Scalar QED Action Density and Schwinger Pair Production in (A)dS₂

We review the one-loop effective action in scalar QED and the Schwinger effect in a uniform electric field in a two-dimensional (anti-) de Sitter space. The Schwinger effect has a thermal interpretation in terms of the effective temperature introduced by Cai and Kim. We propose a method to find the density of states for the charged scalar and obtain the QED action density and the pair-production rate in the in-out formalism.