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

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\^ıtre 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\^ıtre-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\^ıtre 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.

Minor technical refinement, 16 pages, RevTex, 8 eps figures

References in corpus (2)

• Large Scale Inhomogeneity Versus Source Evolution -- Can We Distinguish Them Observationally?
• Caustics of Compensated Spherical Lens Models

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