Quantum Einstein Gravity

Abstract

We give a pedagogical introduction to the basic ideas and concepts of the Asymptotic Safety program in Quantum Einstein Gravity. Using the continuum approach based upon the effective average action, we summarize the state of the art of the field with a particular focus on the evidence supporting the existence of the non-trivial renormalization group fixed point at the heart of the construction. As an application, the multifractal structure of the emerging space-times is discussed in detail. In particular, we compare the continuum prediction for their spectral dimension with Monte Carlo data from the Causal Dynamical Triangulation approach.

87 pages, 13 figures, review article prepared for the New Journal of Physics focus issue on Quantum Einstein Gravity

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Cited by in corpus (249)

• The nonperturbative functional renormalization group and its applications
• Matter matters in asymptotically safe quantum gravity
• Asymptotic safety guaranteed
• Further evidence for asymptotic safety of quantum gravity
• Asymptotic safety of gravity-matter systems
• The Gravitational Two-Loop Counterterm is Asymptotically Safe
• Geometric entropy and edge modes of the electromagnetic field
• Asymptotic safety in the f(R) approximation
• Towards apparent convergence in asymptotically safe quantum gravity
• Top mass from asymptotic safety
• Global Flows in Quantum 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
• Asymptotic safety of quantum gravity beyond Ricci scalars
• Renormalization group fixed points of foliated gravity-matter systems
• Generalized Parametrization Dependence in Quantum Gravity
• Black holes within Asymptotic Safety
• Asymptotically safe cosmology - a status report
• Resolving Spacetime Singularities within Asymptotic Safety
• Lectures on renormalization and asymptotic safety
• 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
• 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
• Quantum-gravity-induced matter self-interactions in the asymptotic-safety scenario
• Upper bound on the Abelian gauge coupling from asymptotic safety
• Curvature dependence of quantum gravity
• Quantum gravity fluctuations flatten the Planck-scale Higgs potential
• Viability of quantum-gravity induced ultraviolet completions for matter
• Higher order quark-mesonic scattering processes and the phase structure of QCD
• Functional Renormalisation Group Approach for Tensorial Group Field Theory: a Rank-3 Model
• A proper fixed functional for four-dimensional Quantum Einstein Gravity
• The local potential approximation in quantum gravity
• Mass difference for charged quarks from asymptotically safe quantum gravity
• Asymptotic safety in an interacting system of gravity and scalar matter
• Quantum gravity and Standard-Model-like fermions
• Chiral fermions in asymptotically safe quantum gravity
• How perturbative is quantum gravity?
• Asymptotically safe f(R)-gravity coupled to matter I: the polynomial case
• Black hole thermodynamics under the microscope
• Higgs scalar potential in asymptotically safe quantum gravity
• The R^2 phase-diagram of QEG and its spectral dimension
• Probing the quantum nature of spacetime by diffusion
• Second- and First-Order Phase Transitions in CDT
• Asymptotic safety of higher derivative quantum gravity non-minimally coupled with a matter system
• Effective universality in quantum gravity
• On the number of relevant operators in asymptotically safe gravity
• Zooming in on fermions and quantum gravity
• Dilaton Quantum Gravity
• A functional renormalization group equation for foliated spacetimes
• Gauge hierarchy problem in asymptotically safe gravity--the resurgence mechanism
• Correlation functions on a curved background
• Nonminimal hints for asymptotic safety
