Horndeski theory and beyond: a review

Abstract

This article is intended to review the recent developments in the Horndeski theory and its generalization, which provide us with a systematic understanding of scalar-tensor theories of gravity as well as a powerful tool to explore astrophysics and cosmology beyond general relativity. This review covers the generalized Galileons, (the rediscovery of) the Horndeski theory, cosmological perturbations in the Horndeski theory, cosmology with a violation of the null energy condition, degenerate higher-order scalar-tensor theories and their status after GW170817, the Vainshtein mechanism in the Horndeski theory and beyond, and hairy black hole solutions.

arXiv commentReview paper. 54 pages, no figure v2: published version

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• No slip gravity in light of LISA standard sirens
• Primordial non-Gaussianity from Galilean Genesis without strong coupling problem
• Stable non-singular cosmologies in beyond Horndeski theory and disformal transformations
• A stellar constraint on Eddington-inspired Born-Infeld gravity from cataclysmic variable binaries
• 3D Lovelock Gravity and the Holographic c-Theorem
• Cosmographic analysis of sign-switching dark energy
• Weak gravity on a $\Lambda$CDM background
• Cooling process of substellar objects in scalar-tensor gravity
• First-order thermodynamics of Horndeski cosmology
• Gravitational baryogenesis in non-minimal kinetic coupling model
• First-order thermodynamics of scalar-tensor gravity
• Tailoring cosmologies in cubic shift-symmetric Horndeski gravity
• Lower-dimensional Limits of Cubic Lovelock Gravity
• Higher Derivative Scalar Tensor Theory in Unitary Gauge
• Complete classification of Friedmann-Lemaître-Robertson-Walker solutions with linear equation of state: parallelly propagated curvature singularities for general geodesics
• Towards the extended SU(2) Proca theory
• Black Hole Shadows Constrain Extended Gravity
• Chaotic Inflation and Reheating in Generalized Scalar-Tensor Gravity
• Stability of a viable non-minimal bounce
• Exploring cosmological imprints of phantom crossing with dynamical dark energy in Horndeski gravity
• Interacting Models of Dark Energy and Dark Matter in Einstein scalar Gauss Bonnet Gravity
• Perturbations of massless external fields in Horndeski hairy black hole
• First test of the consistency relation for the large-scale structure using the anisotropic three-point correlation function of BOSS DR12 galaxies (An explanatory video is available at https://youtu.be/Zi36ooLPhss.)
• Master field equations for spherically symmetric gravitational fields beyond general relativity
• Nonminimal global monopole
• Transport properties in the Horndeski holographic two-currents model
• Covariant formulation of refracted gravity
• Birth of de Sitter Universe from time crystal
• Generalized McVittie geometry in Horndeski gravity with matter
• Effective Potential of Scalar-Tensor Gravity
• Horndeski theories and beyond from higher dimensions
• Shift-symmetric Horndeski gravity in the asymptotic-safety paradigm
• Self-tuning kinetic gravity braiding: Cosmological dynamics, shift symmetry, and the tadpole
• Stars disformally coupled to a shift-symmetric scalar field
• Understanding large scale CMB anomalies with the generalized non-minimal derivative coupling during inflation
• Dwarf Galaxies without Dark Matter: constraints on Modified Gravity
• 2-form gauge theory dual to scalar-tensor theory
• Conformal and kinetic couplings as two Jordan frames of the same theory
• Phantom attractors in Kinetic Gravity Braiding theories: a dynamical system approach
• Exploring Modified Gravity: Constraints on the $\mu$ and $\Sigma$ Parametrization with WMAP, ACT, and SPT
• Generalizations and challenges for the spacetime block-diagonalization
• Dark energy with a shift-symmetric scalar field: obstacles, loophole hunting and dead ends
• Testing generalized scalar-tensor theories of gravity with clusters of galaxies
• Simple traversable wormholes violating energy conditions only near the Planck scale
• Confronting quantum-corrected teleparallel cosmology with observations
