Schwinger effect impacting primordial magnetogenesis

We explore the enhancement of an electromagnetic field in an inflationary background with an anti-conductive plasma of scalar particles. The scalar particles are created by Schwinger effect in curved spacetime and backreact to the electromagnetic field. The possibility of a negative conductivity was recently put forward in the context of the renormalization of the Schwinger induced current in de Sitter spacetime. While a negative conductivity enhances the produced magnetic field, we find that it is too weak to seed the observed intergalactic magnetic field today. This results on pair creation in inflationary scenario is however important for primordial scenarios of magnetogenesis as the presence of a conductivity alters the spectral index of the magnetic field. This also shows on a specific example that backreaction can increase the electromagnetic field and not only suppress it.