Bianchi models with vorticity: The type III bifurcation

Abstract

We study the late-time behaviour of tilted perfect fluid Bianchi type III models using a dynamical systems approach. We consider models with dust, and perfect fluids stiffer than dust, and eludicate the late-time behaviour by studying the centre manifold which dominates the behaviour of the model at late times. In the dust case, this centre manifold is 3-dimensional and can be considered as a double bifurcation as the 2 parameters ($h$ and $\gamma$) of the type VI${}_h$ model are varied. We calculate the decay rates and show that for dust or stiffer the models approach a vacuum spacetime, however, it does so rather slowly: $\rho /H^2\sim 1/\ln t$.

12 pages

References in corpus (2)

• Late-time behaviour of the tilted Bianchi type VIh models
• Late-time behaviour of the tilted Bianchi type VI${}_{-1/9}$ models