Generation of large scale magnetic fields in single-field inflation

We consider the generation of large scale magnetic fields in slow-roll inflation. The inflaton field is described in a supergravity framework where the conformal invariance of the electromagnetic field is generically and naturally broken. For each class of inflationary scenarios, we determine the functional dependence of the gauge coupling that is consistent with the observations on the magnetic field strength at various astrophysical scales and, at the same time, avoid a back-reaction problem. Then, we study whether the required coupling functions can naturally emerge in well motivated, possibly string inspired, models. We argue that this is non-trivial and can be realized only for a restricted class of scenarios. This includes power-law inflation where the inflaton field is interpreted as a modulus. However, this scenario seems to be consistent only if the energy scale of inflation is low and the reheating stage prolonged. Another reasonable possibility appears to be small field models since no back-reaction problem is present in this case but, unfortunately, the corresponding scenario cannot be justified in a stringy framework. Finally, large field models do not lead to sensible model building