The late-time behaviour of tilted Bianchi type VIII universes in presence of diffusion

Abstract

We apply the dynamical systems approach to ever-expanding Bianchi type VIII cosmologies filled with a tilted $\gamma$-fluid undergoing velocity diffusion on a scalar field. We determine the future attractors and investigate the late-time behaviour of the models. We find that at late times the normalized energy density $\Omega$ tends to zero, while the scalar potential $\Phi$ approaches 1 and dominates the evolution. Moreover, we demonstrate that in presence of diffusion fluids with $\gamma <3/2$, which includes physically important cases of dust $(\gamma =1)$ and radiation $(\gamma =4/3)$, are asymptotically non-tilted; the velocity of the fluid with $\gamma =3/2$ tends to a constant value $0<\bar{V}<1$; and stiffer fluids evolve towards a state of extreme tilt. Finally, we show that diffusion significantly reduces the decay rates of energy density for dust and fluids stiffer than dust $(\gamma \ge 1)$; for example, at $\gamma =4/3$ (radiation) we obtain $\rho /H^2\propto e^{-3H_{0}t}$ at late times, while $\rho /H^2\propto e^{-4H_{0}t}$ when diffusion is absent.

13 pages, no figures

References in corpus (2)

• Bianchi models with vorticity: The type III bifurcation
• Evolution of a Simple Inhomogeneous Anisotropic Cosmological Model with Diffusion

Cited by in corpus (4)

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