Bianchi cosmologies, magnetic fields, and singularities

We study the effects of a spatially homogenous magnetic field in Bianchi-I cosmological models. The cases of a pure magnetic field and two models with additional dust and a massless scalar field (stiff matter) are also considered. At the beginning of the cosmological evolution, i.e., in the neighborhood of the singularity, the Universe is described by one of Kasner's solutions, and asymptotically by another Kasner solution when the volume of the Universe tends to infinity. The transition law between these two Kasner regimes is established, and shown to coincide with the analogous law for the empty Bianchi-II universe. The universe filled with dust and a magnetic field undergoes the process of isotropization, while the presence of a massless scalar field induces a modification of the relations between Kasner indices in the two asymptotic regimes. In all of these cases, we analyze the approach to the singularity in some detail and comment on the issue of the possible singularity crossing.