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The $R^2$ term in the Starobinsky inflationary model can be regarded as aleading quantum correction to the gravitational effective action. We assumethat parity-preserving and parity-violating (axial) non-minimal couplingsbetween curvature and electromagnetic field are also present in the effectiveaction. In the Einstein frame, they turn into non-trivial couplings of thescalaron and curvature to the electromagnetic field. We make an assessment ofinflationary magnetogenesis in this model. In the case of parity-preservingcouplings, amplification of magnetic field is negligibly small. In the case ofaxial couplings, magnetogenesis is hampered by strong back-reaction on theinflationary process, resulting in possible amplification of magnetic field atmost by the factor $10^5$ relative to its vacuum fluctuations.

Magnetogenesis by non-minimal coupling to gravity in the Starobinsky inflationary model