Some effects of magnetic fields in spatially homogeneous universes with conductivity

Abstract

Magnetic fields and fluids with a finite conductivity are introduced in Bianchi type-I universes. The fluid then behaves like a perfect fluid in a universe of higher Bianchi type. It is as though the magnetofluid contribution to the stress-energy tensor becomes a pseudocurvature of the spacetime. A nonzero vorticity exists although the notion of translational invariance is fundamental to Bianchi type-I homogeneous three-spaces. Perturbation methods are used to obtain the solutions. We find in a magnetohydrodynamic universe that the microwave background radiation isotropy sets limits on the rotation of $\ensuremath{\omega}\ensuremath{\lesssim}{10}^{\ensuremath{-}19}$ rad/yr and on the magnetic field of $H\ensuremath{\lesssim}5.38\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$ G.