Essential Renormalization Group Equation for Gravity coupled to a Scalar field

TL;DR

This paper investigates the essential renormalization group equation for Einstein gravity coupled with a massive scalar field, revealing that nonrenormalizable terms can be eliminated and identifying a nontrivial fixed point for key couplings.

Contribution

It introduces an analysis of the essential RG equation in gravity-scalar systems, showing the impact of the cosmological constant on renormalizability and fixed points.

Findings

Nonrenormalizable terms can be eliminated by the cosmological constant.

A nontrivial fixed point exists for the Newton coupling.

Perturbation around curved spacetime differs from flat spacetime in renormalization behavior.

Abstract

We study the essential renormalization group equation, in which inessential couplings are removed via field redefinitions, for Einstein gravity coupled to a massive scalar field in the presence of a cosmological constant. Our results indicate that perturbatively nonrenormalizable terms can be eliminated due to the cosmological term, in contrast to the case of perturbation around flat spacetime. We find a nontrivial fixed point for the Newton coupling and the cosmological term.