An Infinite Number of Closed FLRW Universes for Any Value of the Spatial Curvature

TL;DR

This paper reveals that FLRW cosmological models can have infinitely many compact, finite-volume spatial sections regardless of curvature, challenging the usual assumption of simple connectivity.

Contribution

It demonstrates the existence of infinitely many multiply connected FLRW models with finite volume for any spatial curvature, expanding the scope of cosmological model possibilities.

Findings

Infinite models with compact spatial sections exist for all curvature types.

Such models have potential observational implications.

They challenge the traditional view of simply connected FLRW universes.

Abstract

The Friedman-Lemaitre-Robertson-Walker (FLRW) cosmological models are based on the assumptions of large-scale homogeneity and isotropy of the distribution of matter and energy. They are usually taken to have spatial sections that are simply connected; they have finite volume in the positive curvature case, and infinite volume in the null and negative curvature ones. I want to call the attention to the existence of an infinite number of models, which are based on these same metrics, but have compact, finite volume, multiply connected spatial sections. Some observational implications are briefly mentioned.