A proper fixed functional for four-dimensional Quantum Einstein Gravity

Abstract

Realizing a quantum theory for gravity based on Asymptotic Safety hinges on the existence of a non-Gaussian fixed point of the theory's renormalization group flow. In this work, we use the functional renormalization group equation for the effective average action to study the fixed point underlying Quantum Einstein Gravity at the functional level including an infinite number of scale-dependent coupling constants. We formulate a list of guiding principles underlying the construction of a partial differential equation encoding the scale-dependence of $f(R)$-gravity. We show that this equation admits a unique, globally well-defined fixed functional describing the non-Gaussian fixed point at the level of functions of the scalar curvature. This solution is constructed explicitly via a numerical double-shooting method. In the UV, this solution is in good agreement with results from polynomial expansions including a finite number of coupling constants, while it scales proportional to $R^2$, dressed up with non-analytic terms, in the IR. We demonstrate that its structure is mainly governed by the conformal sector of the flow equation. The relation of our work to previous, partial constructions of similar scaling solutions is discussed.

35 pages, 11 figures

References in corpus (18)

• Exact evolution equation for the effective potential
• Nonperturbative Quantum Gravity
• Asymptotic safety in higher-derivative gravity
• Ultraviolet properties of f(R)-Gravity
• Asymptotically Safe Lorentzian Gravity
• Taming perturbative divergences in asymptotically safe gravity
• Bimetric Renormalization Group Flows in Quantum Einstein Gravity
• Asymptotic safety in the f(R) approximation
• Search of scaling solutions in scalar-tensor gravity
• The Renormalization Group flow of unimodular f(R) gravity
• En route to Background Independence: Broken split-symmetry, and how to restore it with bi-metric average actions
• Matter Induced Bimetric Actions for Gravity
• Fixed-Functionals of three-dimensional Quantum Einstein Gravity
• Background independent exact renormalization group for conformally reduced gravity
• Asymptotic freedom in Horava-Lifshitz gravity
• Perturbative quantum gravity with the Immirzi parameter
• Towards a $C$-function in 4D quantum gravity
• A new functional flow equation for Einstein-Cartan quantum gravity

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