Classical constant electric fields and the Schwinger effect in de Sitter

TL;DR

This paper investigates the behavior of constant electric fields and the Schwinger effect in de Sitter space, revealing that a tachyonic photon mass is necessary to sustain such fields and revising the understanding of the induced current.

Contribution

It introduces a consistent on-shell renormalization approach with a tachyonic photon mass, providing finite, positive Schwinger currents in de Sitter space for charged particles.

Findings

A tachyonic photon mass of order the Hubble scale is required to sustain a constant electric field.

The Schwinger current is finite and positive even for massless charge carriers.

In the conformal limit, the scalar and fermion currents closely match.

Abstract

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.