The Futures of Bianchi type VII0 cosmologies with vorticity

Abstract

We use expansion-normalised variables to investigate the Bianchi type VII${}_0$ model with a tilted $\gamma$-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 $\gamma <4/3$ (which includes the important case of dust, $\gamma =1$) the tilt velocity tends to zero at late times, while for a radiation fluid, $\gamma =4/3$, the fluid is tilted and its vorticity is dynamically significant at late times. For fluids stiffer than radiation ($\gamma >4/3$), the future asymptotic state is an extremely tilted spacetime with vorticity.

arXiv comment23 pages, v2:references and comments added, typos fixed, to appear in CQG

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