Quantum scalar field in FRW Universe with constant electromagnetic background

TL;DR

This paper develops explicit proper-time representations for scalar Green functions in a FRW universe with a constant electromagnetic field, analyzing particle creation, vacuum instability, and back reaction effects.

Contribution

It provides the first explicit construction of proper-time Green functions in this setting and explores their implications for vacuum stability and particle production.

Findings

Explicit proper-time Green functions are derived.

Vacuum instability and particle creation are quantified.

Back reaction effects are estimated in different regimes.

Abstract

We discuss massive scalar field with conformal coupling in Friedmann-Robertson-Walker (FRW) Universe of special type with constant electromagnetic field. Treating an external gravitational-electromagnetic background exactly, at first time the proper-time representations for out-in, in-in, and out-out scalar Green functions are explicitly constructed as proper-time integrals over the corresponding (complex) contours. The vacuum-to-vacuum transition amplitudes and number of created particles are found and vacuum instability is discussed. The mean values of the current and energy-momentum tensor are evaluated, and different approximations for them are investigated. The back reaction of the particles created to the electromagnetic field is estimated in different regimes. The connection between proper-time method and effective action is outlined. The effective action in scalar QED in weakly-curved FRW Universe (De Sitter space) with weak constant electromagnetic field is found as derivative expansion over curvature and electromagnetic field strength. Possible further applications of the results are briefly mentioned.