Bianchi cosmologies: a tale of two tilted fluids

摘要

We use a dynamical systems approach to study Bianchi type VI0 cosmological models containing two tilted gamma-law perfect fluids. The full state space is 11-dimensional, but the existence of a monotonic function simplifies the analysis considerably. We restrict attention to a particular, physically interesting, invariant subspace and find all equilibrium points that are future stable in the full 11-dimensional state space; these are consequently local attractors and serve as late-time asymptotes for an open set of tilted type VI0 models containing two tilted fluids. We find that if one of the fluids has an equation of state parameter (y) over cap < 6/5, the stiffest fluid will be dynamically insignificant at late times. For the value (y) over cap = 6/5 there is a two-dimensional bifurcation set and, if both fluids are stiffer than (y) over cap = 6/5, both fluids will have extreme tilt asymptotically. We investigate in detail the case in which one fluid is extremely tilted. We also consider the case with one stiff fluid ((y) over cap = 2) close to the initial singularity and find that the chaotic behaviour which occurs in general Bianchi models with (y) over cap < 2 is suppressed.