Schwinger effect in de Sitter space

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 phi 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)>> eE,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 mH less than or similar to eE << H-2 leads to a very large current J similar to H-3/E. We also show that all Hadamard states for phi necessarily break de Sitter invariance. Finally, we comment on the role of initial conditions, and "persistence of memory" effects.