Repeatable light paths in the shearfree normal cosmological models

TL;DR

This paper investigates the conditions under which repeatable light paths occur in shearfree normal cosmological models, revealing that such paths are limited to specific symmetric cases and are more prevalent in conformally flat models.

Contribution

It characterizes the existence of repeatable light paths in shearfree normal models, identifying special symmetric subcases where all null geodesics are RLPs, extending understanding beyond standard FLRW models.

Findings

In conformally nonflat models, only radial null geodesics are RLPs.

In conformally flat Stephani models, all null geodesics are RLPs in certain symmetric subcases.

Special cases of Stephani solutions have some null geodesics as RLPs.

Abstract

Conditions for the existence of repeatable light paths (RLPs) in the shearfree normal cosmological models are investigated. It is found that in the conformally nonflat models the only RLPs are radial null geodesics (in the spherical case) and their analogues in the plane- and hyperbolically symmetric cases. In the conformally flat Stephani models, there exist special spherically-, plane- and hyperbolically symmetric subcases, in which all null geodesics are RLPs. They are slightly more general than the Friedmann -- Lema\^{\i}tre -- Robertson -- Walker (FLRW) models of the corresponding symmetries: their curvature index function $k(t)$ and the scale factor $R(t)$ are expressed through a single function of time. In addition to that, there exist special cases of the Stephani solution in which some of the null geodesics are RLPs. All these special cases are identified.