Late-time electric screening in dS from EAdS loops

Abstract

We compute the one-loop gauge-field two-point functions analytically in scalar QED on dS$_{d+1}$ for general dimension and scalar mass, using the EAdS reformulation of the in-in formalism arXiv:2007.09993. The Dirichlet EAdS gauge field acquires a Schwinger-type mass, with its longitudinal mode supplied by a composite of charged scalars obeying opposite boundary conditions, while the Neumann mode remains protected by gauge invariance. In dS, the Dirichlet correction induces an anomalous dimension $γ_J$ for the boundary current and modifies the late-time falloff of the electric field. This bulk calculation reproduces the boundary multiplet-recombination result of arXiv:2509.18888. Summing over the in-in contour branches gives the retarded dS bubble kernel, making direct contact with the Bros-Moschella framework. We establish a spectral Cutkosky rule that expresses the discontinuity of this kernel across the principal-series cut in the Casimir plane in terms of a two-particle cut, with both internal scalar lines placed on shell. Although the full bubble coefficient involves a ${}_7F_6$ hypergeometric function, the cut collapses to a closed product of Gamma functions and determines the complete non-local part of the kernel through a dispersion relation. Analytic continuation of the same cut reproduces the complete one-loop result for $γ_J$. In the complex Casimir plane, the loop-corrected Dirichlet photon appears as a pole on the second sheet and is therefore naturally interpreted as a dS resonance, or quasinormal mode, whose frequency is shifted at one loop.