The phase diagram of quantum gravity from diffeomorphism-invariant   RG-flows
  We evaluate the phase diagram of quantum gravity within a fully diffeomorphism-invariant renormalisation group approach. The construction is based on the geometrical or Vilkovisky-DeWitt effective action. We also resolve the difference between the fluctuation metric and the background metric. This allows for fully background-independent flows in gravity. The results provide further evidence for the ultraviolet fixed point scenario in quantum gravity with quantitative changes for the fixed point physics. We also find a stable infrared fixed point related to classical Einstein gravity. Implications and possible extensions are discussed. 
Ivan Donkin and Jan M. Pawlowski
hep-th gr-qc