The late-time behaviour of vortic Bianchi type VIII Universes

Abstract

We use the dynamical systems approach to investigate the Bianchi type VIII models with a tilted $\gamma$-law perfect fluid. We introduce expansion-normalised variables and investigate the late-time asymptotic behaviour of the models and determine the late-time asymptotic states. For the Bianchi type VIII models the state space is unbounded and consequently, for all non-inflationary perfect fluids, one of the curvature variables grows without bound. Moreover, we show that for fluids stiffer than dust ($1<\gamma <2$), the fluid will in general tend towards a state of extreme tilt. For dust ($\gamma =1$), or for fluids less stiff than dust ($0<\gamma <1$), we show that the fluid will in the future be asymptotically non-tilted. Furthermore, we show that for all $\gamma \ge 1$ the universe evolves towards a vacuum state but does so rather slowly, $\rho /H^2\propto 1/\ln t$.

19 pages, 3 ps figures, v2:typos fixed, refs and more discussion added

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• Tilted two-fluid Bianchi type I models
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• Bianchi type I models with two tilted fluids
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• Dynamics of tilted Bianchi models of types III, IV, V in presence of diffusion
• Cosmology: a bird's eye view
• Tilted Bianchi VII_0 cosmologies -- the radiation bifurcation
• Approaching Wonderland
• Collins in Wonderland