Dynamics of the anisotropic preinflationary universe

The dynamics of anisotropic Bianchi type-IX model (Mixmaster Universe) with matter and cosmological constant is studied. The model can be considered a s describing the preinflationary universe where the cosmological constant i s arised from the vacuum energy of the inflation field. There are a critica l saddle-point in the phase space of the system and a strong asymptotic de Sitter attractor. The structure of the phase space neat the critical point is very complicated, presenting the unbounded orbits escaping from unstable periodic orbits. Even for very small anisotropy, the universe oscillates a long time in the neighborhood of the critical point before collapsing or e scaping to the de Sitter universe, exhibiting the chaotic behavior. Our res ults extend the results of Oliviera et al. [Phys. Rev: D 56 (1997) 730] for the case of two anisotropic scale functions.