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

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 $(\frac{6}{5},\frac{3}{2})$. 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.

Latex, 7 pages, no figures; (v2) some clarification comments are added in the discussion and one reference; (v3) minor corrections in equations (1), (3) and (19)

References in corpus (3)

• The Future of Tilted Bianchi Universes
• The Asymptotic Behaviour of Tilted Bianchi type VI${}_0$ Universes
• Self-similar Bianchi models: I. Class A models

Cited by in corpus (6)

• Self-similar Bianchi models: II. Class B models
• Late-time behaviour of the tilted Bianchi type VIh models
• Equilibrium points of the tilted perfect fluid Bianchi VI${}_h$ state space
• Bianchi type I models with two tilted fluids
• Uniqueness of Petrov type D spatially inhomogeneous irrotational silent models
• A positive cosmological constant as a geometrical artifact