RG Analysis for Quantum Gravity with A Single Dimensionless Coupling

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.

18 pages, 2 figures, added many sentences and paragraphs to explain the model more in detail, and corrected an error in the text

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Cited by in corpus (5)

• Two-Loop Quantum Gravity Corrections to Cosmological Constant in Landau Gauge
• Diffeomorphism Invariance Demands Conformal Anomalies
• Localized massive excitation of quantum gravity as a dark particle
• Physical Cosmological Constant in Asymptotically Background Free Quantum Gravity
• Quantum Gravity Effective Action Provides Entropy of The Universe