The late-time behaviour of vortic Bianchi type VIII Universes

Original · EN

We use the dynamical systems approach to investigate the Bianchi type VIII models with a tilted γ-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<γ<2), the fluid will in general tend towards a state of extreme tilt. For dust (γ=1), or for fluids less stiff than dust (0<γ< 1), we show that the fluid will in the future be asymptotically non-tilted. Furthermore, we show that for all γ≥ 1 the universe evolves towards a vacuum state but does so rather slowly, ρ/H²∝ 1/ t.