The Futures of Bianchi type VII0 cosmologies with vorticity

TL;DR

This paper investigates the late-time behavior of Bianchi type VII$_0$ cosmologies with tilted perfect fluids, revealing divergence in curvature variables and different tilt and vorticity outcomes depending on the fluid's equation of state.

Contribution

It provides a detailed analysis of the asymptotic states of Bianchi type VII$_0$ models, highlighting their unbounded state space and the impact of fluid tilt and vorticity.

Findings

Curvature variables diverge at late times for general fluids.

Tilt velocity tends to zero for $oldsymbol{ extit{ extbf{ extgamma}}}<4/3$.

Fluid vorticity remains significant for $oldsymbol{ extit{ extgamma}=4/3}$ and above.

Abstract

We use expansion-normalised variables to investigate the Bianchi type VII$_0$ model with a tilted $\gamma$-law perfect fluid. We emphasize the late-time asymptotic dynamical behaviour of the models and determine their asymptotic states. Unlike the other Bianchi models of solvable type, the type VII$_0$ state space is unbounded. Consequently we show that, for a general non-inflationary perfect fluid, one of the curvature variables diverges at late times, which implies that the type VII$_0$ model is not asymptotically self-similar to the future. Regarding the tilt velocity, we show that for fluids with $\gamma<4/3$ (which includes the important case of dust, $\gamma=1$) the tilt velocity tends to zero at late times, while for a radiation fluid, $\gamma=4/3$, the fluid is tilted and its vorticity is dynamically significant at late times. For fluids stiffer than radiation ($\gamma>4/3$), the future asymptotic state is an extremely tilted spacetime with vorticity.