Role of Regularization in Quantum Corrections to the Scalar-Tensor Theories of Gravity

TL;DR

This paper investigates how regularization affects quantum corrections in scalar-tensor gravity theories, showing that the weak equivalence principle remains valid in Brans-Dicke theory but can be violated in scale-invariant models, implying potential fifth-force effects.

Contribution

It demonstrates the importance of regularization in quantum corrections and clarifies the validity of the weak equivalence principle in different scalar-tensor theories.

Findings

WEP is robust in Brans-Dicke theory beyond classical level

Regularization is crucial for quantum corrections in gravity

Scale-invariant theories may violate WEP, suggesting fifth-force phenomena

Abstract

We show that regularizing divergent integrals is crucially important when applied to the loop diagrams corresponding to quantum corrections to the coupling of the ``gravitational" scalar field due to the interaction among matter fields. We use the method of continuous spacetime dimensions to demonstrate that WEP is a robust property of the Brans-Dicke theory beyond the classical level, hence correcting our previous assertion of the contrary. The same technique can be used to yield the violation of WEP when applied to the scale-invariant theory, thus providing another reason for expecting fifth- force-type phenomena.