Finite quantum gravity in dS and AdS spacetimes

TL;DR

This paper investigates a broad class of weakly nonlocal quantum gravity theories in (A)dS spacetimes, showing they share the same perturbative spectrum as Einstein's gravity and can be superrenormalizable or finite.

Contribution

It demonstrates that these nonlocal theories have the same graviton spectrum as Einstein-Hilbert gravity and are classically equivalent to it via metric redefinition, with improved quantum properties.

Findings

The kinetic operator matches Einstein-Hilbert theory on (A)dS backgrounds.

The theories are superrenormalizable or finite with suitable higher-curvature terms.

Classical equivalence to Einstein-Hilbert gravity via metric redefinition is established.

Abstract

We hereby study the properties of a large class of weakly nonlocal gravitational theories around the (anti-) de Sitter spacetime background. In particular, we explicitly prove that the kinetic operator for the graviton field has the same structure as the one in Einstein-Hilbert theory around any maximally symmetric spacetime. Therefore, the perturbative spectrum is the same of standard general relativity, while the propagator on any maximally symmetric spacetime is a mere generalization of the one from Einstein's gravity derived and extensively studied in several previous papers. At quantum level the range of theories here presented is superrenormalizable or finite when proper (non affecting the propagator) terms cubic or higher in curvatures are added. Finally, it is proven that for a large class of nonlocal theories, which in their actions do involve neither the Weyl nor the Riemann tensor, the theory is classically equivalent to the Einstein-Hilbert one with cosmological constant by means of a metric field redefinition at any perturbative order.