Effective Action and Gravitational Pair Production in (A)dS Spacetime

TL;DR

This paper calculates the effective action for a scalar field in (A)dS spacetime, revealing a non-trivial imaginary part in even-dimensional de Sitter space that relates to gravitational pair production, and compares different computational methods.

Contribution

It demonstrates the non-perturbative imaginary part of the effective action in (A)dS spacetime and highlights limitations of perturbative approaches in capturing this effect.

Findings

Effective action has a non-trivial imaginary part in even-dimensional dS.

Euclidean heat kernel and Lorentzian Green's function methods agree.

Perturbation theory nearly fails to capture the imaginary part.

Abstract

We compute the effective action for a massive scalar field in (A)dS spacetime using the Euclidean heat kernel method. We highlight that in even-dimensional dS spacetimes, the effective action exhibits a non-trivial imaginary part, reminiscent of the Schwinger effect in quantum electrodynamics. We find consistency between the results obtained from the Euclidean heat kernel method with those from the Green's function approach in Lorentzian signature. Additionally, we compare our results with the perturbative calculations and find that the perturbation theory almost fails to capture the correct non-perturbative imaginary part of the effective action. This discrepancy presents a challenge to computing the gravitational pair production using the perturbation theory.