On avoiding Ostrogradski instabilities within Asymptotic Safety

TL;DR

This paper investigates the impact of higher-derivative terms in scalar matter coupled to gravity within the Asymptotic Safety framework, showing that Ostrogradski ghosts become infinitely massive and decouple, ensuring the theory's stability.

Contribution

It demonstrates that including higher-derivative scalar terms in the renormalization group flow leads to a fixed point where ghosts decouple, maintaining the consistency of asymptotically safe gravity-matter systems.

Findings

Ostrogradski ghosts acquire infinite mass and decouple.

Existence of a fixed point with stable propagators.

Trajectories match those without higher-derivative terms.

Abstract

We study the renormalization group flow of gravity coupled to scalar matter using functional renormalization group techniques. The novel feature is the inclusion of higher-derivative terms in the scalar propagator. Such terms give rise to Ostrogradski ghosts which signal an instability of the system and are therefore dangerous for the consistency of the theory. Since it is expected that such terms are generated dynamically by the renormalization group flow they provide a potential threat when constructing a theory of quantum gravity based on Asymptotic Safety. Our work then establishes the following picture: upon incorporating higher-derivative terms in the scalar propagator the flow of the gravity-matter system possesses a fixed point structure suitable for Asymptotic Safety. This structure includes an interacting renormalization group fixed point where the Ostrogradski ghosts acquire an infinite mass and decouple from the system. Tracing the flow towards the infrared it is found that there is a subset of complete renormalization group trajectories which lead to stable renormalized propagators. This subset is in one-to-one correspondence to the complete renormalization group trajectories obtained in computations which do not track of the higher-derivative terms. Thus our asymptotically safe gravity-matter systems are not haunted by Ostrogradski ghosts.