N ov 1 99 9 Kasner Asymptotics of Mixmaster Hořava - Witten Cosmology .

Bianchi type I and type IX (’Mixmaster’) geometries are investigated within the framework of Hořava-Witten cosmology. We consider the models for which the fifth coordinate is a S/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 CalabiYau 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 [10]. Finally, we discuss if such Bianchi IX configuration can result in chaotic behaviour of these Hořava-Witten cosmologies. PACS number(s): 98.80.Hw, 04.50.+h, 11.25.Mj, 98.80.Cq