On the cutoff identification and the quantum improvement in asymptotically safe gravity

Applying the exact renormalization group method to search the nonGaussian fixed points of gravitational coupling, is frequently followed by two steps: cutoff identification and improvement. Although there are various models for identifying the cutoff momentum by some physical length, saving the general covariance should be considered as an important property in the procedure. In this paper, use of an arbitrary function of curvature invariants for cutoff identification is suggested. It is shown that the field equations for this approach differs from the ones obtained from the conventional cutoff identification and improvement, even for nonvacuum solutions of the improved Einstein equations. Indeed, it is concluded that these two steps are correlated to each other.