Schwinger Pair Production in dS_2 and AdS_2

TL;DR

This work analyzes Schwinger pair production for a charged scalar field in a uniform electric field within $dS_2$ and $AdS_2$ spacetimes by solving the Klein-Gordon equation exactly in each geometry. The authors show that, with suitable boundary conditions, the production rates are governed by the same analytic function of the scalar curvature $R$, connected by an analytic continuation between the geometries. They derive explicit instanton-like actions $S_{ m dS}$ and $S_{ m AdS}$ that control the production rates and discuss limiting cases where results reproduce known flat-space and de Sitter results. They also reveal how AdS confinement suppresses production and imposes a threshold electric field, highlighting the role of curvature in pair creation.

Abstract

We study Schwinger pair production in scalar QED from a uniform electric field in dS_2 with scalar curvature R_{dS} = 2 H^2 and in AdS_2 with R_{AdS} = - 2 K^2. With suitable boundary conditions, we find that the pair-production rate is the same analytic function of the scalar curvature in both cases.