On the renormalization group flow of f(R)-gravity

Abstract

We use the functional renormalization group equation for quantum gravity to construct a non-perturbative flow equation for modified gravity theories of the form $S=\int d^{d}x\sqrt{g}f(R)$. Based on this equation we show that certain gravitational interactions monomials can be consistently decoupled from the renormalization group (RG) flow and reproduce recent results on the asymptotic safety conjecture. The non-perturbative RG flow of non-local extensions of the Einstein-Hilbert truncation including $\int d^{d}x\sqrt{g}\ln (R)$ and $\int d^{d}x\sqrt{g}{R}^{-n}$ interactions is investigated in detail. The inclusion of such interactions resolves the infrared singularities plaguing the RG trajectories with positive cosmological constant in previous truncations. In particular, in some $R^{-n}$-truncations all physical trajectories emanate from a Non-Gaussian (UV) fixed point and are well-defined on all RG scales. The RG flow of the $\ln (R)$-truncation contains an infrared attractor which drives a positive cosmological constant to zero dynamically.

55 pages, 7 figures, typos corrected, references added, version to appear in Phys. Rev. D

References in corpus (68)

• Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology
• Introduction to Modified Gravity and Gravitational Alternative for Dark Energy
• Is Cosmic Speed-Up Due to New Gravitational Physics?
• Modified gravity with negative and positive powers of the curvature: unification of the inflation and of the cosmic acceleration
• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
• Nonperturbative Evolution Equation for Quantum Gravity
• Optimised Renormalisation Group Flows
• Renormalization group improved black hole spacetimes
• Spectral Dimension of the Universe
• Fixed points of quantum gravity
• Renormalization Group Flow of Quantum Gravity in the Einstein-Hilbert Truncation
• Emergence of a 4D World from Causal Quantum Gravity
• One-loop f(R) gravity in de Sitter universe
• Modified gravity with $\ln R$ terms and cosmic acceleration
• Ultraviolet Fixed Point and Generalized Flow Equation of Quantum Gravity
• Reconstructing the Universe
• Nonlocal Cosmology
• 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
• Cosmology of the Planck Era from a Renormalization Group for Quantum Gravity
• Ultraviolet properties of f(R)-Gravity
• The Asymptotic Safety Scenario in Quantum Gravity -- An Introduction
• The Running Gravitational Couplings
• Spacetime Structure of an Evaporating Black Hole in Quantum Gravity
• Asymptotic Safety of Gravity Coupled to Matter
• Is Quantum Einstein Gravity Nonperturbatively Renormalizable?
• Critical exponents from optimised renormalisation group flows
• Cosmology with Self-Adjusting Vacuum Energy Density from a Renormalization Group Fixed Point
• Contraints on Matter from Asymptotic Safety
• Taming perturbative divergences in asymptotically safe gravity
• Renormalization group improved gravitational actions: a Brans-Dicke approach
• Fixed points of quantum gravity in extra dimensions
• Mind The Gap
• The Universe from Scratch
• Running Newton Constant, Improved Gravitational Actions, and Galaxy Rotation Curves
• Quantum Gravity at Astrophysical Distances?
