One-loop renormalization of a gravity-scalar system

TL;DR

This paper performs a systematic one-loop renormalization of a gravity-scalar system using a foliation-based scheme, revealing how the graviton propagator gains a mass term and affecting fundamental constants.

Contribution

It introduces a novel foliation-based quantization method for renormalizing gravity-matter systems and explicitly demonstrates renormalization of a gravity-scalar system with a Higgs potential.

Findings

Renormalization achieved via metric field redefinition.

Graviton propagator acquires a mass term.

One-loop calculations modify cosmological and Newton's constants.

Abstract

Extending the renormalizability proposal of the physical sector of 4D Einstein gravity, we have recently proposed renormalizability of the 3D physical sector of gravity-matter systems. The main goal of the present work is to conduct systematic one-loop renormalization of a gravity-matter system by applying our foliation-based quantization scheme. In this work we explicitly carry out renormalization of a gravity-scalar system with a Higgs-type potential. With the fluctuation part of the scalar field gauged away, the system becomes renormalizable through a metric field redefinition. We use dimensional regularization throughout. One of the salient aspects of our analysis is how the graviton propagator acquires the"mass" term. One-loop calculations lead to renormalization of the cosmological and Newton's constants. We discuss other implications of our results as well: time-varying vacuum energy density and masses of the elementary particles as well as the potential relevance of Neumann boundary condition for black hole information.