Abstract
We use expansion-normalized variables to investigate the Bianchi type VII0 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 VII0 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 VII0 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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