Renormalization equations in gravitational theory with higher derivatives

The structure of renormalization equations in gravitational theories with higher derivatives is considered. The gauge dependence of invariant divergences of the effective action is found to be nontrivial. The external source technique is used to construct a consistent Green's function renormalization. One- and two-loop divergences of the effective action are explicitly calculated for an arbitrary parametrization and gauge. These calculations fit the general structure of the obtained renormalization equations. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 121, No. 3, pp. 387–411, December, 1999.