Taming perturbative divergences in asymptotically safe gravity

Abstract

We use functional renormalization group methods to study gravity minimally coupled to a free scalar field. This setup provides the prototype of a gravitational theory which is perturbatively non-renormalizable at one-loop level, but may possess a non-trivial renormalization group fixed point controlling its UV behavior. We show that such a fixed point indeed exists within the truncations considered, lending strong support to the conjectured asymptotic safety of the theory. In particular, we demonstrate that the counterterms responsible for its perturbative non-renormalizability have no qualitative effect on this feature.

31 pages, revised and expanded version, 3 appendices added with full details, typos corrected

References in corpus (31)

• Exact evolution equation for the effective potential
• General relativity as an effective field theory: The leading quantum corrections
• Nonperturbative Evolution Equation for Quantum Gravity
• Optimised Renormalisation Group Flows
• Quantum Gravity in Everyday Life: General Relativity as an Effective Field Theory
• Investigating the Ultraviolet Properties of Gravity with a Wilsonian Renormalization Group Equation
• Spectral Dimension of the Universe
• Fixed points of quantum gravity
• Renormalization Group Flow of Quantum Gravity in the Einstein-Hilbert Truncation
• Ultraviolet Fixed Point and Generalized Flow Equation of Quantum Gravity
• Reconstructing the Universe
• Flow Equation of Quantum Einstein Gravity in a Higher-Derivative Truncation
• Non-Trivial Ultraviolet Fixed Point in Quantum Gravity
• Fixed Points of Higher Derivative Gravity
• Ultraviolet properties of f(R)-Gravity
• The Running Gravitational Couplings
• On the renormalization group flow of f(R)-gravity
• Asymptotic Safety of Gravity Coupled to Matter
• Is Quantum Einstein Gravity Nonperturbatively Renormalizable?
• Contraints on Matter from Asymptotic Safety
• The Nonperturbative Quantum de Sitter Universe
• The renormalization group for non-renormalizable theories: Einstein gravity with a scalar field
• Conformal Quantum Gravity with the Gauss-Bonnet Term
• Towards Nonperturbative Renormalizability of Quantum Einstein Gravity
• Conformal sector of Quantum Einstein Gravity in the local potential approximation: non-Gaussian fixed point and a phase of unbroken diffeomorphism invariance
• Dimensionally reduced gravity theories are asymptotically safe
• Renormalisation group flows for gauge theories in axial gauges
• Bare Action and Regularized Functional Integral of Asymptotically Safe Quantum Gravity
• Renormalization and asymptotic safety in truncated quantum Einstein gravity
• Exact Renormalization Group for O(4) Gauged Supergravity
• Effective average action and nonperturbative renormalization group equation in higher derivative quantum gravity

Cited by in corpus (127)

