Repeatable light paths in the conformally flat cosmological models

TL;DR

This paper investigates shearfree normal cosmological models with repeatable light paths, revealing their conformally flat nature and static metric dependence, and discusses properties of conformal transformations and non-repeatable paths in Minkowski spacetime.

Contribution

It identifies the defining feature of shearfree normal models with repeatable light paths as a static metric factor in comoving coordinates, extending understanding of light propagation in cosmology.

Findings

Repeatable light paths occur in conformally flat models with static metric factors.

Non-repeatable paths can exist even in Minkowski spacetime under certain conditions.

The models are less general than Stephani but more general than Robertson-Walker.

Abstract

This is a supplement to an earlier paper (PRD 84, 023510 (2011)), where those shearfree normal cosmological models were identified, in which all light rays have repeatable paths. All of them are conformally flat, but less general than the Stephani model and more general than Robertson --Walker. In this note, their defining feature is identified: in each of them, in comoving coordinates, the time-dependence factors out so that the cofactor is a static metric. Some related properties of conformal transformations are briefly discussed. Using an explicit example, it is shown that, with a suitably defined congruence of test observers and sources, non-repeatable light paths exist even in the Minkowski spacetime.