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We consider vacuum polarization from massless scalar electrodynamics in de Sitter inflation. The theory exhibits a 3+1 dimensional analog of the Schwinger mechanism in which a photon mass is dynamically generated. The mechanism is generic for light scalar fields that couple minimally to gravity. The nonvanishing of the photon mass during inflation may result in magnetic fields on cosmological scales.
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Prokopec et al. (2002) studied this question.
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