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.

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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