The Future of Tilted Bianchi Universes

TL;DR

This paper investigates the stability of Bianchi type universes with tilted perfect fluids, revealing that non-tilted equilibrium points are unstable under certain tilted conditions, and explores potential new solutions.

Contribution

It provides the first comprehensive stability analysis of all Bianchi class B models with tilted perfect fluids, identifying instability of non-tilted equilibria under specific tilt conditions.

Findings

Non-tilted equilibrium points are unstable against stiffer-than-radiation tilted fluids.

The analysis covers all Bianchi class B models and type VI_0.

Potential regions for new tilted exact solutions are identified.

Abstract

An asymptotic stability analysis of spatially homogeneous models of Bianchi type containing tilted perfect fluids is performed. Using the known attractors for the non-tilted Bianchi type universes, we check whether they are stable against perturbations with respect to tilted perfect fluids. We perform the analysis for all Bianchi class B models and the Bianchi type VI_0 model. In particular, we find that none of the non-tilted equilibrium points are stable against tilted perfect fluids stiffer than radiation. We also indicate parts of the phase space where new tilted exact solutions might be found.