Inflationary solutions and inhomogeneous Kaluza-Klein cosmology in 4+n dimensions

TL;DR

This paper investigates inflationary solutions in an inhomogeneous Kaluza-Klein cosmology across 4+n dimensions, highlighting special cases where the system is integrable, especially in 5-dimensional models.

Contribution

It identifies specific conditions under which inflationary solutions exist and the system's integrability in higher-dimensional Kaluza-Klein cosmology.

Findings

5-dimensional case is generally integrable for any k

k=0 and k=1/3 cases are integrable only when n=1

The system's behavior varies significantly with the number of extra dimensions

Abstract

We analyze the existence of inflationary solutions in an inhomogeneous Kaluza-Klein cosmological model in 4+n dimensions. It is shown that the 5-dimensional case is the exception rather than the rule, in the sense that the system is integrable (under the assumption of the equation of state $\rho= kp$) for any value of k. It is also shown that the cases k=0 and k=1/3 are integrable if and only if n=1.