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The Futures of Bianchi type VII0 cosmologies with vorticity

S. Hervik·R. J. van den Hoogen·W. C. Lim·A. A. Coley
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Abstract

We use expansion-normalised variables to investigate the Bianchi type VII$_0$ model with a tilted $γ$-law perfect fluid. We emphasize the late-time asymptotic dynamical behaviour of the models and determine their asymptotic states. Unlike the other Bianchi models of solvable type, the type VII$_0$ state space is unbounded. Consequently we show that, for a general non-inflationary perfect fluid, one of the curvature variables diverges at late times, which implies that the type VII$_0$ model is not asymptotically self-similar to the future. Regarding the tilt velocity, we show that for fluids with $γ<4/3$ (which includes the important case of dust, $γ=1$) the tilt velocity tends to zero at late times, while for a radiation fluid, $γ=4/3$, the fluid is tilted and its vorticity is dynamically significant at late times. For fluids stiffer than radiation ($γ>4/3$), the future asymptotic state is an extremely tilted spacetime with vorticity.

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S. Hervik, R. J. van den Hoogen, W. C. Lim, A. A. Coley. 2005-12-15. The Futures of Bianchi type VII0 cosmologies with vorticity. https://doi.org/10.1088/0264-9381%2F23%2F3%2F018

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