Abstract
In this contribution, we discuss the asymptotic safety scenario for quantum gravity with a functional renormalization group approach that disentangles dynamical metric fluctuations from the background metric. We review the state of the art in pure gravity and general gravity–matter systems. This includes the discussion of results on the existence and properties of the asymptotically safe ultraviolet fixed point, full ultraviolet-infrared trajectories with classical gravity in the infrared, and the curvature dependence of couplings also in gravity–matter systems. The results in gravity–matter systems concern the ultraviolet stability of the fixed point and the dominance of gravity fluctuations in minimally coupled gravity–matter systems. Furthermore, we discuss important physics properties such as locality of the theory, diffeomorphism invariance, background independence, unitarity, and access to observables, as well as open challenges.
Highlights
One of the major challenges in theoretical physics is the unification of the standard model of particle physics (SM) with quantum gravity
We have reviewed the state of the art of the fluctuation approach to quantum gravity
This approach is based upon the computation of the correlation functions of the dynamical graviton fluctuation field hμ] within a systematic vertex expansion
Summary
One of the major challenges in theoretical physics is the unification of the standard model of particle physics (SM) with quantum gravity. The present review outlines the properties and results of the fRG approach to asymptotically safe quantum gravity in terms of background and fluctuation correlation functions of gravitons, shortly baptized the fluctuation approach to gravity. The fluctuation approach resolves these differences, and it has matured enough to host a large number of results: this includes investigations of the Reuter fixed point in pure gravity in a rather elaborate truncation within a vertex expansion with momentum-dependent two-, three-, and four-point functions; the computation of the background-effective action for backgrounds with constant curvature; investigations of the stability of general gravity–matter systems; investigation of convergence properties of the expansion (apparent convergence); and a potential close perturbativeness of the asymptotically safe UV regime (effective universality).
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