Physics applications of asymptotically safe gravity

The asymptotic safety approach to quantum gravity provides a nonperturbative notion of renormalization in order to find a consistent and predictive quantum field theory of the gravitational interaction and spacetime geometry. It is based upon a nontrivial fixed point of the corresponding renormalization group (RG) flow such that the running coupling constants approach this fixed point in the ultraviolet (UV) limit. This suffices to avoid divergences in physical observables. Moreover, it has predictive power: Generically an arbitrary starting configuration of coupling constants given at some RG scale does not run into the fixed point for increasing scale, but a subset of configurations might have the desired UV properties. For this reason it is possible that — assuming a particular set of couplings has been measured in an experiment — the requirement of asymptotic safety fixes all remaining couplings in such a way that the UV fixed point is approached. Asymptotic safety, if realized in Nature, has far reaching consequences in all areas where quantum effects of gravity are to be expected. Their exploration, however, is still in its infancy. By now there are some phenomenological studies concerning the implications of asymptotic safety in particle physics, astrophysics and cosmology, for instance. The Standard Model in combination with asymptotic safety might be valid up to arbitrarily high energies. Based on the assumption that this is indeed correct it is possible to make a statement about the Higgs boson mass. The first concrete results were obtained by Shaposhnikov and Wetterich in 2010. Depending on the sign of the gravity induced anomalous dimension there are two possibilities: For the Higgs mass is restricted to the window . If, on the other hand, which is the favored possibility, must take the value with an uncertainty of a few GeV only. In this spirit one can consider a prediction of asymptotic safety. The result is in surprisingly good agreement with the latest experimental data measured at CERN in 2013 by the ATLAS and CMS collaborations, where a value of has been determined.