Magnetogenesis by non-minimal coupling to gravity in the Starobinsky
  inflationary model
  The $R^2$ term in the Starobinsky inflationary model can be regarded as a
leading quantum correction to the gravitational effective action. We assume
that parity-preserving and parity-violating (axial) non-minimal couplings
between curvature and electromagnetic field are also present in the effective
action. In the Einstein frame, they turn into non-trivial couplings of the
scalaron and curvature to the electromagnetic field. We make an assessment of
inflationary magnetogenesis in this model. In the case of parity-preserving
couplings, amplification of magnetic field is negligibly small. In the case of
axial couplings, magnetogenesis is hampered by strong back-reaction on the
inflationary process, resulting in possible amplification of magnetic field at
most by the factor $10^5$ relative to its vacuum fluctuations.
