Primordial magnetic fields from pseudo-Goldstone bosons
  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. 
W. Daniel Garretson, George B. Field, and Sean M. Carroll   (Harvard-Smithsonian Center for Astrophysics)