Inhomogeneous Multidimensional Cosmologies

TL;DR

This paper derives and analyzes solutions to Einstein's equations in higher-dimensional inhomogeneous cosmologies, highlighting singularities, dynamical compactification, and the role of stabilization mechanisms for extra dimensions.

Contribution

It presents a family of exact solutions for inhomogeneous 4+n-dimensional cosmologies with arbitrary functions, and studies their dynamics and stabilization.

Findings

Solutions exhibit a singularity at t=0

Extra dimensions undergo dynamical compactification

Post-compactification behavior depends on stabilization mechanisms

Abstract

Einstein's equations for a 4+n-dimensional inhomogeneous space-time are presented, and a special family of solutions is exhibited for an arbitrary n. The solutions depend on two arbitrary functions of time. The time development of a particular member of this family is studied. This solution exhibits a singularity at t=0 and dynamical compactification of the n dimensions. It is shown that the behaviour of the system in the 4-dimensional i.e. post-compactification phase is constrained by the way in which the compactified dimensions are stabilized. The fluid that generates the solution is analyzed by means of the energy conditions.