Asymptotically nonlocal gravity

Abstract

Asymptotically nonlocal field theories interpolate between Lee-Wick theories with multiple propagator poles, and ghost-free nonlocal theories. Previous work on asymp- totically nonlocal scalar, Abelian, and non-Abelian gauge theories has demonstrated the existence of an emergent regulator scale that is hierarchically smaller than the lightest Lee-Wick partner, in a limit where the Lee-Wick spectrum becomes dense and decoupled. We generalize this construction to linearized gravity, and demonstrate the emergent regula- tor scale in three examples: by studying the resolution of the singularity (i) at the origin in the classical solution for the metric of a point particle, and (ii) in the nonrelativistic gravitational potential computed via a one-graviton exchange amplitude; (iii) we also show how this derived scale regulates the one-loop graviton contribution to the self energy of a real scalar field. We comment briefly on the generalization of our approach to the full, nonlinear theory of gravity.

Suppression of spacetime singularities in quantum gravity

“…Actions of the form (30) are moreover of relevance for the form-factor program in asymptotically safe quantum gravity [90][91][92]. As infinite-derivative expansions they appear in non-local ghostfree gravity [93][94][95][96][97][98], asymptotically non-local gravity [99] and as effective actions in loop quantum gravity [100,101]. The analysis of this paper suggests that actions of the form (30) are incompatible with a dynamical singularity-suppression principle, unless an equivalence to an action of infinite order in the curvature can be established.…”