We consider the gravitational generation of the massive Z boson field of the standard model, due to the natural breaking of its conformal invariance during inflation. The electroweak symmetry restoration at the end of inflation turns the almost scale-invariant superhorizon Z spectrum into a hypermagnetic field, which transforms into a regular magnetic field at the electroweak phase transition. The mechanism is generic and is shown to generate a superhorizon spectrum of the form B∝1/l on a length scale l regardless of the choice of the inflationary model. Scaled to the epoch of galaxy formation such a field suffices to trigger the galactic dynamo and explain the observed galactic magnetic fields in the case of a spatially flat, dark energy dominated universe with grand-unified-theory-scale inflation. The possibility of further amplification of the generated field by preheating is also investigated. To this end we study a model of supersymmetric hybrid inflation with a flipped SU(5) grand unified symmetry group.
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Dimopoulos et al. (2002) studied this question.
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