  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.

General Relativity and Quantum Cosmology