• From renormalization group flows to cosmology
• Background independence in a background dependent renormalization group
• Continuum limit in matrix models for quantum gravity from the Functional Renormalization Group
• Realization of DSR-relativistic symmetries in Finsler geometries
• The Higgs Mass and the Scale of New Physics
• Field Parametrization Dependence in Asymptotically Safe Quantum Gravity
• Renormalization Group Flow in CDT
• Quantum Improved Schwarzschild-(A)dS and Kerr-(A)dS Space-times
• Variable Planck mass from the gauge invariant flow equation
• Functional Renormalisation Group analysis of Tensorial Group Field Theories on ${\mathbb{R}}^d$
• 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
• RG flows of Quantum Einstein Gravity on maximally symmetric spaces
• Asymptotically Safe Starobinsky Inflation
• Scaling solutions for Dilaton Quantum Gravity
• Impact of topology in foliated Quantum Einstein Gravity
• Large curvature and background scale independence in single-metric approximations to asymptotic safety
• Constraining power of asymptotic safety for scalar fields
• Background independent exact renormalization group for conformally reduced gravity
• Running boundary actions, Asymptotic Safety, and black hole thermodynamics
• Higgs Mass Bounds from Renormalization Flow for a Higgs-top-bottom model
• Consistency of matter models with asymptotically safe quantum gravity
• $d=4$ as the critical dimensionality of asymptotically safe interactions
• Towards reconstructing the quantum effective action of gravity
• Solutions to the reconstruction problem in asymptotic safety
• Asymptotic safety in three-dimensional SU(2) Group Field Theory: evidence in the local potential approximation
• Lorentz symmetry is relevant
• Asymptotic solutions in asymptotic safety
• Asymptotic freedom in Horava-Lifshitz gravity
• Inflation in an effective gravitational model & asymptotic safety
• Essential Quantum Einstein Gravity
• Asymptotically Safe Grand Unification
• Singularity-free gravitational collapse and asymptotic safety
• Renormalizable Group Field Theory beyond melonic diagrams: an example in rank four
• Towards phase transitions between discrete and continuum quantum spacetime from the Renormalization Group
• Fermions in gravity with local spin-base invariance
• On the physical mechanism underlying Asymptotic Safety
• Light charged fermions in quantum gravity
• Gravitational wave from dark sector with dark pion
• An asymptotic safety scenario for gauged chiral Higgs-Yukawa models
• Dimensional flow in discrete quantum geometries
• Einstein-Cartan gravity, Asymptotic Safety, and the running Immirzi parameter
• BTZ black hole assuming running couplings
• On avoiding Ostrogradski instabilities within Asymptotic Safety
• Physical renormalization schemes and asymptotic safety in quantum gravity
• Faddeev-Popov ghosts in quantum gravity beyond perturbation theory
• Gravity in the infrared and effective nonlocal models
• Safety in darkness: Higgs portal to simple Yukawa systems
• The Planck scale, the Higgs mass and scalar dark matter
• Renormalization group flow of Hořava-Lifshitz gravity at low energies
• Quantum gravity with torsion and non-metricity
• Starobinsky-type Inflation in Dynamical Supergravity Breaking Scenarios
• Fixed point structure of the conformal factor field in quantum gravity
• Functional Renormalization Group analysis of rank 3 tensorial group field theory: The full quartic invariant truncation
• On the impact of Majorana masses in gravity-matter systems
• Infinite order quantum-gravitational correlations
• Bouncing and emergent cosmologies from ADM RG flows
• Scalar-Tensor theories within Asymptotic Safety
• Constraining the Asymptotically Safe Cosmology: cosmic acceleration without dark energy
• Why are tensor field theories asymptotically free?
