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Primordial magnetic fields are generated during inflation by consideringactions that break the conformal invariance of the electromagnetic field. Tobreak the conformal invariance, the electromagnetic fields are coupled eitherto the inflaton or to the scalar curvature. Also, a parity violating term isoften added to the action in order to enhance the amplitudes of the primordialelectromagnetic fields. In this work, we examine the effects of deviations fromslow roll inflation on the spectra of non-helical as well as helicalelectromagnetic fields. We find that, in the case of the coupling to the scalarcurvature, there arise certain challenges in generating electromagnetic fieldsof the desired shapes and strengths even in slow roll inflation. When the fieldis coupled to the inflaton, it is possible to construct model-dependentcoupling functions which lead to nearly scale invariant magnetic fields in slowroll inflation. However, we show that sharp features in the scalar powerspectrum generated due to departures from slow roll inflation inevitably leadto strong features in the power spectra of the electromagnetic fields.Moreover, we find that such effects can also considerably suppress thestrengths of the generated electromagnetic fields over the scales ofcosmological interest. We illustrate these aspects with the aid of specificinflationary models that have been considered to produce specific features inthe scalar power spectrum. Further, we find that, in such situations, if thestrong features in the electromagnetic power spectra are to be undone, thechoice of the coupling function requires considerable fine tuning. We discusswider implications of the results we obtain.

On the challenges in the choice of the non-conformal coupling function in inflationary magnetogenesis