Kasner Asymptotics of Horava-Witten Cosmology

TL;DR

This paper explores Kasner asymptotics in Hořava-Witten cosmology, analyzing Bianchi type I and IX models with compactified extra dimensions, and investigates potential chaotic behavior in these higher-dimensional cosmological solutions.

Contribution

It provides new Kasner-type solutions and asymptotic analysis for Bianchi I and IX models within Hořava-Witten cosmology, including conditions for isotropy and chaos.

Findings

Recovered isotropic 3-space solutions.

Analyzed Kasner asymptotics of Bianchi IX.

Discussed potential chaotic behavior.

Abstract

Bianchi type I and type IX ('Mixmaster') geometries are investigated within the framework of Ho\v{r}ava-Witten cosmology. We consider the models for which the fifth coordinate is a $S^1/Z_2$ orbifold while the four coordinates are such that the 3-space is homogeneous and has geometry of Bianchi type I or IX while the rest six dimensions have already been compactified on a Calabi-Yau space. In particular, we study Kasner-type solutions of the Bianchi I field equations and discuss Kasner asymptotics of Bianchi IX field equations. We are able to recover the isotropic 3-space solutions found by Lukas {\it et al}. Finally, we discuss if such Bianchi IX configuration can result in chaotic behaviour of these Ho\v{r}ava-Witten cosmologies.