Scales and hierachies in asymptotically safe quantum gravity: a review

Abstract: The asymptotic safety program strives for a consistent description of gravity as a non-perturbatively renormalizable quantum field theory. In this framework the gravitational interactions are encoded in a renormalization group flow connecting the quantum gravity regime at trans-Planckian scales to observable low-energy physics. Our proceedings reviews the key elements underlying the predictive power of the construction and summarizes the state-of-the-art in determining its free parameters. The explicit construction of a realistic renormalization group trajectory describing our world shows that the flow dynamically generates two scales: the Planck scale where Newton's coupling becomes constant and a terrestrial scale where the cosmological constant freezes out. We also review the perspectives of determining the free parameters of the theory through cosmological observations.