Kasner asymptotics of mixmaster Hořava–Witten cosmology

Bianchi type I and type IX (ʹMixmasterʹ) geometries are investigated within the framework of Hořava–Witten cosmology. We consider the models for which the fifth coordinate is a S1/Z2 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 et al. . Finally, we discuss if such Bianchi IX configuration can result in chaotic behaviour of these Hořava–Witten cosmologies.