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It is known that Vilkovisky-DeWitt's effective action is gauge invariantoff-shell and independent of quantum field parametrization. In this work, weperform the calculation of the divergences in two-loop Vilkovisky-DeWitt'seffective action for the theory of a massive scalar field minimally coupled togravity. We quantize both gravity and scalar field around a flat Minkowskimetric and a constant scalar field background. The quantum corrections arecomputed up to second order in the background scalar field for the purpose ofmass renormalization.

Two-loop Vilkovisky-DeWitt effective action for scalar field minimally coupled with gravity