On tilted perfect fluid Bianchi type VI$_0$ self-similar models

TL;DR

This paper analyzes tilted perfect fluid Bianchi VI$_0$ self-similar cosmological models, identifying their stability, parameter ranges, and late-time behavior, including tilt significance and potential as future attractors.

Contribution

It demonstrates that these models form the most general class of tilted self-similar solutions with specific parameter constraints and explores their stability and asymptotic tilt behavior.

Findings

Model has a four-dimensional stable manifold.

Tilt angle becomes asymptotically significant at late times.

Parameter $ ext{γ}$ lies in the interval (6/5, 3/2).

Abstract

We show that the tilted perfect fluid Bianchi VI$_0$ family of self-similar models found by Rosquist and Jantzen [K. Rosquist and R. T. Jantzen, \emph{% Exact power law solutions of the Einstein equations}, 1985 Phys. Lett. \textbf{107}A 29-32] is the most general class of tilted self-similar models but the state parameter $\gamma $ lies in the interval $(\frac 65,\frac 32) $. The model has a four dimensional stable manifold indicating the possibility that it may be future attractor, at least for the subclass of tilted Bianchi VI$_0$ models satisfying $n_\alpha ^\alpha =0$ in which it belongs. In addition the angle of tilt is asymptotically significant at late times suggesting that for the above subclasses of models the tilt is asymptotically extreme.