Limits on the Detectability of Cosmic Topology in Hyperbolic Universes

TL;DR

This paper investigates the limits of detecting cosmic topology in nearly flat hyperbolic universes, considering recent observational data and mathematical advances, highlighting how uncertainties affect detectability.

Contribution

It provides updated bounds on cosmic topology detectability using recent observational constraints and mathematical results, emphasizing the sensitivity to parameter uncertainties.

Findings

New bounds on detectability of cosmic topology.

Detectability is highly sensitive to observational uncertainties.

Mathematical results on small hyperbolic 3-manifolds inform bounds.

Abstract

We reexamine the possibility of the detection of the cosmic topology in nearly flat hyperbolic Friedmann-Lemaitre-Robertson-Walker (FLRW) universes by using patterns repetition. We update and extend our recent results in two important ways: by employing recent observational constraints on the cosmological density parameters as well as the recent mathematical results concerning small hyperbolic 3-manifolds. This produces new bounds with consequences for the detectability of the cosmic topology. In addition to obtaining new bounds, we also give a concrete example of the sensitive dependence of detectability of cosmic topology on the uncertainties in the observational values of the density parameters.