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D. Benedetti and F. Caravelli, “The Local potential approximation in quantum gravity,” JHEP 1206
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J. A. Dietz and T. R. Morris, “Background independent exact renormalization group for conformally reduced gravity,” JHEP 1504
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K. Falls, D. F. Litim, K. Nikolakopoulos and C. Rahmede, “Further evidence for asymptotic safety of quantum gravity,” Phys. Rev. D 93
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2017

Background Scale Independence in Quantum Gravity

Ohta, Nobuyoshi

Understand

We study the background scale independence in single-metric approximation to the functional renormalization group equation (FRGE) for quantum gravity and show that it is possible to formulate it without using higher-derivative gauge fixing in arbitrary dimensions if we adopt the Landau gauge and suitable cutoff scheme.

We discuss this problem for both the linear and exponential splits of the metric into background and fluctuations.
The obtained modified Ward identity for the global rescalings of the background metric can be combined with the FRGE to give a manifestly scale-invariant solution.
An explicit example of the FRGE is given for four-dimensional $f(R)$ gravity in this framework.