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

Scalar QED Action Density and Schwinger Pair Production in (A)dS_2