Gauge and parametrization ambiguity in quantum gravity

The gauge and parametrization dependence is discussed in quantum gravity in an arbitrary dimension $D$. Explicit one-loop calculations are performed within the most general parametrization of quantum metric with seven arbitrary parameters. On the other hand, some of the gauge fixing parameters are fixed to make the calculations relatively simple. We confirm the general theorem stating that the on-shell local terms in the one-loop effective action are independent on the gauge and parametrization ambiguity.