Primordial Magnetic Fields and the Peccei-Quinn Scale
  A strong primordial magnetic field can induce a relaxation of the present bound on the PQ-constant. We show that, considering the present limits on primordial magnetic fields, a value for the PQ-constant very close to the GUT scale is not excluded. This result naturally opens the possibility for the axion to be defined in the context of the GUT theories. 
Leonardo Campanelli and Maurizio Giannotti