• The nonperturbative functional renormalization group and its applications
• Quantum Einstein Gravity
• On the renormalization group flow of f(R)-gravity
• Further evidence for asymptotic safety of quantum gravity
• Renormalisation group and the Planck scale
• Bimetric Renormalization Group Flows in Quantum Einstein Gravity
• The Gravitational Two-Loop Counterterm is Asymptotically Safe
• QED coupled to QEG
• Bimetric Truncations for Quantum Einstein Gravity and Asymptotic Safety
• Asymptotically Safe Inflation
• Asymptotic freedom of Yang-Mills theory with gravity
• Quantum gravity on foliated spacetime - asymptotically safe and sound
• Renormalization group fixed points of foliated gravity-matter systems
• Generalized Parametrization Dependence in Quantum Gravity
• Black holes and asymptotically safe gravity
• Black holes within Asymptotic Safety
• Resolving Spacetime Singularities within Asymptotic Safety
• An asymptotically safe solution to the U(1) triviality problem
• Structural aspects of asymptotically safe black holes
• Matter Induced Bimetric Actions for Gravity
• Running Gauge Coupling in Asymptotically Safe Quantum Gravity
• Form Factors in Asymptotic Safety: conceptual ideas and computational toolbox
• Non-minimal coupling in Higgs-Yukawa model with asymptotically safe gravity
• Viability of quantum-gravity induced ultraviolet completions for matter
• Fractal space-times under the microscope: A Renormalization Group view on Monte Carlo data
• A proper fixed functional for four-dimensional Quantum Einstein Gravity
• Ghost wave-function renormalization in Asymptotically Safe Quantum Gravity
• The local potential approximation in quantum gravity
• Higher Derivative Gravity and Asymptotic Safety in Diverse Dimensions
• Consistent closure of renormalization group flow equations in quantum gravity
• The Universal RG Machine
• Asymptotically safe f(R)-gravity coupled to matter I: the polynomial case
• Higgs scalar potential in asymptotically safe quantum gravity
• Black hole thermodynamics under the microscope
• Renormalisation of Newton's constant
• Asymptotic safety of higher derivative quantum gravity non-minimally coupled with a matter system
• On the number of relevant operators in asymptotically safe gravity
• Asymptotically safe inflation from quadratic gravity
• A functional renormalization group equation for foliated spacetimes
• Asymptotic Safety in Einstein Gravity and Scalar-Fermion Matter
• Status of the asymptotic safety paradigm for quantum gravity and matter
• Super-renormalizable or finite completion of the Starobinsky theory
• From renormalization group flows to cosmology
• Functional renormalization with fermions and tetrads
• Towards the determination of the dimension of the critical surface in asymptotically safe gravity
• Variable Planck mass from the gauge invariant flow equation
• On the UV structure of quantum unimodular gravity
• Fixed-Functionals of three-dimensional Quantum Einstein Gravity
• Asymptotic safety and field parametrization dependence in the f(R) truncation
• Asymptotically Safe Starobinsky Inflation
• RG flows of Quantum Einstein Gravity on maximally symmetric spaces
• Asymptotically Safe Cosmology
• Impact of topology in foliated Quantum Einstein Gravity
• Asymptotic Safety, Fractals, and Cosmology
• Renormalization Group Flow of the Holst Action
• Scale Setting for Self-consistent Backgrounds
• Essential Quantum Einstein Gravity
• Cosmological bounds on the field content of asymptotically safe gravity-matter models
• Gauges and functional measures in quantum gravity II: Higher derivative gravity
• Asymptotic Safety, Emergence and Minimal Length
• Physical renormalization schemes and asymptotic safety in quantum gravity
• Ultraviolet Fixed Points in Conformal Gravity and General Quadratic Theories
• Characterizing black hole metrics in quadratic gravity
• Perturbative quantum gravity with the Immirzi parameter
• Asymptotic safety goes on shell
• Polyakov Effective Action from Functional Renormalization Group Equation
• RG flow of Weyl-invariant dilaton gravity
• One loop beta functions and fixed points in Higher Derivative Sigma Models
• On the impact of Majorana masses in gravity-matter systems
• Dynamical System Analysis of Cosmologies with Running Cosmological Constant from Quantum Einstein Gravity
• Scalar-Tensor theories within Asymptotic Safety
• Price of Asymptotic Safety
• Asymptotic Safety: Swampland or Wonderland?
• Euclidian 4d quantum gravity with a non-trivial measure term
• Essential nature of Newton's constant in unimodular gravity
• Higher Derivative Gravity from the Universal Renormalization Group Machine
• Asymptotically Safe Gravity with Fermions
• Propagating gravitons vs. dark matter in asymptotically safe quantum gravity
• Modulated Ground State of Gravity Theories with Stabilized Conformal Factor
• Higgs inflation and quantum gravity: An exact renormalisation group approach
• Avoidance of singularities in asymptotically safe Quantum Einstein Gravity
• Fixed Points of Quantum Gravity and the Dimensionality of the UV Critical Surface
• Universality and symmetry breaking in conformally reduced quantum gravity
• Scalegenesis and fermionic dark matters in the flatland scenario
• Phase transition and critical behavior of d=3 chiral fermion models with left/right asymmetry
• Asymptotic freedom and safety in quantum gravity
• Exploring new corners of asymptotically safe unimodular quantum gravity
• Comment on Asymptotically Safe Inflation
• Renormalisation group improvement of scalar field inflation
• How universe evolves with cosmological and gravitational constants
• Functional Renormalisation for $f(R_{\mu \nu \rho \sigma })$ Quantum Gravity
• Asymptotic safety and Kaluza-Klein gravitons at the LHC
• Asymptotic Safety, Asymptotic Darkness, and the hoop conjecture in the extreme UV
• Large N Quantum Gravity
• Background independent exact renormalisation
• Signs and Stability in Higher-Derivative Gravity
• One Loop Beta Functions in Topologically Massive Gravity
• The phase diagram of Einstein-Weyl gravity
• Evolution of cosmological perturbations in an RG-driven inflationary scenario
• $f(R,R_{\mu \nu }^2)$ at one loop
• On the scaling of composite operators in Asymptotic Safety
• On the cutoff identification and the quantum improvement in asymptotically safe gravity
• Heat kernel coefficients on the sphere in any dimension
• Higgs scalar potential coupled to gravity in the exponential parametrization in arbitrary gauge
• Exorcising Ghosts in Induced Gravity
• Effective Action from the Functional Renormalization Group
• Wave Function Renormalization and Flow of Couplings in Asymptotically Safe Quantum Gravity
• Non-symmetric wormholes and localized Big Rip singularities in Einstein-Weyl gravity
• Geodesic congruences in quantum improved spacetimes
• IR quantum gravity solves naturally cosmic acceleration and its coincidence problem
• Infrared behavior of Weyl Gravity: Functional Renormalization Group approach
• The trouble with asymptotically safe inflation
• Charged black holes in the Einstein-Maxwell-Weyl gravity
• Redundant operators in the exact renormalisation group and in the f(R) approximation to asymptotic safety
• Dark side of Weyl gravity
• The Possibility of Inflation in Asymptotically Safe Gravity
• Scaling solutions for asymptotically free quantum gravity
• RG flows of Quantum Einstein Gravity in the linear-geometric approximation
• Regulator dependence of fixed points in quantum Einstein gravity with $R^2$ truncation
• Black holes in asymptotic safety with higher derivatives: accretion and stability analysis
• Preferred foliation effects in Quantum General Relativity
• Scales and hierachies in asymptotically safe quantum gravity: a review
• An asymptotic-safety mechanism for chiral Yukawa systems
• Infrared behavior of Weyl Gravity
• Asymptotically Safe Gravity-Fermion systems on curved backgrounds
• Gravitationally Induced UV Completion of an $O(N)$ Scalar Theory
• Quantum fields in the non-perturbative regime - Yang-Mills theory and gravity