Multidimensional Cosmology: Spatially Homogeneous models of dimension 4+1

TL;DR

This paper classifies all 4+1 dimensional spatially homogeneous cosmological models, analyzing their algebraic structures, deriving equations of motion, and exploring compactification possibilities within the Kaluza-Klein framework.

Contribution

It provides a comprehensive classification of 4+1 homogeneous cosmological models, including multiply and simply transitive types, and derives their equations of motion.

Findings

Five multiply transitive models identified

Derived equations of motion for orthogonal models

Explored compactification via Kaluza-Klein mechanism

Abstract

In this paper we classify all 4+1 cosmological models where the spatial hypersurfaces are connected and simply connected homogeneous Riemannian manifolds. These models come in two categories, multiply transitive and simply transitive models. There are in all five different multiply transitive models which cannot be considered as a special case of a simply transitive model. The classification of simply transitive models, relies heavily upon the classification of the four dimensional (real) Lie algebras. For the orthogonal case, we derive all the equations of motion and give some examples of exact solutions. Also the problem of how these models can be compactified in context with the Kaluza-Klein mechanism, is addressed.