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The cosmological solutions of the non-minimal $ Y (R)F^2 $ theory which arecompatible with FRW space-time are investigated. In order to avoid the isotropyviolation of a vector field, it can be considered that the presence of atriplet of vector fields satisfying $SO(3)$ symmetry, or the average ofrandomly oriented electromagnetic fields over the sufficiently large volume. Byconsidering the symmetry arguments, the inflation driven by the non-minimallycoupled vector fields is studied. Then the cosmological solutions andcorresponding models are obtained with the power law, hyperbolic and hybridscale functions.

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