On avoiding Ostrogradski instabilities within Asymptotic Safety

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 keep track of the higher-derivative terms. Thus our asymptotically safe gravity-matter systems are not haunted by Ostrogradski ghosts.

Form factors in asymptotic safety: conceptual ideas and computational toolbox

“…This indicates that our analysis provides the first study of the gravity-matter fixed point identified in [12,31,83,100] at the level of self-consistent form factors. Comparing the critical exponents (112) and (113) furthermore suggests that the properties of the fixed point are essentially determined by the gravitational contributions [100].…”

“…reference η s * ∆ [12] −0.361 - [100] 0 - [31] −0.771this work −0.176 1.051 of the differential operators leads to surface terms in Γ k . Thus G k=0 and Λ k=0 are numbers which are independent of the external momenta in a scattering process.…”

Hamiltonian formulation of a class of constrained fourth-order differential equations in the Ostrogradsky framework

“…In the context of gravity, higher derivative theories have been studied as modified theories in their own right or as the expected result of renormalization. Under certain conditions, instabilities associated with higher derivative terms can be avoided in renormalization group flows to a nontrivial fixed point [4]. Instabilities can alternatively be avoided by constraints [5] or complexification [6], where the physical relevance of complex theories is not yet clear.…”

f(R,Rμν2) at one loop

“…The main issue with this theory is the presence of ghosts in the perturbative spectrum. Over time, several ways out have been suggested [18][19][20][21], and more recently [22][23][24][25][26][27][28], but this point remains unsettled, for the time being.…”