Inroads into Ghost-free Euclidean and Lorentzian Quantum Gravity

Abstract

Higher-curvature gravity can offer UV completions of GR, but generically suffers from 4th-order propagating degrees of freedom often spoiling unitarity, e.g. Stelle gravity. Recently it was noticed that “Einsteinian gravities” allow for higher curvature interactions match Einstein’s spectrum at the linearised level, avoiding the dangerous 4th-order propagating degrees of freedom. We investigate the renormalisation group flow of Einstein cubic gravity couplings and identify the entire phase diagram of the theory, showing that Einstein cubic gravity remains ghost-free in the quantum regime. To tackle questions of unitarity and causality directly, we make a Lorentzian computation of the asymptotically safe graviton propagators of the transverse-traceless and scalar mode. We showed that beyond the requirement of using a causality-preserving regulator, such as Callan-Symanzik, setting up differential equations for coupled spectral functions must satisfy additional constraints related to diffeomorphism and BRST symmetry. We found three avenues to solve the coupled system of running Kallen-Lehmann spectral representations, leading to 1-loop exact spectral functions which are compatible with causality and unitarity. Furthermore, they provide the first direct asymptotically safe predictions to the full quantum propagators, the corresponding Weyl-tensor and Ricci-scalar form factors in the quantum effective action.