A Dynamical Systems Approach to a Bianchi Type I Viscous Magnetohydrodynamic Model

Abstract

We use the expansion-normalized variables approach to study the dynamics of a non-tilted Bianchi Type I cosmological model with both a homogeneous magnetic field and a viscous fluid. In our model the perfect magnetohydrodynamic approximation is made, and both bulk and shear viscous effects are retained. The dynamical system is studied in detail through a fixed-point analysis which determines the local sink and source behavior of the system. We show that the fixed points may be associated with Kasner-type solutions, a flat universe FLRW solution, and interestingly, a new solution to the Einstein Field equations involving non-zero magnetic fields, and non-zero viscous coefficients. It is further shown that for certain values of the bulk and shear viscosity and equation of state parameters, the model isotropizes at late times.

References in corpus (2)

• Cosmology with inhomogeneous magnetic fields
• Bianchi VI0 viscous fluid cosmology with magnetic field

Cited by in corpus (6)

• Bianchi I Model: An Alternative Way To Model The Presentday Universe
• On The Dynamics of a Closed Viscous Universe
• A non-perturbative study of the evolution of cosmic magnetised sources
• Comments On: A Universe From Nothing
• The Dynamics of a Two-Fluid Bianchi Type I Universe
• The oscillatory anisotropy in the spatially flat cosmological models