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The existence of large-scale magnetic fields in galaxies is well established, but there is no accepted mechanism for generating a primordial field which could grow into what is observed today. We discuss a model which attempts to account for the necessary primordial field by invoking a pseudo Goldstone boson coupled to electromagnetism. The evolution of this boson during inflation generates a magnetic field; however, it seems difficult on rather general grounds to obtain fields of sufficient strength on astrophysically interesting scales.
Garretson et al. (Tue,) studied this question.