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

Abstract

The Friedman-Lemaître-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. I. Friedman-Lemaître-Robertson-Walker ModelsAs is well known, the Friedman-Lemaître Then I learned, from Efimov's Higher Geometry 3 [2], that the plane could be tessellated into a mosaic of regular, 4g-sided, hyperbolic polygons, where g ≥ 2; the tessellation (or 'honeycomb') is generated by a symmetry group such that