Are Small Hyperbolic Universes Observationally Detectable?

TL;DR

This paper discusses how small hyperbolic universe models might be indistinguishable observationally due to pattern repetitions, especially when the universe is nearly flat, which has implications for quantum cosmology and inflationary theories.

Contribution

It combines recent observational constraints with mathematical results on small hyperbolic manifolds to show the potential undetectability of such universes' topology.

Findings

Small hyperbolic universes can be observationally indistinguishable due to pattern repetitions.

The likelihood of undetectability increases when the universe is nearly flat.

Quantum cosmology may favor small-volume hyperbolic universes.

Abstract

Using recent observational constraints on cosmological density parameters, together with recent mathematical results concerning small volume hyperbolic manifolds, we argue that, by employing pattern repetitions, the topology of nearly flat small hyperbolic universes can be observationally undetectable. This is important in view of the facts that quantum cosmology may favour hyperbolic universes with small volumes, and from the expectation coming from inflationary scenarios, that $\Omega_0$ is likely to be very close to one.