  In this paper, we discuss the inflationary magnetogenesis scenario, in which
the coupling function is introduced to break the conformal invariance of
electromagnetic action. Unlike in conventional models, we deduce the Maxwell's
equations under the perturbed FRW metric. We found that, the self-consistency
of the action depends on the form of the coupling function when the scalar mode
perturbations have been considered. Therefore, this self-consistency can be
seen as a restriction on the coupling function. In this paper, we give the
restrictive equation for coupling function then obtain the specific form of the
coupling function in a simple model. We found that the coupling function
depends on the potential of the inflaton and thus is model dependent. We obtain
the power spectrum of electric field and magnetic field in large-field
inflation model. We also found that the coupling function is a incresing
function of time during slow-roll era as most of inflationary magnetogenesis
models, it will lead to strong coupling problem. This issue is discussed
qualitatively by introducing a correction function during the preheating.
