Background Scale Independence in Quantum Gravity

TL;DR

This paper demonstrates that background scale independence in quantum gravity's functional renormalization group approach can be achieved without higher-derivative gauge fixing by using Landau gauge and specific cutoff schemes, ensuring scale-invariant solutions.

Contribution

It introduces a method to formulate background scale independence in quantum gravity without higher-derivative gauge fixing, applicable in arbitrary dimensions.

Findings

Achieves background scale independence using Landau gauge and suitable cutoff schemes.

Derives a modified Ward identity for background rescaling.

Provides an explicit example with four-dimensional f(R) gravity.

Abstract

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.