• Gravitational Theory, Galaxy Rotation Curves and Cosmology without Dark Matter
• Proper Time Flow Equation for Gravity
• Quantum Gravity effects near the null black hole singularity
• Semiclassical Universe from First Principles
• From Big Bang to Asymptotic de Sitter: Complete Cosmologies in a Quantum Gravity Framework
• A class of nonlocal truncations in Quantum Einstein Gravity and its renormalization group behavior
• Flow Equations for Yang-Mills Theories in General Axial Gauges
• Confronting the IR Fixed Point Cosmology with High Redshift Observations
• Gauge invariance and background field formalism in the exact renormalisation group
• Functional Integration Over Geometries
• Effective Nonlocal Euclidean Gravity
• Towards Nonperturbative Renormalizability of Quantum Einstein Gravity
• Effective average action in statistical physics and quantum field theory
• Functional Renormalization Group Equations, Asymptotic Safety, and Quantum Einstein Gravity
• Cosmological Perturbations in Renormalization Group Derived Cosmologies
• Dimensionally reduced gravity theories are asymptotically safe
• Asymptotic behaviours of the heat kernel in covariant perturbation theory
• Conformally reduced quantum gravity revisited
• Signatures of gravitational fixed points at the LHC
• On the Ultraviolet Behaviour of Newton's constant
• Renormalization and asymptotic safety in truncated quantum Einstein gravity
• Nonlocal Quantum Gravity and the Size of the Universe
• Arnowitt-Deser-Misner gravity with variable G and Lambda and fixed point cosmologies from the renormalization group
• Collider Signals of Gravitational Fixed Points
• Fractal Geometry of Quantum Spacetime at Large Scales
• A Class of Renormalization Group Invariant Scalar Field Cosmologies
• The Accelerated expansion of the Universe as a crossover phenomenon
• The Renormalization Group, Systems of Units and the Hierarchy Problem
• Renormalization Group and Black Hole Production in Large Extra Dimensions
• A fixed point for truncated quantum Einstein gravity
• Nonperturbative heat kernel and nonlocal effective action

Cited by in corpus (190)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• f(R) theories
• Beyond the Cosmological Standard Model
• The nonperturbative functional renormalization group and its applications
• Future of the universe in modified gravitational theories: Approaching to the finite-time future singularity
• Quantum Einstein Gravity
• Asymptotic safety in higher-derivative gravity
• Fermion Interactions and Universal Behavior in Strongly Interacting Theories
• Matter matters in asymptotically safe quantum gravity
• Further evidence for asymptotic safety of quantum gravity
• Taming perturbative divergences in asymptotically safe gravity
• Renormalisation group and the Planck scale
• Asymptotic safety of gravity-matter systems
• Bimetric Renormalization Group Flows in Quantum Einstein Gravity
• Renormalization Group Flow in Scalar-Tensor Theories. I
• Local Quantum Gravity
• The Gravitational Two-Loop Counterterm is Asymptotically Safe
• Towards apparent convergence in asymptotically safe quantum gravity
• Bimetric Truncations for Quantum Einstein Gravity and Asymptotic Safety
• Asymptotically Safe Inflation
• Search of scaling solutions in scalar-tensor gravity
• One force to rule them all: asymptotic safety of gravity with matter
• The Renormalization Group flow of unimodular f(R) gravity
• Quantum gravity on foliated spacetime - asymptotically safe and sound
• Physics searches at the LHC
• Asymptotic safety of quantum gravity beyond Ricci scalars
• Asymptotic safety: a simple example
• Renormalization group fixed points of foliated gravity-matter systems
• Generalized Parametrization Dependence in Quantum Gravity
• Ghost anomalous dimension in asymptotically safe quantum gravity
• Black holes and asymptotically safe gravity
• Light fermions in quantum gravity
• Black holes within Asymptotic Safety
• A flow equation for f(R) gravity and some of its exact solutions
• Structural aspects of asymptotically safe black holes
• An asymptotically safe solution to the U(1) triviality problem
• Quantum-gravity effects on a Higgs-Yukawa model
• Matter Induced Bimetric Actions for Gravity
• Aspects of asymptotic safety for quantum gravity
• Form Factors in Asymptotic Safety: conceptual ideas and computational toolbox
• Background Independence and Asymptotic Safety in Conformally Reduced Gravity
• Non-minimal coupling in Higgs-Yukawa model with asymptotically safe gravity
• Curvature dependence of quantum gravity
• Dynamical renormalization of black-hole spacetimes
• Viability of quantum-gravity induced ultraviolet completions for matter
• Dark energy, inflation and dark matter from modified F(R) gravity
• Renormalization Group Equation and scaling solutions for f(R) gravity in exponential parametrization
• Ghost wave-function renormalization in Asymptotically Safe Quantum Gravity
• Quantum Gravity Effects in the Kerr Spacetime
• Asymptotic safety in an interacting system of gravity and scalar matter
• Chiral fermions in asymptotically safe quantum gravity
• Consistent closure of renormalization group flow equations in quantum gravity
• Asymptotically safe f(R)-gravity coupled to matter I: the polynomial case
