Causality, unitarity and stability in quantum gravity: a non-perturbative perspective

TL;DR

This paper establishes criteria for the graviton propagator in quantum gravity to ensure unitarity, causality, and stability within a non-perturbative framework, addressing key open questions about its properties.

Contribution

It provides a detailed analysis of conditions for the graviton propagator's momentum dependence that ensure physical consistency in a non-perturbative quantum gravity setting.

Findings

Derived criteria for non-local graviton propagators

Identified conditions avoiding tachyonic and vacuum instabilities

Presented examples satisfying unitarity and causality

Abstract

Resumming quantum fluctuations at the level of the gravitational path integral is expected to result in non-local effective actions and thus in a non-trivial momentum dependence of the propagator. Which properties the (dressed) graviton propagator has to satisfy and whether they can all be met are key open questions. In this work we present criteria and conditions for the momentum dependence of a graviton propagator which is consistent with unitarity, causality, and stability in a non-perturbative setting. To this end, we revisit several aspects of these conditions, highlighting some caveats and subtleties that got lost in recent discussions, and spelling out others that to our best knowledge have not been studied in detail. We discuss the consequences of these concepts for the properties of the graviton propagator. Finally, we provide examples of propagators satisfying unitarity and causality, while avoiding tachyonic and vacuum instabilities, and allowing for an analytic Wick rotation.