TL;DR
This paper explores the properties and implications of closed, compact spatial sections in relativistic cosmologies, focusing on geometric classifications and observational consequences of global inhomogeneity.
Contribution
It clarifies the relationship between Thurston's geometries and Bianchi-Kantowski-Sachs metrics in closed cosmological models and analyzes observational effects of global inhomogeneity.
Findings
Clarified the connection between Thurston's geometries and Bianchi-Kantowski-Sachs metrics.
Analyzed observational implications of global inhomogeneity in constant curvature 3-spaces.
Abstract
This paper deals with two aspects of relativistic cosmologies with closed (compact and boundless) spatial sections. These spacetimes are based on the theory of General Relativity, and admit a foliation into space sections S(t), which are spacelike hypersurfaces satisfying the postulate of the closure of space: each S(t) is a 3-dimensional, closed Riemannian manifold. The discussed topics are: (1) A comparison, previously obtained, between Thurston's geometries and Bianchi-Kantowski-Sachs metrics for such 3-manifolds is here clarified and developed. (2) Some implications of global inhomogeneity for locally homogeneous 3-spaces of constant curvature are analyzed from an observational viewpoint.
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