The Asymptotic Behaviour of Tilted Bianchi type VI$_0$ Universes

TL;DR

This paper investigates the long-term dynamics of tilted Bianchi type VI$_0$ universes with a perfect fluid, identifying attractors, bifurcations, and chaotic initial behavior depending on the equation of state parameter.

Contribution

It provides a comprehensive analysis of the asymptotic states and stability transitions in tilted Bianchi VI$_0$ universes, including bifurcation phenomena at specific parameter values.

Findings

Identification of late-time attractors in the full state space.

Discovery of a bifurcation at $oxed{ ext{γ=6/5}}$ indicating a stability change.

Chaotic initial behavior for $oxed{ ext{γ<2}}$.

Abstract

We study the asymptotic behaviour of the Bianchi type VI$_0$ universes with a tilted $\gamma$-law perfect fluid. The late-time attractors are found for the full 7-dimensional state space and for several interesting invariant subspaces. In particular, it is found that for the particular value of the equation of state parameter, $\gamma=6/5$, there exists a bifurcation line which signals a transition of stability between a non-tilted equilibrium point to an extremely tilted equilibrium point. The initial singular regime is also discussed and we argue that the initial behaviour is chaotic for $\gamma<2$.