RG Analysis for Quantum Gravity with A Single Dimensionless Coupling

TL;DR

This paper investigates quantum conformal gravity with a single dimensionless coupling, analyzing its renormalization group behavior, conformal symmetry, and implications for cosmology, including inflation and CMB.

Contribution

It introduces a systematic method to incorporate the Euler term dynamics into quantum conformal gravity using RG analysis and confirms the approach through three-loop anomalous dimension calculations.

Findings

Three-loop anomalous dimension matches the exact BRST conformal symmetry result.

The Euler term induces Riegert conformal-factor dynamics quantum mechanically.

Implications for inflation and cosmic microwave background are discussed.

Abstract

We study the quantum conformal gravity whose dynamics is governed by a single dimensionless gravitational coupling with negative beta function. Since the Euler term is not dynamical classically, the constant in front of it is not an independent coupling. Quantum mechanically, however, it induces the Riegert conformal-factor dynamics with BRST conformal symmetry representing background free nature. In this paper, we propose how to handle the Euler term systematically incorporating such dynamics on the basis of renormalization group analysis using dimensional regularization. As a non-trivial test of renormalization, we explicitly calculate the three-loop anomalous dimension of the cosmological constant operator and show that it agrees with the exact expression derived using the BRST conformal symmetry. The physical significance to inflation and CMB is also discussed.