Classical constant electric fields and the Schwinger effect in de Sitter

We study constant classical electric fields and the Schwinger effect in de Sitter space, with potential implications for magnetogenesis and inflationary dark matter production. Treating the photon as a dynamical field, we show that sustaining a constant electric field in de Sitter requires a tachyonic photon mass of order the Hubble scale. This observation has physical implications, as it alters the infrared behaviour of the induced Schwinger current. Using an on-shell renormalization condition consistent with a tachyonic photon, we recompute the current for charged fermions and scalars, finding it to be finite and positive even in the massless limit of the charge carriers-contrary to earlier results predicting a puzzling negative IR divergence. For scalars, we include a non-minimal coupling to the Ricci curvature, enabling us to analyze the conformal limit, where the current closely matches that of charged fermions.