Schwinger effect in de Sitter space

Markus B. Fröb; Jaume Garriga; Sugumi Kanno; Misao Sasaki; Jiro Soda; Takahiro Tanaka; Alexander Vilenkin

doi:10.1088/1475-7516/2014/04/009

paper

Schwinger effect in de Sitter space

arXiv:1401.4137 · doi:10.1088/1475-7516/2014/04/009

Abstract

We consider Schwinger pair production in 1+1 dimensional de Sitter space, filled with a constant electric field $E$ . This can be thought of as a model for describing false vacuum decay beyond the semiclassical approximation, where pairs of a quantum field $ϕ$ of mass $m$ and charge $e$ play the role of vacuum bubbles. We find that the adiabatic "in" vacuum associated with the flat chart develops a space-like expectation value for the current $J$ , which manifestly breaks the de Sitter invariance of the background fields. We derive a simple expression for $J (E)$ , showing that both "upward" and "downward" tunneling contribute to the build-up of the current. For heavy fields, with $m^{2} ≫ e E, H^{2}$ , the current is exponentially suppressed, in agreement with the results of semiclassical instanton methods. Here $H$ is the inverse de Sitter radius. On the other hand, light fields with $m ≪ H$ lead to a phenomenon of infrared hyperconductivity, where a very small electric field $m H ≲ e E ≪ H^{2}$ leads to a very large current $J \sim H^{3} / E$ . We also show that all Hadamard states for $ϕ$ necessarily break de Sitter invariance. Finally, we comment on the role of initial conditions, and "persistence of memory" effects.

34 pages, 2 figures. Comment and references added

Schwinger effect in de Sitter space

Abstract

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