• Evidence for Asymptotic Safety from Dimensional Reduction in Causal Dynamical Triangulations
• Hamiltonian Renormalisation I: Derivation from Osterwalder-Schrader Reconstruction
• Asymptotic safety and the cosmological constant
• Quantum Equivalence of $f(R)$ Gravity and Scalar-tensor Theories in the Jordan and Einstein Frames
• Essential nature of Newton's constant in unimodular gravity
• Manifestly diffeomorphism invariant classical Exact Renormalization Group
• Spectral dimension of quantum geometries
• Asymptotically Safe Gravity with Fermions
• 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
• Exact RG Flow Equations and Quantum Gravity
• Infrared fixed point in quantum Einstein gravity
• Modulated Ground State of Gravity Theories with Stabilized Conformal Factor
• Propagating gravitons vs. dark matter in asymptotically safe quantum gravity
• Exact black hole solution for scale dependent gravitational couplings and the corresponding coupling flow
• Higgs inflation and quantum gravity: An exact renormalisation group approach
• Predictive power of grand unification from quantum gravity
• Asymptotically Safe gravity and non-singular inflationary Big Bang with vacuum birth
• Avoidance of singularities in asymptotically safe Quantum Einstein Gravity
• Functional Renormalization Group flows on Friedman-Lema\^ıtre-Robertson-Walker backgrounds
• Starobinsky-Like Inflation in Dilaton-Brane Cosmology
• Quantum Gravity signatures in the Unruh effect
• Non-Singular Black Holes, the Cosmological Constant and Asymptotic Safety
• Scalegenesis and fermionic dark matters in the flatland scenario
• Improved Reissner-Nordström-(A)dS Black Hole in Asymptotic Safety
• A curvature bound from gravitational catalysis
• Constructive Tensor Field Theory: The $T_3^4$ Model
• Inflation via Gravitino Condensation in Dynamically Broken Supergravity
• Global surpluses of spin-base invariant fermions
• Inflation from Asymptotically Safe Theories
• Accretion disk around a Schwarzschild black hole in asymptotic safety
• The weak-gravity bound in asymptotically safe gravity-gauge systems
• Spacetime condensation in (2+1)-dimensional CDT from a Horava-Lifshitz minisuperspace model
• From quantum gravity to gravitational waves through cosmic strings
• Quantum Critical Behaviour of Semi-Simple Gauge Theories
• Emergent Gravity requires (kinematic) non-locality
• Gauge and parametrization ambiguity in quantum gravity
• Universal critical behavior in tensor models for four-dimensional quantum gravity
• Brans-Dicke theory in the local potential approximation
• Asymptotic freedom and safety in quantum gravity
• Spin-base invariance of Fermions in arbitrary dimensions
• Towards a $C$-function in 4D quantum gravity
• Is scale-invariance in gauge-Yukawa systems compatible with the graviton?
• Towards the map of quantum gravity
• How universe evolves with cosmological and gravitational constants
• Renormalization-group flow of the effective action of cosmological large-scale structures
• Searching for a continuum limit in causal dynamical triangulation quantum gravity
• Spontaneous symmetry breaking and optimization of functional renormalization group
• Can we see quantum gravity? Photons in the asymptotic-safety scenario
• An algebraic QFT approach to the Wetterich equation on Lorentzian manifolds
• Scattering amplitudes in affine gravity
• A curvature bound from gravitational catalysis in thermal backgrounds
• A solution of the dark energy and its coincidence problem based on local antigravity sources without fine-tuning or new scales
• Confinement and Renormalization Group Equations in String-inspired Non-local Gauge Theories
• The fate of non-polynomial interactions in scalar field theory
• A new functional flow equation for Einstein-Cartan quantum gravity
• Finite Entanglement Entropy in Asymptotically Safe Quantum Gravity
• Quantum gravity lights up spinning black holes
• Hamiltonian Renormalisation IV. Renormalisation Flow of D+1 dimensional free scalar fields and Rotation Invariance
• Effective field equations and scale-dependent couplings in gravity
• Hamiltonian Renormalisation II. Renormalisation Flow of 1+1 dimensional free scalar fields: Derivation
• Newtonian Binding from Lattice Quantum Gravity
• Quantum Gravity: the view from particle physics
• Renormalizable, asymptotically free gravity without ghosts or tachyons
• Asymptotically safe and free chiral theories with and without scalars
• FeynGrav 2.0
• Critical exponents in quantum Einstein gravity
• Spectrum of the Laplace-Beltrami Operator and the Phase Structure of Causal Dynamical Triangulation
• Canonical tensor model through data analysis -- Dimensions, topologies, and geometries --
• Higgs scalar potential coupled to gravity in the exponential parametrization in arbitrary gauge
• Functional flows in QED and the modified Ward-Takahashi identity
• Heat kernel coefficients on the sphere in any dimension
• Symmetric configurations highlighted by collective quantum coherence
• The metric on field space, functional renormalization, and metric-torsion quantum gravity
• Quantum Gravity on the computer: Impressions of a workshop
• Alternative flow equation for the functional renormalization group
• Wilson loops in CDT quantum gravity
• Antiscreening in perturbative quantum gravity and resolving the Newtonian singularity
• A Conformal Fixed-Point Equation for the Effective Average Action
• Critical behaviors of black hole in an asymptotically safe gravity with cosmological constant
• The Numerically Optimized Regulator and the Functional Renormalization Group
• The Fröhlich-Morchio-Strocchi mechanism and quantum gravity
• On characterizing the Quantum Geometry underlying Asymptotic Safety
• Towards a unitary, renormalizable and ultraviolet-complete quantum theory of gravity
• Renormalization flow towards gravitational catalysis in the 3d Gross-Neveu model
• Reflection positivity in higher derivative scalar theories
• Quantum Phase Transitions in the BKL Universe
• Reconstructing the graviton
• On selfdual spin-connections and Asymptotic Safety
• Is asymptotically safe inflation eternal?
