  It is shown that the evolution of the (Abelian) gauge coupling during an
inflationary phase of de Sitter type drives the growth of the two-point
function of the magnetic inhomogeneities. After examining the constraints on
the variation of the gauge coupling arising in a standard model of inflationary
and post-inflationary evolution, magnetohydrodynamical equations are
generalized to the case of time evolving gauge coupling. It is argued that
large scale magnetic fields can be copiously generated. Other possible
implications of the model are outlined.
