The asymptotic safety approach to quantum gravity offers a nonperturbative renormalization framework for constructing a consistent, predictive quantum field theory of gravity and spacetime geometry. It is based on a nontrivial fixed point of the renormalization group (RG) flow: the running coupling constants approach this fixed point in the ultraviolet (UV) limit, preventing divergences in physical observables. It also has predictive power: only a subset of initial coupling configurations at some RG scale flow into the fixed point as the scale increases, so if certain couplings are measured experimentally, asymptotic safety can fix the remaining ones to ensure the UV fixed point is reached. If realized in nature, asymptotic safety would have far-reaching consequences wherever quantum gravitational effects matter, but exploration of these implications—so far including phenomenological studies in particle physics, astrophysics, and cosmology—remains in its infancy. Asymptotic safety and the parameters of the Standard Model

The mass of the Higgs boson
The Standard Model in combination with asymptotic safety might be valid up to arbitrarily high energies. Based on this assumption, 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 one sign, the Higgs mass is restricted to a narrow window. If, on the other hand, the other sign holds—which is the favored possibility—the Higgs mass must take a specific value with an uncertainty of only a few GeV. In this spirit one can consider a prediction of asymptotic safety. The result is in surprisingly good agreement with the experimental data measured at CERN in 2013 by the ATLAS and CMS collaborations, which determined a value consistent with the prediction.

The fine-structure constant
By taking into account the gravitational correction to the running of the fine-structure constant in quantum electrodynamics, Harst and Reuter studied the impact of asymptotic safety on the infrared (renormalized) value of the constant. They found two fixed points suitable for the asymptotic safety construction, both of which imply a well-behaved UV limit without a Landau-pole-type singularity. The first fixed point is characterized by a vanishing gauge coupling, in which case the infrared value is a free parameter. In the second case, however, the fixed-point value is non-zero, and its infrared value is a computable prediction of the theory. In a more recent study, Christiansen and Eichhorn showed that quantum fluctuations of gravity generically generate self-interactions for gauge theories, which must be included in a discussion of a potential ultraviolet completion. Depending on the gravitational and gauge parameters, they conclude that the fine-structure constant might be asymptotically free and not run into a Landau pole, while the induced coupling for the gauge self-interaction is irrelevant and thus its value can be predicted. This is an explicit example where asymptotic safety solves a problem of the Standard Model—the triviality of the U(1) sector—without introducing new free parameters.

Phenomenological consequences of asymptotic safety can also be expected in astrophysics and cosmology. Bonanno and Reuter investigated the horizon structure of "renormalization group improved" black holes and computed quantum gravity corrections to the Hawking temperature and the corresponding thermodynamic entropy. Using an RG improvement of the Einstein–Hilbert action, Reuter and Weyer obtained a modified form of the Einstein equations that alters the Newtonian limit, potentially explaining flat galaxy rotation curves without postulating dark matter. In cosmology, Bonanno and Reuter argued that asymptotic safety changes the very early Universe, possibly resolving the horizon and flatness problems of standard cosmology. Moreover, asymptotic safety could drive inflation without an inflaton field, with the cosmological constant providing the driving term. The scale invariance associated with the non-Gaussian fixed point underlying asymptotic safety may account for the near scale invariance of primordial density perturbations. Using different methods, Weinberg further analyzed asymptotically safe inflation.