The late-time behaviour of vortic Bianchi type VIII Universes

Details The late-time behaviour of vortic Bianchi type VIII Universes The late-time behaviour of vortic Bianchi type VIII Universes

2005-12-12

arxiv.org/abs/gr-qc/0512070v2

Class.Quant.Grav.23:3017-3035,2006

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

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

Scientific paper

10.1088/0264-9381/23/9/015

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 $\gamma\geq 1$ the universe evolves towards a vacuum state but does so rather slowly, $\rho/H^2\propto 1/\ln t$.

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