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

Abstract: It is known that Vilkovisky-DeWitt's effective action is gauge invariant off-shell and independent of quantum field parametrization. In this work, we perform the calculation of the divergences in two-loop Vilkovisky-DeWitt's effective action for the theory of a massive scalar field minimally coupled to gravity. We quantize both gravity and scalar field around a flat Minkowski metric and a constant scalar field background. The quantum corrections are computed up to second order in the background scalar field for the purpose of mass renormalization.