Renormalization Group Running of Newton's G: The Static Isotropic Case

Abstract

Corrections are computed to the classical static isotropic solution of general relativity, arising from non-perturbative quantum gravity effects. A slow rise of the effective gravitational coupling with distance is shown to involve a genuinely non-perturbative scale, closely connected with the gravitational vacuum condensate, and thereby, it is argued, related to the observed effective cosmological constant. Several analogies between the proposed vacuum condensate picture of quantum gravitation, and non-perturbative aspects of vacuum condensation in strongly coupled non-abelian gauge theories are developed. In contrast to phenomenological approaches, the underlying functional integral formulation of the theory severely constrains possible scenarios for the renormalization group evolution of couplings. The expected running of Newton's constant $G$ is compared to known vacuum polarization induced effects in QED and QCD. The general analysis is then extended to a set of covariant non-local effective field equations, intended to incorporate the full scale dependence of $G$, and examined in the case of the static isotropic metric. The existence of vacuum solutions to the effective field equations in general severely restricts the possible values of the scaling exponent $\nu$.

arXiv comment61 pages, 3 figures

References in corpus (17)

• Is Cosmic Speed-Up Due to New Gravitational Physics?
• Scalar-Tensor-Vector Gravity Theory
• Palatini form of 1/R gravity
• Scaling Exponents in Quantum Gravity near Two Dimensions
• Ultraviolet Stable Fixed Point and Scaling Relations in 2+$\epsilon$ Dimensional Quantum Gravity
• Gravitational Theory, Galaxy Rotation Curves and Cosmology without Dark Matter
• Nonlocal Effective Gravitational Field Equations and the Running of Newton's G
• Newtonian Potential in Quantum Regge Gravity
• On the Measure in Simplicial Gravity
• On the Gravitational Scaling Dimensions
• Two-loop Prediction for Scaling Exponents in (2 + ε)-dimensional Quantum Gravity
• Non-Perturbative Gravity and the Spin of the Lattice Graviton
• A new determination of the QED coupling alpha(M_Z^2) lets the Higgs off the hook
• Invariant Correlations in Simplicial Gravity
• Quantum Gravity in Large Dimensions
• Scaling Behavior of Ricci Curvature at Short Distance near Two Dimensions
• Nonlocal Effective Field Equations for Quantum Cosmology

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• Scale-Dependent Newton's Constant G in the Conformal Newtonian Gauge
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• From maximum force to the field equations of general relativity -- and implications
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