-redshift relations, introducing a new gauge for exact null cone location.

Findings

Lensing causes significant distortion in area distance-redshift relations.

Inhomogeneity can lead to errors in standard FL distance estimates.

A new gauge simplifies locating the past null cone in these models.

Abstract

This paper and the others in the series challenge the standard model of the effects of gravitational lensing on observations at large distances. We show that due to the cumulative effect of lensing, areas corresponding to an observed solid angle can be quite different than would be estimated from the corresponding Friedmann-Lema\^{\i}tre model, even when averaged over large angular scales. This paper concentrates on the specific example of spherically symmetric but spatially inhomogeneous dust universes, the Lema\^{\i}tre-Tolman-Bondi models, and shows that radial lensing significantly distorts the area distance-redshift and density-redshift relations in these exact solutions compared with the standard ones for Friedmann-Lema\^{\i}tre models. Thus inhomogeneity may introduce significant errors into distance estimates based on the standard FL relations, even after all-sky averaging. In addition a useful new gauge choice is presented for these models, solving the problem of locating the past null cone exactly.