Higher Dimensional Cosmology: Relations among the radii of two homogeneous spaces

TL;DR

This paper explores a higher-dimensional cosmological model with two homogeneous spaces, analyzing the relationships between their scale factors and deriving solutions for the evolution of the universe in such a framework.

Contribution

It provides a general analysis of field equations in a multi-dimensional cosmology and derives specific solutions involving two scale factors, including detailed study for D=3, d=1.

Findings

Derived solutions for scale factors a(t) and b(t)

Analyzed the field equations for higher-dimensional models

Detailed case study for D=3, d=1

Abstract

We study a cosmological model in 1+D+d dimensions where D dimensions are associated with the usual Friedman-Robertson-Walker type metric with radio a(t) and d dimensions corresponds to an additional homogeneous space with radio b(t). We make a general analysis of the field equations and then we obtain solutions involving the two cosmological radii, a(t) and b(t). The particular case D=3, d=1 is studied in some detail.