Gravity is infamously perturbatively non-renormalizable and non-predictive. The asymptotic safety scenario proposes that gravity is non-perturbatively renormalizable and predictive, thanks to an ultraviolet (UV) renormalization group (RG) fixed point.

Higher-curvature gravities can lead to UV completions of GR, but they generically suffer from 4th-order propagating degrees of freedom often spoiling unitarity (e.g. Stelle gravity). “Einsteinian gravities” allow for higher curvature interactions while matching Einstein’s spectrum at the linearised level. I will present the RG flow of Einsteinian cubic gravity, including the entire phase diagram of the theory, and show that Einstein cubic gravity is ghost-free in the quantum regime.
I will also discuss Lorentzian asymptotically safe graviton propagators of the transverse-traceless and scalar mode. The corresponding 1-loop exact Källén-Lehmann spectral representations are compatible with causality and unitarity. They provide direct access to the full quantum propagators, Weyl-tensor and Ricci-scalar form factors in the quantum effective action.

Based on a realisation of asymptotic safety to UV complete gravity, we predict that the couplings between ultralight scalar dark matter and photons or gluons vanish. This may provide a test for asymptotic safety, thanks to the recent progress in nuclear clocks, which are projected to increase the sensitivity to such couplings by several orders of magnitude.