Constant electric fields in de Sitter require a tachyonic photon mass ~H, yielding finite positive Schwinger currents for massless fermions and scalars after on-shell renormalization.
Berdyugin et al., Out-of-equilibrium criticalities in graphene superlattices , Science 375 (2022) 430 [ 2106.12609]
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Classical constant electric fields and the Schwinger effect in de Sitter
Constant electric fields in de Sitter require a tachyonic photon mass ~H, yielding finite positive Schwinger currents for massless fermions and scalars after on-shell renormalization.