• Black hole thermodynamics under the microscope
• The R^2 phase-diagram of QEG and its spectral dimension
• Conformal sector of Quantum Einstein Gravity in the local potential approximation: non-Gaussian fixed point and a phase of unbroken diffeomorphism invariance
• Asymptotically free scalar curvature-ghost coupling in Quantum Einstein Gravity
• Effective universality in quantum gravity
• On the number of relevant operators in asymptotically safe gravity
• Black hole shadow of a rotating scale--dependent black hole
• Bare Action and Regularized Functional Integral of Asymptotically Safe Quantum Gravity
• Status of the asymptotic safety paradigm for quantum gravity and matter
• Correlation functions on a curved background
• Inflationary solutions in asymptotically safe f(R) theories
• Functional renormalization with fermions and tetrads
• Renormalization Group Equation for $f(R)$ gravity on hyperbolic spaces
• Fixed-Functionals of three-dimensional Quantum Einstein Gravity
• On the UV structure of quantum unimodular gravity
• Asymptotic safety and field parametrization dependence in the f(R) truncation
• Asymptotically Safe Starobinsky Inflation
• Fixed Points of Nonlinear Sigma Models in d>2
• The role of Background Independence for Asymptotic Safety in Quantum Einstein Gravity
• Scaling solutions for Dilaton Quantum Gravity
• Large curvature and background scale independence in single-metric approximations to asymptotic safety
• Algorithmic derivation of functional renormalization group equations and Dyson-Schwinger equations
• Asymptotically Safe Cosmology
• Impact of topology in foliated Quantum Einstein Gravity
• Renormalization Group Flow in Scalar-Tensor Theories. II
• Asymptotic Safety, Fractals, and Cosmology
• An effective action for asymptotically safe gravity
• Higgs Mass Bounds from Renormalization Flow for a Higgs-top-bottom model
• The background scale Ward identity in quantum gravity
• Towards conditions for black-hole singularity-resolution in asymptotically safe quantum gravity
• Asymptotic solutions in asymptotic safety
• Scale Setting for Self-consistent Backgrounds
• Essential Quantum Einstein Gravity
• Cosmological bounds on the field content of asymptotically safe gravity-matter models
• Asymptotic Safety, Emergence and Minimal Length
• Einstein-Cartan gravity, Asymptotic Safety, and the running Immirzi parameter
• Light charged fermions in quantum gravity
• Minimal models for $g-2$ and dark matter confront asymptotic safety
• Physical renormalization schemes and asymptotic safety in quantum gravity
• RG flow of Weyl-invariant dilaton gravity
• Polyakov Effective Action from Functional Renormalization Group Equation
• Asymptotic safety goes on shell
• Fixed point structure of the conformal factor field in quantum gravity
• On de Sitter solutions in asymptotically safe $f(R)$ theories
• On the impact of Majorana masses in gravity-matter systems
• Low energy Quantum Gravity from the Effective Average Action
• Bouncing and emergent cosmologies from ADM RG flows
• Infinite order quantum-gravitational correlations
• Scalar-Tensor theories within Asymptotic Safety
• Asymptotic Safety: Swampland or Wonderland?
• Quantum Equivalence of $f(R)$ Gravity and Scalar-tensor Theories in the Jordan and Einstein Frames
• Asymptotic safety and the cosmological constant
• Fixed Points of Quantum Gravity and the Renormalisation Group
• Background Scale Independence in Quantum Gravity
• Consistent early and late time cosmology from the RG flow of gravity
• Infrared fixed point in quantum Einstein gravity
• Modulated Ground State of Gravity Theories with Stabilized Conformal Factor
• One-loop divergences for $f(R)$ gravity
• Higgs inflation and quantum gravity: An exact renormalisation group approach
• Avoidance of singularities in asymptotically safe Quantum Einstein Gravity
• Asymptotically Safe gravity and non-singular inflationary Big Bang with vacuum birth
• Gravitational antiscreening in stellar interiors
• Effective Potential of the Conformal Factor: Gravitational Average Action and Dynamical Triangulations
• Fixed Points of Quantum Gravity and the Dimensionality of the UV Critical Surface
• Scalegenesis and fermionic dark matters in the flatland scenario
• Naturally small Yukawa couplings from trans-Planckian asymptotic safety
• Universality and symmetry breaking in conformally reduced quantum gravity
• A curvature bound from gravitational catalysis
• The weak-gravity bound in asymptotically safe gravity-gauge systems
• Flavor anomalies from asymptotically safe gravity
• Exploring new corners of asymptotically safe unimodular quantum gravity
• Brans-Dicke theory in the local potential approximation
• Universal critical behavior in tensor models for four-dimensional quantum gravity
• Renormalisation group improvement of scalar field inflation
• Renormalization Group Equations of Higgs-$R^2$ Inflation
• Entropy Production during Asymptotically Safe Inflation
• Functional Renormalisation for $f(R_{\mu \nu \rho \sigma })$ Quantum Gravity
• How universe evolves with cosmological and gravitational constants
• Quantum gravity effects in Myers-Perry space-times
• Lessons from conformally reduced quantum gravity
• Are there ALPs in the asymptotically safe landscape?
