Functional renormalization group approach and gauge dependence in gravity theories

We investigate the gauge symmetry and gauge-fixing dependence properties of the effective average action for quantum gravity models of general form. Using the background field formalism and the standard Becchi-Rouet-Stora-Tyutin (BRST)-based arguments, one can establish the special class of regulator functions that preserves the background field symmetry of the effective average action. Unfortunately, regardless if the gauge symmetry is preserved at the quantum level, the noninvariance of the regulator action under the global BRST transformations leads to the gauge-fixing dependence even under the use of the on-shell conditions.