Real or Imaginary? (On pair creation in de Sitter space)

TL;DR

This paper resolves a controversy about imaginary contributions to the one-loop scalar effective action in de Sitter space by advocating a path-integral–based in-out propagator that obeys the composition principle. It demonstrates that the Bunch-Davies propagator alone yields no imaginary part, while a Polyakov-type propagator derived from the path integral produces a finite ${S_{eff}}$ imaginary part, corresponding to vacuum decay at the Gibbons–Hawking rate with particle production ${S_{eff}}$ imaginary part ∝ $e^{-2π m}$ for $m^2 ound{≫} H^2$. The work clarifies how to obtain the correct propagator via analytic continuation from EAdS rather than the sphere, computes the relevant heat-kernel path integral, and links the dS result to its EAdS counterpart. Overall, it provides a consistent framework for in-out amplitudes and vacuum instability in curved backgrounds, with implications for quantum fields in cosmological spaces.

Abstract

Using properly defined Feynman propagator we obtain non--zero imaginary contribution to the scalar field effective action in even dimensional de Sitter space. Such a propagator follows from the path integral in de Sitter space and obeys composition principle proposed in arXiv:0709.2899. The obtained expression for the effective action shows particle production with the Gibbons--Hawking rate.