• Will-Nordtvedt PPN formalism applied to renormalization group extensions of general relativity
• Stability of fixed points and generalized critical behavior in multifield models
• Steps towards Lorentzian quantum gravity with causal sets
• Conformal Phase Diagram of Complete Asymptotically Free Theories
• The effects of running gravitational coupling on three dimensional black holes
• Spectral Methods and Running Scales in Causal Dynamical Triangulations
• Solar System constraints on Renormalization Group extended General Relativity: The PPN and Laplace-Runge-Lenz analyses with the external potential effect
• Is Lattice Quantum Gravity Asymptotically Safe? Making contact between Causal Dynamical Triangulations and the Functional Renormalization Group
• Symmetric black-to-white hole solutions with a cosmological constant
• Scale and confinement phase transitions in scale invariant $SU(N)$ scalar gauge theory
• A Lorentzian renormalisation group equation for gauge theories
• Irreversible vierbein postulate: Emergence of spacetime from quantum phase transition
• On the Perturbative Quantization of Einstein-Hilbert Gravity Embedded in a Higher Derivative Model
• Asymptotic safety in the sine-Gordon model
• Black Hole Remnants from Dynamical Dimensional Reduction?
• Non-perturbative Lee-Wick gauge theory: Towards Confinement and RGE with strong couplings
• On quantum gravity, Asymptotic Safety, and paramagnetic dominance
• UV completion of extradimensional Yang-Mills theory for Gauge-Higgs unification
• A second look at transition amplitudes in (2+1)-dimensional causal dynamical triangulations
• Vacuum energy, the Casimir effect, and Newton's non-constant
• Scaling solutions for asymptotically free quantum gravity
• Regulator dependence of fixed points in quantum Einstein gravity with $R^2$ truncation
• Constraining the swiss-cheese IR-fixed point cosmology with cosmic expansion
• Is the local linearity of space-time inherited from the linearity of probabilities?
• Geometry-Information Duality: Quantum Entanglement Contributions to Gravitational Dynamics
• Nonperturbative aspects of two-dimensional $T\bar{T}$-deformed scalar theory from functional renormalization group
• Singularities and Phenomenological aspects of Asymptotic Safe Gravity
• Tensors and Algebras: An Algebraic Spacetime Interpretation for Tensor Models
• Reformulations of Yang-Mills Theories with Space-time Tensor Fields
• Weyl Curvature Hypothesis in light of Quantum Backreaction at Cosmological Singularities or Bounces
• Exploratory applications of the Fröhlich-Morchio-Strocchi mechanism in quantum gravity
• Indications against dynamical CPT symmetry restoration in quantum gravity
• The Fröhlich-Morchio-Strocchi mechanism: A underestimated legacy
• Coarse-graining of the Einstein-Hilbert Action rewritten by the Fisher information metric
• A quantum theory of gravity
• Geodesics in Quantum Gravity
• Tidal Deformation Bounds and Perturbation Transfer in Bounded Curvature Spacetimes
• Cosmology with Logarithmic Corrected Horizon Entropy According to the Generalized Entropy and Variable-G Correspondence
• Fate of chiral symmetry in Riemann-Cartan geometry
• Shadows of naked singularities and superspinars related to the revisited Kerr-de Sitter spacetimes
• Conceptual and Geometric Foundations for a Teleparallel Approach to Quantum Gravity