Asymptotic Regimes of Magnetic Bianchi Cosmologies

Abstract

We consider the asymptotic dynamics of the Einstein-Maxwell field equations for the class of non-tilted Bianchi cosmologies with a barotropic perfect fluid and a pure homogeneous source-free magnetic field, with emphasis on models of Bianchi type VII_{0}, which have not been previously studied. Using the orthonormal frame formalism and Hubble-normalized variables, we show that, as is the case for the previously studied class A magnetic Bianchi models, the magnetic Bianchi VII_{0} cosmologies also exhibit an oscillatory approach to the initial singularity. However, in contrast to the other magnetic Bianchi models, we rigorously establish that typical magnetic Bianchi VII_{0} cosmologies exhibit the phenomena of asymptotic self-similarity breaking and Weyl curvature dominance in the late-time regime.

26 pages, 6 figures, submitted to Gen. Rel. Grav