Asymptotic dynamics of the exceptional Bianchi cosmologies

Abstract

In this paper we give, for the first time, a qualitative description of the\nasymptotic dynamics of a class of non-tilted spatially homogeneous (SH)\ncosmologies, the so-called exceptional Bianchi cosmologies, which are of\nBianchi type VI$_{-1/9}$. This class is of interest for two reasons. Firstly,\nit is generic within the class of non-tilted SH cosmologies, being of the same\ngenerality as the models of Bianchi types VIII and IX. Secondly, it is the SH\nlimit of a generic class of spatially inhomogeneous $G_{2}$ cosmologies.\n Using the orthonormal frame formalism and Hubble-normalized variables, we\nshow that the exceptional Bianchi cosmologies differ from the non-exceptional\nBianchi cosmologies of type VI$_{h}$ in two significant ways. Firstly, the\nmodels exhibit an oscillatory approach to the initial singularity and hence are\nnot asymptotically self-similar. Secondly, at late times, although the models\nare asymptotically self-similar, the future attractor for the vacuum-dominated\nmodels is the so-called Robinson-Trautman SH model instead of the vacuum SH\nplane wave models.\n