Probing the Vacuum Structure of Spacetime

TL;DR

This paper investigates how a massive scalar field interacts with background gravitons to probe the vacuum structure of spacetime, deriving an effective action that reveals vacuum instability and particle production in curved backgrounds.

Contribution

It introduces a nonperturbative effective action for a scalar field in curved spacetime using $b3$-regularization, extending analogies from quantum electrodynamics to gravity.

Findings

The effective action indicates vacuum instability due to particle production.

The scalar field's vacuum state becomes unstable, with a decay rate derived from the imaginary part of the effective action.

The in- and out-vacua are unitarily inequivalent, showing nontrivial vacuum structure.

Abstract

We explore the question of how to probe the vacuum structure of space time by a massive scalar field through interaction with background gravitons. Using the $\Gamma$-regularization for the in-/out-state formalism, we find the effective action of a scalar field in a conformally, asymptotically flat spacetime and a four-dimensional de Sitter space, which is a gravitational analog of the Heisenberg-Euler and Schwinger effective action for a charged scalar in a constant electric field. The effective action is nonperturbative in that it sums all one-loop diagrams with arbitrary number of external lines of gravitons. The massive scalar field becomes unstable due to particle production, the effective action has an imaginary part that determines the decay rate of the vacuum, and the out-vacuum is unitarily inequivalent to the in-vacuum.