Inflation of the Universe by the Non-minimal $Y(R)F^2$ Models

The cosmological solutions of the non-minimal $Y(R)F^2$ theory which are compatible with FRW space-time are investigated. In order to avoid the isotropy violation of a vector field, it can be considered that the presence of a triplet of vector fields satisfying $SO(3)$ symmetry, or the average of randomly oriented electromagnetic fields over the sufficiently large volume. By considering the symmetry arguments, the inflation driven by the non-minimally coupled vector fields is studied. Then the cosmological solutions and corresponding models are obtained with the power law, hyperbolic and hybrid scale functions.