• Stealth Ellis Wormholes In Horndeski theories
• Chromo-natural inflation supported by enhanced friction from Horndeski gravity
• A particle's perspective on screening mechanisms
• Post-Newtonian Dynamics of Spinning Black Hole Binaries in Einstein-Scalar-Gauss-Bonnet Gravity
• On the Coupling of Generalized Proca Fields to Degenerate Scalar-Tensor Theories
• Causality and Stability from Acoustic Geometry
• Higher derivative SVT theories from Kaluza-Klein reductions of Horndeski theory
• Investigating the Linearized Second Law in Horndeski Gravity
• Decoupling-limit consistency of the generalized SU(2) Proca theory
• Stealth black hole perturbations in kinetic gravity braiding
• Scalar-Connection Gravity and Spontaneous Scalarization
• FeynMG: a FeynRules extension for scalar-tensor theories of gravity
• Effective geometrodynamics for renormalization-group improved black-hole spacetimes in spherical symmetry
• Strong Gravitational Lensing in Horndeski theory
• Second-order peculiar velocity field as a novel probe of scalar-tensor theories
• Rotating stealth black holes with a cohomogeneity-1 metric
• Numerical computation of quasinormal modes in the first-order approach to black hole perturbations in modified gravity
• Beyond Horndeski interactions induced by quantum effects
• Scalar fields with derivative coupling to curvature in the Palatini and the metric formulation
• Thermodynamic and observational constraints on black holes with primary hair in Beyond Horndeski Gravity: Stability and shadows
• Black holes in the quadratic-order extended vector-tensor theories
• Cosmological attractors to general relativity and spontaneous scalarization with disformal coupling
• Testing kinetically coupled inflation models with CMB distortions
• Gravitational odd-parity perturbation of a Horndeski hairy black hole: quasinormal mode and parameter constraint
• General analysis of Noether symmetries in Horndeski gravity
• Regular black holes from pure gravity in four dimensions
• An issue with the classification of the scalar-tensor theories of gravity
• Gravitational wave signatures from dark sector interactions
• Black hole perturbations in spatially covariant gravity with just two tensorial degrees of freedom
• Anisotropy in constraint 4D Gauss-Bonnet gravity
• In hot pursuit of a stable wormhole in beyond Horndeski theory
• Spatial correlations of dark energy from quantum fluctuations in inflation
• Rotating black holes in valid vector-tensor theories after GW170817
• Holographic Boundary Conformal Field Theory within Horndeski Gravity
• Next step in gravity and cosmology: fundamental theory or data-driven models?
• Microscopic entropy of static black holes in 3d Lovelock gravities
• Purely metric Horndeski theories and spontaneous curvaturization of black holes
• Can Horndeski Genesis be Nonpathological?
• Classical and quantum cosmology of Fab Four John theories
• Quartic Horndeski-Cartan theories in a FLRW universe
• Non-linear density-velocity dynamics in $f(R)$ gravity from spherical collapse
• New model of spontaneous scalarization of black holes induced by curvature and matter
• Fab-Four cosmography to tackle the Hubble tension
• Domain walls in Horndeski gravity
• Stationary spacetimes with time-dependent real scalar fields
• The Stringy Origins of Galileons and their Novel Limit
• Gödel-type Solutions in Cubic Galileon Gravity
• Prospects of constraining on the polarizations of gravitational waves from binary black holes using space- and ground-based detectors
• All $2D$ generalised dilaton theories from $d\ge 4$ gravities
• Black branes in asymptotically Lifshitz spacetimes in $\kappa$-deformed Horndeski gravity
• Running vacuum and H^4-inflation
• First-order correction of tunneling and entropy in the Horndeski gravity-like hairy black hole
• Teleparallel dark energy in a nonflat universe
• Post-Newtonian Binary Dynamics in Effective Field Theory of Horndeski Gravity
• Healthy Horndeski cosmologies with torsion
• Special Issue on Modified Gravity Approaches to the Tensions of $\Lambda$CDM: Goals and Highlights
• Gravitational wave stochastic background in reduced Horndeski theories
