Complex effective actions and gravitational pair creation

TL;DR

This paper analyzes the imaginary part of the gravitational one-loop effective action for a massless scalar field with nonminimal coupling, focusing on perturbative and nonperturbative viewpoints. It derives the imaginary part using a metric-perturbation expansion up to second order in the graviton field, showing that Im $W$ is encoded in curvature-squared structures and can be written in the Weyl-form $C^{(2)}_{\mu\nu\alpha\beta}C^{(2)\mu\nu\alpha\beta}$, with local $R^2$ contributions appearing in FLRW backgrounds where the Weyl tensor vanishes. The heat-kernel (Barvinsky–Vilkovisky) approach yields a nonlocal form-factor representation of $W$ that reproduces the same Im $W$ to $O(R^2)$, but clarifies the role of nonlocal terms and the dependence on spacetime geometry (static vs. FLRW). A central tension is the discrepancy with Wondrak et al., who obtain a Euclidean, locally computed imaginary part that differs by a factor of two, which the authors attribute to the omission of Lorentzian constraints and nonlocal contributions, underscoring the importance of staying in Lorentzian signature for gravitational pair creation analyses and highlighting caveats in the massless limit and time-dependent backgrounds.

Abstract

We use different methods to calculate the imaginary part of the gravitational effective action due to a massless scalar field, with a view on perturbative vs. non-pertubative and the results of ArXiv:2305.18521.