Covariant effective action for scalar-tensor theories of gravity

We develop the calculation of the divergent part of one-loop covariant effective action for scalar fields minimally and non-minimally coupled to gravity using the generalized Schwinger-DeWitt technique. We derive the field-space metric using Vilkovisky's prescrip-tion and obtain new terms in the one-loop corrections which are absent in past literature with trivial choices of field-space metric. We further calculate the covariant versions of past results, obtained using the standard approach, by applying Barvinsky and Vilkovisky's exten-sion to the ordinary Schwinger-DeWitt approach. For completeness, we study the one-loop gravitational corrections for a dilaton-extended two-field Starobinsky model and compare with known results.

Automated summary

In this work, the calculation of the divergent part of one-loop covariant effective action for scalar fields coupled to gravity was developed using the generalized Schwinger-DeWitt technique. New terms in the one-loop corrections were derived and compared with past literature. Additionally, the covariant versions of past results were obtained by extending the ordinary Schwinger-DeWitt approach with Barvinsky and Vilkovisky's method. The one-loop gravitational corrections for a dilaton-extended two-field Starobinsky model were also studied and compared with existing results.