A flow equation for f(R) gravity and some of its exact solutions

Abstract

We write a Renormalization Group (RG) equation for the function f in a theory of gravity in the f(R) truncation. Our equation differs from previous ones due to the exponential parametrization of the quantum fluctuations and to the choice of gauge. The cutoff procedure depends on three free parameters, and we find that there exist discrete special choices of parameters for which the flow equation has fixed points where f=f_0+f_1 R+f_2 R^2. For other values of the parameters the solution seems to be continuously deformed.

5 pages, minor changes, comments added, to appear on PRD

References in corpus (10)

• Ultraviolet properties of f(R)-Gravity
• On the renormalization group flow of f(R)-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
• The local potential approximation in quantum gravity
• Field Parametrization Dependence in Asymptotically Safe Quantum Gravity
• Fixed-Functionals of three-dimensional Quantum Einstein Gravity
• Background independent exact renormalization group for conformally reduced gravity

Cited by in corpus (83)

• The nonperturbative functional renormalization group and its applications
• The Gravitational Two-Loop Counterterm is Asymptotically Safe
• Towards apparent convergence in asymptotically safe quantum gravity
• One force to rule them all: asymptotic safety of gravity with matter
• Quantum gravity on foliated spacetime - asymptotically safe and sound
• Asymptotic safety of quantum gravity beyond Ricci scalars
• Renormalization group fixed points of foliated gravity-matter systems
• Generalized Parametrization Dependence in Quantum Gravity
• Aspects of asymptotic safety for quantum gravity
• Form Factors in Asymptotic Safety: conceptual ideas and computational toolbox
• Quantum gravity: a fluctuating point of view
• Non-minimal coupling in Higgs-Yukawa model with asymptotically safe gravity
• Curvature dependence of quantum gravity
• Dynamical renormalization of black-hole spacetimes
• Renormalization Group Equation and scaling solutions for f(R) gravity in exponential parametrization
• Asymptotic safety in an interacting system of gravity and scalar matter
• Quantum gravity and Standard-Model-like fermions
• Asymptotically safe f(R)-gravity coupled to matter I: the polynomial case
• Nonminimal hints for asymptotic safety
• Correlation functions on a curved background
• Background independence in a background dependent renormalization group
• Renormalization Group Equation for $f(R)$ gravity on hyperbolic spaces
• Scalar induced gravitational waves from primordial black hole Poisson fluctuations in $f(R)$ gravity
• Asymptotic safety and field parametrization dependence in the f(R) truncation
• Large curvature and background scale independence in single-metric approximations to asymptotic safety
• Constraining power of asymptotic safety for scalar fields
• Unimodular quantum gravity and the cosmological constant
• The background scale Ward identity in quantum gravity
• Towards conditions for black-hole singularity-resolution in asymptotically safe quantum gravity
• Lorentz symmetry is relevant
• Asymptotic solutions in asymptotic safety
• Cosmological bounds on the field content of asymptotically safe gravity-matter models
• Gauges and functional measures in quantum gravity II: Higher derivative gravity
• Light charged fermions in quantum gravity
• Physical renormalization schemes and asymptotic safety in quantum gravity
• Cyclic and heteroclinic flows near general static spherically symmetric black holes
• On de Sitter solutions in asymptotically safe $f(R)$ theories
• Fixed point structure of the conformal factor field in quantum gravity
• Bouncing and emergent cosmologies from ADM RG flows
• Infinite order quantum-gravitational correlations
• Asymptotically Safe $f(R)$-Gravity Coupled to Matter II: Global Solutions
• Scalar-Tensor theories within Asymptotic Safety
• Quantum Equivalence of $f(R)$ Gravity and Scalar-tensor Theories in the Jordan and Einstein Frames
• Background Scale Independence in Quantum Gravity
• The unitary conformal field theory behind 2D Asymptotic Safety
• Consistent early and late time cosmology from the RG flow of gravity
• Splitting Ward identity
• Predictive power of grand unification from quantum gravity
• One-loop divergences for $f(R)$ gravity
• Higgs inflation and quantum gravity: An exact renormalisation group approach
• Fixed Points of Quantum Gravity and the Dimensionality of the UV Critical Surface
• A curvature bound from gravitational catalysis
• Dynamics and center of mass energy of colliding particles around black hole in f(R) gravity
• The weak-gravity bound in asymptotically safe gravity-gauge systems
• Split Weyl transformations in quantum gravity
• Exploring new corners of asymptotically safe unimodular quantum gravity
• Functional Renormalisation for $f(R_{\mu \nu \rho \sigma })$ Quantum Gravity
• Nonabelian Higgs models: paving the way for asymptotic freedom
• Are there ALPs in the asymptotically safe landscape?
• The fate of non-polynomial interactions in scalar field theory
• Finite Entanglement Entropy in Asymptotically Safe Quantum Gravity
• Background independent exact renormalisation
• On the weak-gravity bound for a shift-symmetric scalar field
• Geometric operators in the asymptotic safety scenario for quantum gravity
• $f(R,R_{\mu \nu }^2)$ at one loop
• On the scaling of composite operators in Asymptotic Safety
• Provable properties of asymptotic safety in $f(R)$ approximation
• Effective Action from the Functional Renormalization Group
• Higgs scalar potential coupled to gravity in the exponential parametrization in arbitrary gauge
• An asymptotically safe guide to quantum gravity and matter
• On characterizing the Quantum Geometry underlying Asymptotic Safety
• On the Renormalization Group perspective of $\alpha$-attractors
• Thermodynamics of Black holes With Higher Order Corrected Entropy
• Shift-symmetric Horndeski gravity in the asymptotic-safety paradigm
• The weak-gravity bound and the need for spin in asymptotically safe matter-gravity models
• Ruling out models of vector dark matter in asymptotically safe quantum gravity
• Asymptotic safe nonassociative quantum gravity with star R-flux products, Goroff-Sagnotti counter-terms, and geometric flows
• On the Thermodynamical Black Hole Stability in the Space-time of a Global Monopole in $f(R)$-Gravity
• Scales and hierachies in asymptotically safe quantum gravity: a review
• Renormalization Flow of Nonlinear Electrodynamics
• Coarse-graining of the Einstein-Hilbert Action rewritten by the Fisher information metric
• Gravitationally Induced UV Completion of an $O(N)$ Scalar Theory
• Asymptotically Safe Gravity-Fermion systems on curved backgrounds