• The fate of non-polynomial interactions in scalar field theory
• A new functional flow equation for Einstein-Cartan quantum gravity
• On the weak-gravity bound for a shift-symmetric scalar field
• Neutrino masses, vacuum stability and quantum gravity prediction for the mass of the top quark
• Role of Extended Gravity Theory in Matter Bounce Dynamics
• Background independent exact renormalisation
• Off-diagonal heat-kernel expansion and its application to fields with differential constraints
• RG flow equations for the proper-vertices of the background effective average action
• One Loop Beta Functions in Topologically Massive Gravity
• Constraints on $Z^{\prime }$ solutions to the flavor anomalies with trans-Planckian asymptotic safety
• Functional Renormalization of Noncommutative Scalar Field Theory
• Evolution of cosmological perturbations in an RG-driven inflationary scenario
• $f(R,R_{\mu \nu }^2)$ at one loop
• Critical scaling in the large-$N$ $O(N)$ model in higher dimensions and its possible connection to quantum gravity
• Provable properties of asymptotic safety in $f(R)$ approximation
• On the scaling of composite operators in Asymptotic Safety
• Naturally small neutrino mass with asymptotic safety and gravitational-wave signatures
• Small Cosmological Constant from Running Gravitational Coupling
• Heat kernel coefficients on the sphere in any dimension
• The Spectral Geometry of de Sitter Space in Asymptotic Safety
• On the traversability of wormhole solutions in asymptotically safe gravity
• How robust are particle physics predictions in asymptotic safety?
• Degeneracy induced scaling of the correlation length for periodic models
• On characterizing the Quantum Geometry underlying Asymptotic Safety
• On the Renormalization Group perspective of $\alpha$-attractors
• Perturbative Asymptotic Safety and Its Phenomenological Applications
• An asymptotically safe guide to quantum gravity and matter
• Towards a unitary, renormalizable and ultraviolet-complete quantum theory of gravity
• Scale-invariance at the core of quantum black holes
• Asymptotically safe phantom cosmology
• Schwarzschild-like Wormholes in Asymptotically Safe Gravity
• Five-dimensional scale-dependent black holes with constant curvature and Solv horizons
• Generalized Ellis-Bronnikov wormholes in asymptotically safe gravity
• Shift-symmetric Horndeski gravity in the asymptotic-safety paradigm
• A non-local way around the no-global-symmetries conjecture in quantum gravity?
• Fixed Functionals in Asymptotically Safe Gravity
• Redundant operators in the exact renormalisation group and in the f(R) approximation to asymptotic safety
• Asymptotically Safe Hilbert-Palatini Gravity in an On-Shell Reduction Scheme
• Non-perturbative quantum Galileon in the exact renormalization group
• Variable $G$ and $\Lambda$ gravity theory and analytical Cosmological Solutions using Noether symmetry approach
• Ruling out models of vector dark matter in asymptotically safe quantum gravity
• The weak-gravity bound and the need for spin in asymptotically safe matter-gravity models
• Regulator dependence of fixed points in quantum Einstein gravity with $R^2$ truncation
• RG flows of Quantum Einstein Gravity in the linear-geometric approximation
• Stabilizing dark matter with quantum scale symmetry
• Black holes in asymptotic safety with higher derivatives: accretion and stability analysis
• Causality, unitarity and stability in quantum gravity: a non-perturbative perspective
• Scales and hierachies in asymptotically safe quantum gravity: a review
• Renormalization Flow of Nonlinear Electrodynamics
• Dynamical analysis and cosmological viability of varying $G$ and $\Lambda$ cosmology
• Stability of the de-Sitter universe: One-loop nonlocal $f(R)$ gravity
• Gravitationally Induced UV Completion of an $O(N)$ Scalar Theory
• The stability of the de-Sitter universe in nonlocal gravity
• Asymptotically Safe Gravity-Fermion systems on curved backgrounds
• BUSSTEPP lecture notes: Exact Wilsonian Renormalisation
• Quantum fields in the non-perturbative regime - Yang-Mills theory and gravity