Anisotropic cosmological models with non-minimally coupled magnetic   field
  Motivated by the structure of one-loop vacuum polarization effects in curved spacetime we discuss a non-minimal extension of the Einstein-Maxwell equations. This formalism is applied to Bianchi I models with magnetic field. We obtain several exact solutions of the non-minimal system including those which describe an isotropization process. We show that there are inflationary solutions in which the cosmological constant is determined by the non-minimal coupling parameters. Furthermore, we find an isotropic de Sitter solution characterized by a "screening" of the magnetic field as a consequence of the non-minimal coupling. 
Alexander B. Balakin and Winfried Zimdahl