Asymptotic dynamics of the exceptional Bianchi cosmologies

TL;DR

This paper provides a qualitative analysis of the asymptotic behavior of exceptional Bianchi cosmologies, revealing oscillatory singularity approach and a different future attractor compared to non-exceptional models.

Contribution

It offers the first qualitative description of the asymptotic dynamics of exceptional Bianchi type VI_{-1/9} cosmologies, highlighting their unique oscillatory approach and future attractor.

Findings

Models exhibit oscillatory approach to initial singularity.

At late times, models are asymptotically self-similar.

Future attractor is the Robinson-Trautman SH model.

Abstract

In this paper we give, for the first time, a qualitative description of the asymptotic dynamics of a class of non-tilted spatially homogeneous (SH) cosmologies, the so-called exceptional Bianchi cosmologies, which are of Bianchi type VI$_{-1/9}$. This class is of interest for two reasons. Firstly, it is generic within the class of non-tilted SH cosmologies, being of the same generality as the models of Bianchi types VIII and IX. Secondly, it is the SH limit of a generic class of spatially inhomogeneous $G_{2}$ cosmologies. Using the orthonormal frame formalism and Hubble-normalized variables, we show that the exceptional Bianchi cosmologies differ from the non-exceptional Bianchi cosmologies of type VI$_{h}$ in two significant ways. Firstly, the models exhibit an oscillatory approach to the initial singularity and hence are not asymptotically self-similar. Secondly, at late times, although the models are asymptotically self-similar, the future attractor for the vacuum-dominated models is the so-called Robinson-Trautman SH model instead of the vacuum SH plane wave models.