Inhomogeneous Cosmological Models Containing Homogeneous Inner Hypersurface Geometry. Changes of the Bianchi Type

TL;DR

This paper explores cosmological models with homogeneous spatial sections that can change Bianchi types over time, analyzing the mathematical conditions and physical constraints governing such transitions.

Contribution

It introduces models allowing time-dependent Bianchi type changes, expanding the understanding of spatial homogeneity in cosmology beyond traditional assumptions.

Findings

Certain Bianchi type transitions are mathematically permitted.

Physical energy conditions restrict possible Bianchi type changes.

Type I transition is trivial and always possible.

Abstract

There are investigated such cosmological models which instead of the usual spatial homogeneity property only fulfil the condition that in a certain synchronized system of reference all spacelike sections t = const. are homogeneous manifolds. This allows time-dependent changes of the BIANCHI type. Discussing differential geometrical theorems it is shown which of them are permitted. Besides the trivial case of changing into type I there exist some possible changes between other types. However, physical reasons like energy inequalities partially exclude them.