• The reheating constraints to natural inflation in Horndeski gravity
• Generalized Horndeski-Like Einstein Gauss-Bonnet Inflation with Massless Primordial Gravitons
• Void Lensing in Cubic Galileon Gravity
• Measuring the modified gravitational waves propagation beyond general relativity from CMB observations
• On the equivalence between Sáez-Ballester theory and Einstein-scalar field system
• Ghost Free Theory in Unitary Gauge: A New Candidate
• Tidal deformation of black holes in Lovelock gravity
• Propagating Gravitational Waves in Teleparallel Gauss-Bonnet Gravity
• Fast simulation mapping: from standard to modified gravity cosmologies using the bias assignment method
• K-inflation: the legitimacy of classical treatment
• On constrained analysis and diffeomorphism invariance of generalised Proca theories
• Flows into de Sitter space from anisotropic initial conditions: An effective field theory approach
• Shadows of a generic class of spherically symmetric, static spacetimes
• Neutrino mass and kinetic gravity braiding degeneracies
• Gravitational wave energy momentum-tensor in reduced Horndeski theories
• Recent Developments in Degenerate Higher Order Scalar Tensor Theories
• Field transformations and invariant quantities in scalar-teleparallel theories of gravity
• Extending the symmetry of the massless Klein-Gordon equation under the general disformal transformation
• Axial perturbations of black holes in scalar-tensor gravity: near-horizon behaviour
• Scaling symmetry, Smarr relation, and the extended first law in lower-dimensional Lovelock gravity
• Misinterpreting Modified Gravity as Dark Energy: a Quantitative Study
• A Bright Future? Prospects for Cosmological Tests of GR with Multimessenger Gravitational Wave Events
• Non-Singular Bouncing cosmology from Phantom Scalar-Gauss-Bonnet Coupling: Reconstruction with Observational Insights
• Luminal Scalar-Tensor theories for a not so dark Dark Energy
• Modified Friedmann equations and non-singular cosmologies in $d=4$ non-polynomial quasi-topological gravities
• Bouncing and Cyclic Quantum Primordial Universes and the Ordering Problem
• Fifth forces and frame invariance
• The primordial non-Gaussianities for non-singular Horndeski cosmologies
• Constraining the modified friction in gravitational wave propagation with precessing black hole binaries
• Symmetry restoration in the vicinity of neutron stars with a nonminimal coupling
• Metric-affine cosmological models and the inverse problem of the calculus of variations. Part 1: variational bootstrapping -- the method
• K-mouflage at high $k$: extending the reach of $\text{Hi-COLA}$
• Skewness consistency relation in large-scale structure and test of gravity theory
• A Post-Newtonian Analysis of Regularized 4D-EGB Theory: Complete Set of PPN Parameters and Observational Constraints
• PPN meets EFT of dark energy: Post-Newtonian approximation in higher-order scalar-tensor theories
• Vector-tensor gravity from a broken gauge symmetry
• Perturbations in Horndeski theory above anisotropic cosmological background
• Gauge invariant perturbations in teleparallel Horndeski gravity
• Extended Gravity Constraints at Different Scales
• KiDS-Legacy: Constraints on Horndeski gravity from weak lensing combined with galaxy clustering and cosmic microwave background anisotropies
• Hamiltonian Analysis of Nonlocal F(R) Gravity Models
• Holographic Anisotropic Background in 5D Einstien-Gauss-Bonnet Gravity
• Compact stars in Einstein-scalar-Gauss-Bonnet gravity: regular and divergent scalar field configurations
• Inflation with the Chern-Simons term in the Palatini formulation
• Implications of pulsar timing arrays for Gauss-Bonnet Inflation
• Nonminimal Derivative Coupling Cosmology and the Speed of Gravitational Waves
• Primordial gravitational waves in DHOST inflation
• Eckart heat-flux applicability in $F(\Phi ,X)R$ theories and the existence of temperature gradients
• Dark matter candidate induced by Horndeski theory: dark matter halo and cosmological evolution
• Linear and nonlinear clusterings of Horndeski-inspired dark energy models with fast transition
• Equivalence of EFTs and Time-Like Extra Dimensions
