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.
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.
Asymptotic safety, if realized in Nature, has far reaching consequences in all areas where quantum effects of gravity are to be expected.
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 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
of quantum electrodynamics, Ulrich Harst and Martin Reuter were able to study the impacts of asymptotic safety on the infrared (renormalized) value of
[4] They found two fixed points suitable for the asymptotic safety construction both of which imply a well-behaved UV limit, without running into a Landau pole type singularity.
In a more recent study, Nicolai Christiansen and Astrid Eichhorn[5] showed that quantum fluctuations of gravity generically generate self-interactions for gauge theories, which have to 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.
Alfio 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 thermodynamical entropy.
[6] By means of an RG improvement of the Einstein–Hilbert action, Reuter and Holger Weyer obtained a modified version of the Einstein equations which in turn results in a modification of the Newtonian limit, providing a possible explanation for the observed flat galaxy rotation curves without having to postulate the presence of dark matter.
[8] Furthermore, asymptotic safety provides the possibility of inflation without the need of an inflaton field (while driven by the cosmological constant).