Quantum gravitational corrections from the Wheeler-DeWitt equation for scalar-tensor theories

TL;DR

This paper derives quantum gravitational corrections in scalar-tensor theories using the Wheeler-DeWitt equation, highlighting the impact of non-minimal coupling and the transformation to the Einstein frame, with implications for Higgs inflation.

Contribution

It introduces a method to compute quantum gravitational corrections in scalar-tensor theories accounting for non-minimal coupling effects.

Findings

Large non-minimal coupling significantly affects quantum correction terms.

Transformation to Einstein frame is crucial for applying the expansion scheme.

Quantum corrections could influence models like Higgs inflation.

Abstract

We perform the canonical quantization of a general scalar-tensor theory and derive the first quantum gravitational corrections following from a semi-classical expansion of the Wheeler-DeWitt equation. The non-minimal coupling of the scalar field to gravity induces a derivative coupling between the scalar field and the gravitational degrees of freedom, which prevents a direct application of the expansion scheme. We address this technical difficulty by transforming the theory from the Jordan frame to the Einstein frame. We find that a large non-minimal coupling can have strong effects on the quantum gravitational correction terms. We briefly discuss these effects in the context of the specific model of Higgs inflation.