Covariant Effective Action for Scalar-Tensor Theories of Gravity

TL;DR

This paper develops a covariant method to compute one-loop effective actions in scalar-tensor gravity theories, introducing new terms and extending previous results with a focus on field-space geometry.

Contribution

It introduces a covariant calculation framework for one-loop effective actions in scalar-tensor theories, incorporating Vilkovisky's field-space metric and extending past approaches.

Findings

Derived new terms in one-loop corrections absent in previous literature.

Calculated covariant versions of earlier results using Barvinsky and Vilkovisky's extension.

Compared gravitational corrections in a dilaton-extended Starobinsky model with known results.

Abstract

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 prescription 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 extension 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.