Abstract
We derive the effective Lagrangian of a magnetic field in the context of a massless scalar QED coupled to gravity in de Sitter spacetime. It is found that the magnetic field is produced at the beginning of the inflation in a minimally coupled scalar QED, and that the intensity B is proportional to ${\mathrm{eH}}^{2}$ (H is the Hubble constant). When H${=10}^{15}$ GeV, B\ensuremath{\sim}1.3\ifmmode\times\else\texttimes\fi{}${10}^{47}$ G.
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