Bianchi models with vorticity: The type III bifurcation

TL;DR

This paper analyzes the late-time dynamics of tilted Bianchi type III cosmological models with dust and stiffer fluids, revealing a slow approach to vacuum states through a detailed bifurcation analysis using dynamical systems theory.

Contribution

It provides a detailed dynamical systems analysis of Bianchi type III models with vorticity, highlighting the bifurcation structure and decay rates toward vacuum states.

Findings

Models approach vacuum spacetime slowly as 1/ln t.

Centre manifold analysis reveals double bifurcation behavior.

Decay rates depend on fluid stiffness and parameters.

Abstract

We study the late-time behaviour of tilted perfect fluid Bianchi type III models using a dynamical systems approach. We consider models with dust, and perfect fluids stiffer than dust, and eludicate the late-time behaviour by studying the centre manifold which dominates the behaviour of the model at late times. In the dust case, this centre manifold is 3-dimensional and can be considered as a double bifurcation as the 2 parameters ($h$ and $\gamma$) of the type VI$_h$ model are varied. We calculate the decay rates and show that for dust or stiffer the models approach a vacuum spacetime, however, it does so rather slowly: $\rho/H^2\sim 1/\ln t$.