Gauge and parametrization dependence of Quantum Einstein Gravity within the Proper Time flow

Proper time functional flow equations have garnered significant attention in recent years, as they are particularly suitable in analyzing non-perturbative contexts. By resorting to this flow, we investigate the regulator and gauge dependence in quantum Einstein gravity within the asymptotic safety framework, considering various regularization schemes. Our findings indicate that some details of the regulator have minor influence on the critical properties of the theory. In contrast, the selection between linear and exponential parametrizations appears to have a more substantial impact on the scaling behavior of the renormalized flow near the non-Gaussian fixed point.