On the challenges in the choice of the non-conformal coupling function
  in inflationary magnetogenesis
  Primordial magnetic fields are generated during inflation by considering
actions that break the conformal invariance of the electromagnetic field. To
break the conformal invariance, the electromagnetic fields are coupled either
to the inflaton or to the scalar curvature. Also, a parity violating term is
often added to the action in order to enhance the amplitudes of the primordial
electromagnetic fields. In this work, we examine the effects of deviations from
slow roll inflation on the spectra of non-helical as well as helical
electromagnetic fields. We find that, in the case of the coupling to the scalar
curvature, there arise certain challenges in generating electromagnetic fields
of the desired shapes and strengths even in slow roll inflation. When the field
is coupled to the inflaton, it is possible to construct model-dependent
coupling functions which lead to nearly scale invariant magnetic fields in slow
roll inflation. However, we show that sharp features in the scalar power
spectrum generated due to departures from slow roll inflation inevitably lead
to strong features in the power spectra of the electromagnetic fields.
Moreover, we find that such effects can also considerably suppress the
strengths of the generated electromagnetic fields over the scales of
cosmological interest. We illustrate these aspects with the aid of specific
inflationary models that have been considered to produce specific features in
the scalar power spectrum. Further, we find that, in such situations, if the
strong features in the electromagnetic power spectra are to be undone, the
choice of the coupling function requires considerable fine tuning. We discuss
wider implications of the results we obtain.
