  The interplay among the possible variation of gauge coupling and the
inflationary dynamics is investigated in a simplified toy model. Depending upon
various parameters (scalar mass, curvature scale at the end of inflation and at
the onset of the radiation epoch), the two-point function of the magnetic
inhomogeneities grows during the de Sitter stage of expansion and,
consequently, large scale magnetic fields are generated. The requirements
coming from inflationary magnetogenesis are examined together with the
theoretical constraints stemming from the explicit model of the evolution of
the gauge coupling.
