Late-time behaviour of the tilted Bianchi type VIh models

Abstract

We study tilted perfect fluid cosmological models with a constant equation of state parameter in spatially homogeneous models of Bianchi type VI_h using dynamical systems methods and numerical experimentation, with an emphasis on their future asymptotic evolution. We determine all of the equilibrium points of the type VI_h state space (which correspond to exact self-similar solutions of the Einstein equations, some of which are new), and their stability is investigated. We find that there are vacuum plane-wave solutions that act as future attractors. In the parameter space, a `loophole' is shown to exist in which there are no stable equilibrium points. We then show that a Hopf-bifurcation can occur resulting in a stable closed orbit (which we refer to as the Mussel attractor) corresponding to points both inside the loophole and points just outside the loophole; in the former case the closed curves act as late-time attractors while in the latter case these attracting curves will co-exist with attracting equilibrium points. In the special Bianchi type III case, centre manifold theory is required to determine the future attractors. Comprehensive numerical experiments are carried out to complement and confirm the analytical results presented. We note that the Bianchi type VI_h case is of particular interest in that it contains many different subcases which exhibit many of the different possible future asymptotic behaviours of Bianchi cosmological models.

35 pages, 14 figures; v2:added more comments and refs, typos corrected

References in corpus (22)

• Evidence of vorticity and shear at large angular scales in the WMAP data: a violation of cosmological isotropy?
• Self-Similarity in General Relativity \endtitle
• On the Viability of Bianchi Type VIIh Models with Dark Energy
• The asymptotic regimes of tilted Bianchi II cosmologies
• A dynamical systems approach to the tilted Bianchi models of solvable type
• Asymptotic dynamics of the exceptional Bianchi cosmologies
• Future Asymptotic Behaviour of Tilted Bianchi models of type IV and VIIh
• The Future of Tilted Bianchi Universes
• Bianchi Cosmologies: A Tale of Two Tilted fluids
• The Futures of Bianchi type VII0 cosmologies with vorticity
• Fluid observers and tilting cosmology
• The Asymptotic Behaviour of Tilted Bianchi type VI${}_0$ Universes
• The late-time behaviour of vortic Bianchi type VIII Universes
• Self-similar Bianchi models: II. Class B models
• Late-time behaviour of the tilted Bianchi type VIh models
• Kinematic and Weyl singularities
• Equilibrium points of the tilted perfect fluid Bianchi VI${}_h$ state space
• Tilt and phantom cosmology
• On tilted perfect fluid Bianchi type VI${}_0$ self-similar models
• Cosmology: a bird's eye view
• Tilted Bianchi VII_0 cosmologies -- the radiation bifurcation
• Cosmic microwave background limits on spatially homogeneous cosmological models with dark energy

Cited by in corpus (15)

• Cosmology of a Scalar Field Coupled to Matter and an Isotropy-Violating Maxwell Field
• Late-time behaviour of the tilted Bianchi type VIh models
• Mathematical General Relativity
• Future asymptotics of tilted Bianchi type II cosmologies
• Late-time behaviour of the tilted Bianchi type VI${}_{-1/9}$ models
• Bianchi models with vorticity: The type III bifurcation
• Open problems in mathematical physics
• Evolution of a Simple Inhomogeneous Anisotropic Cosmological Model with Diffusion
• Tilted two-fluid Bianchi type I models
• Spatially inhomogeneous and irrotational geometries admitting Intrinsic Conformal Symmetries
• Bianchi type I models with two tilted fluids
• Dynamics of tilted Bianchi models of types III, IV, V in presence of diffusion
• Approaching Wonderland
• Collins in Wonderland
• Mixmaster Fluids Near the Big Bang