• Cuscuton-like contribution to dark energy evolution
• On the KG-constrained general disformal transformation of the Einstein-Hilbert action
• Thermal channels of scalar and tensor waves in Jordan-frame scalar--tensor gravity
• Dynamical Shortcomings in the Generalized SU(2) Proca Theory: Challenges for Cosmic Acceleration
• Regular Black Hole Cores via Gravitational Evanescence of Collapsing Matter
• Ultra-light dark matter with non-canonical kinetics reopening the mass window
• Generalized Galileon Scenario Inspires Chaotic Inflation
• Neutron stars as extreme gravity probes
• Theoretical filters for shift-symmetric Horndeski gravities
• Cosmological scalar perturbations in Horndeski-like gravity
• Galileon versus Quintessence: A comparative phase space analysis and late-time cosmic relevance
• A new mechanism for freezing extra dimensions with higher-order curvature terms
• Spatial Dependence of the Growth Factor in Scalar-Tensor Cosmology
• Stochastic gravitational wave background anisotropies from inflation with non-Bunch-Davies states
• Extremal cosmological black holes in Horndeski gravity and the anti-evaporation regime
• Neural Post-Einsteinian Test of General Relativity with the Third Gravitational-Wave Transient Catalog
• Motion of test particles around an Einstein-dilaton-Gauss-Bonnet black hole in a uniform magnetic field
• Post-Newtonian limit of generalized scalar-teleparallel theories of gravity
• Thick branes in Horndeski gravity
• Infrared Sensitivity of Cosmological Probes in Horndeski Theory
• Cooling-Heating Properties of the FRW Universe in Gravity with a Generalized Conformal Scalar Field
• Linear instability of hairy black holes in Horndeski theory
• Qualitative analysis of a quasi-magnetic universe
• Manifestation of Quantum Forces in Spacetime: Towards a General Theory of Quantum Forces
• Horndeski model in nonlinearly realized supergravity
• Stealth black hole solutions in higher-order Maxwell-Einstein theories
• Unique gravitational wave signatures of GLPV scalar-tensor theories
• CLASH-VLT: The Fifth Force in Chameleon Gravity from Joint Lensing and Kinematics Cluster Mass Profiles
• Non-minimal Effective Scalar-Tensor Gravity in the Early Universe
• Cosmic acceleration from string induced Galileons
• Scalar-scalar-tensor interaction in DHOST theories
• Bayesian and Machine-Learning Analyses of Nonminimal $f(Q)$ Gravity and $H_0$ Tension
• Beyond $f(\varphi )\mathcal{G}$: Gauss--Bonnet inflation with $\mu (\varphi ,X)$
• Effect of primary scalar hair on black hole's strong lensing in Beyond Horndeski Gravity
• Black hole sensitivities in Einstein-scalar-Gauss-Bonnet gravity
• Inflation with the Gauss-Bonnet term in the Palatini formulation
• Tracing Signatures of Modified Gravity in Redshift-Space Galaxy Bispectrum Multipoles: Prospects for Euclid
• Generalized Chern-Pontryagin models
• Testing the Non-circularity of the Spacetime around Sagittarius A* with Orbiting Pulsars
• New brane-like solutions in modified four-dimensional Einstein-Gauss-Bonnet gravity
• Gravitational collapse involving electric charge in the decoupling limit of the dilatonic Gauss--Bonnet gravity
• (Lovelock)${}^2$ inflation: explaining the ACT data and equivalence to Higgs-Gauss-Bonnet inflation
• Straight and Wiggly Cosmic Strings in Horndeski Theory
• EFT of Dark Energy with Cosmic Chronometers: Reconstructing Background EFT Functions
• Higher-order gravity models: corrections up to cubic curvature invariants and inflation
• Neutron Stars in Scalar Torsion Theories with Nonminimal Coupling
• Measuring the speed of scalar induced gravitational waves from observations
• Phenomenology of Schwarzschild-like Black Holes with a Generalized Compton Wavelength
• No-Go theorem in the cubic subclass of Horndeski theory for spherically symmetric dynamical background
• Kaluza-Klein Bubble With Massive Scalar Field
• Perturbations and stability conditions of k-essence and kinetic gravity braiding models in two-field measure theory
• Kinetically stabilized inflation
• Propagation of tensor perturbation in Horndeski-like gravity
• Cherenkov radiation as ghost instability