Revisiting geodesic observers in cosmology

TL;DR

This paper explores geodesic observers in various cosmological models, extending coordinate systems based on freely falling observers to general FLRW universes and analyzing their limitations and explicit relations.

Contribution

It generalizes previous geodesic coordinate constructions to all FLRW universes and studies their explicit relations and limitations.

Findings

Geodesic coordinates are explicit in certain FLRW cases.

They are generally complex and limited to regions below the apparent horizon.

The paper extends previous work to more general cosmological models.

Abstract

Geodesic observers in cosmology are revisited. The coordinates based on freely falling observers introduced by Gautreau in de Sitter and Einstein-de Sitter spaces (and, previously, by Gautreau and Hoffmann in Schwarzschild space) are extended to general FLRW universes. We identify situations in which the relation between geodesic and comoving coordinates can be expressed explicitly in terms of elementary functions. In general, geodesic coordinates in cosmology turn out to be rather cumbersome and limited to the region below the apparent horizon.