Inhomogeneous Cosmological Models with Homogeneous Inner Hypersurface Geometry

TL;DR

This paper investigates inhomogeneous cosmological models with homogeneous inner hypersurfaces, characterizing the topological space of 3D homogeneous Riemannian manifolds to understand the possible changes in Bianchi types over time.

Contribution

It provides a topological characterization of the space of homogeneous 3D manifolds, clarifying which Bianchi type changes are genuinely possible in such cosmological models.

Findings

Identifies the topological structure of the space of homogeneous Riemannian manifolds.

Determines which Bianchi type changes can occur over time.

Clarifies the conditions under which Bianchi types vary in inhomogeneous models.

Abstract

Space-times which allow a slicing into homogeneous spatial hypersurfaces generalize the usual Bianchi models. One knows already that in these models the Bianchi type may change with time. Here we show which of the changes really appear. To this end we characterize the topological space whose points are the 3-dimensional oriented homogeneous Riemannian manifolds; locally isometric manifolds are considered as same.