  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.
