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

TL;DR

This paper analyzes the long-term behavior of a non-tilted Bianchi Type IV viscous fluid cosmological model, demonstrating isotropization and identifying key equilibrium solutions using dynamical systems theory and numerical analysis.

Contribution

It provides a novel dynamical systems analysis of Bianchi Type IV models with viscosity, highlighting isotropization and bifurcation phenomena.

Findings

The flat and open FL solutions are the main future attractors.

Bifurcations occur as bulk viscosity increases.

Numerical analysis confirms late-time isotropization.

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.