The Future Asymptotic Behaviour of a Non-Tilted Bianchi Type IV Viscous Model

Abstract

The future asymptotic behaviour of a non-titled Bianchi Type IV viscous fluid model is analyzed. In particular, we consider the case of a viscous fluid without heat conduction, and constant expansion-normalized bulk and shear viscosity coefficients. We show using dynamical systems theory that the only future attracting equilibrium points are the flat Friedmann-LeMaitre (FL) solution, the open FL solution and the isotropic Milne universe solution. We also show the bifurcations exist with respect to an increasing expansion-normalized bulk viscosity coefficient. It is finally shown through an extensive numerical analysis, that the dynamical system isotropizes at late times.