The late-time behaviour of vortic Bianchi type VIII Universes

TL;DR

This paper analyzes the late-time behavior of Bianchi type VIII cosmological models with tilted perfect fluids, revealing how curvature and tilt evolve depending on the fluid's stiffness, and showing a slow approach to vacuum states.

Contribution

It introduces expansion-normalized variables to study the asymptotic states of Bianchi type VIII models with tilted fluids, providing new insights into their late-time dynamics.

Findings

Curvature variables grow unbounded for non-inflationary fluids.

Fluids stiffer than dust tend toward extreme tilt.

Models approach vacuum states slowly, with density decreasing as 1/ln t.

Abstract

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