Primordial spectrum of gauge fields from inflation

We show that conformal invariance of gauge fields is naturally broken in inflation, having as a consequence amplification of gauge fields. The resulting spectrum of the field strength is approximately Bℓ∝ℓ−1, where ℓ is the relevant coherence scale. One realisation of our scenario is scalar electrodynamics with a scalar whose mass is large enough to evade observational constraints — the obvious candidates being supersymmetric partners of the standard-model fermions. Our mechanism also leads naturally to amplification of the standard-model Z-boson field due to its coupling to the electroweak Higgs field. At preheating, the spectrum of the Z field is transferred to the hypercharge field, which remains frozen in the plasma and is converted into a magnetic field at the electroweak phase transition. With a reasonable model of field evolution one obtains a magnetic field strength of the order of 10−29 Gauss on a scale of 100 pc, the size of the largest turbulent eddy in a virialised galaxy. Resonant amplification in preheating can lead to primordial fields as large as 10−24 Gauss, consistent with the seed field required for the galactic dynamo mechanism.