Azimuthal geodesics in closed FLRW cosmological models

TL;DR

This paper provides a comprehensive analysis of azimuthal geodesics in closed FLRW cosmological models, including explicit solutions and extensions to cases with a cosmological constant and massive particles.

Contribution

It offers the full set of solutions for geodesics in closed FLRW models and extends previous results to more complex scenarios with new explicit formulas.

Findings

Derived the angular distance traveled during one universe cycle.

Extended light ray path results to two-fluid models with cosmological constant.

Provided explicit formulas involving special functions.

Abstract

We study geodesics in Friedmann-Lema{\^\i}tre-Robertson-Walker (FLRW) cosmological models and give the full set of solutions. For azimuthal geodesics, in a closed universe, we give the angular distance travelled by a test particle moving along such a geodesic during one cycle of expansion and re-collapse of the universe. We extend previous results regarding the path followed by light rays to the two-fluid case, also including a cosmological constant, as well as to massive test particles. Our work contains various new results and explicit formulae, often using special functions which naturally appear in this setting.