Dark Energy and Modified Gravity in Degenerate Higher-Order Scalar-Tensor (DHOST) theories: a review

Abstract

This article reviews scalar-tensor theories characterized by a Lagrangian that, despite the presence of second order derivatives, contain a single scalar degree of freedom. These theories, known as Degenerate Higher-Order Scalar-Tensor (DHOST) theories, include Horndeski and Beyond Horndeski theories. They propagate a single scalar mode as a consequence of the degeneracy of their Lagrangian and, therefore, are not plagued by an Ostrodradsky instability. They have been fully classified up to cubic order in second-order derivatives. The study of their phenomenological consequences restricts the subclass of DHOST theories that are compatible with observations. In cosmology, these theories can be described in the language of the unified effective approach to dark energy and modified gravity. Compact objects in the context of DHOST theories are also discussed.

arXiv comment29 pages; 2 figures

References in corpus (121)

• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• Gravitational Waves and Gamma-rays from a Binary Neutron Star Merger: GW170817 and GRB 170817A
• The galileon as a local modification of gravity
• Generalized G-inflation: Inflation with the most general second-order field equations
• From k-essence to generalised Galileons
• Dark Energy after GW170817: dead ends and the road ahead
• Strong constraints on cosmological gravity from GW170817 and GRB 170817A
• Dark Energy after GW170817 and GRB170817A
• Implications of the Neutron Star Merger GW170817 for Cosmological Scalar-Tensor Theories
• Healthy theories beyond Horndeski
• Degenerate higher derivative theories beyond Horndeski: evading the Ostrogradski instability
• Transforming gravity: from derivative couplings to matter to second-order scalar-tensor theories beyond the Horndeski Lagrangian
• The Effective Field Theory of Dark Energy
• The Relation between Physical and Gravitational Geometry
• Exploring gravitational theories beyond Horndeski
• General second order scalar-tensor theory, self tuning, and the Fab Four
• Maximal freedom at minimum cost: linear large-scale structure in general modifications of gravity
• Degenerate higher order scalar-tensor theories beyond Horndeski up to cubic order
• Essential Building Blocks of Dark Energy
• Extended Scalar-Tensor Theories of Gravity
• Mimetic Dark Matter
• Degenerate higher order scalar-tensor theories beyond Horndeski and disformal transformations
• Galilean Genesis: an alternative to inflation
• Dark Energy or Modified Gravity? An Effective Field Theory Approach
• G-Bounce
• Scalar-tensor theories and modified gravity in the wake of GW170817
• Mimetic gravity: a review of recent developments and applications to cosmology and astrophysics
• Disformal invariance of second order tensor-scalar theories: framing the Horndeski action
• Gravitational Rainbows: LIGO and Dark Energy at its Cutoff
• Asymptotically flat black holes in Horndeski theory and beyond
• A unifying description of dark energy
• Hamiltonian analysis of higher derivative scalar-tensor theories
• Unifying framework for scalar-tensor theories of gravity
• Vainshtein screening in a cosmological background in the most general second-order scalar-tensor theory
• The Parameterized Post-Friedmann Framework for Theories of Modified Gravity: Concepts, Formalism and Examples
• Dark Energy in light of Multi-Messenger Gravitational-Wave astronomy
• Effective Description of Higher-Order Scalar-Tensor Theories
• Generalized framework for testing gravity with gravitational-wave propagation. II. Constraints on Horndeski theory
• Classically stable non-singular cosmological bounces
• The Effective Field Theory of nonsingular cosmology
• Black holes and stars in Horndeski theory
• Healthy degenerate theories with higher derivatives
• Breaking of Vainshtein screening in scalar-tensor theories beyond Horndeski
• Effective theory for the Vainshtein mechanism from the Horndeski action
• Vainshtein mechanism after GW170817
• Gravitational Wave Decay into Dark Energy
• Horndeski: beyond, or not beyond?
• Generalized Galileons: instabilities of bouncing and Genesis cosmologies and modified Genesis
• Relativistic Stars in Beyond Horndeski Theories
• Beyond generalized Proca theories
• Slowly rotating neutron stars in the nonminimal derivative coupling sector of Horndeski gravity
• The Observational Future of Cosmological Scalar-Tensor Theories
• Astrophysical Probes of the Vainshtein Mechanism: Stars and Galaxies
• The observational status of Galileon gravity after Planck
• Beyond Lovelock gravity: Higher derivative metric theories
• A Simplified Approach to General Scalar-Tensor Theories
• Hamiltonian analysis of spatially covariant gravity
• Derivative-dependent metric transformation and physical degrees of freedom
• Hydrogen Burning in Low Mass Stars Constrains Alternative Gravity Theories
• Effective Theory of Interacting Dark Energy
• Vainshtein Screening in Scalar-Tensor Theories before and after GW170817: Constraints on Theories beyond Horndeski
• What can Cosmology tell us about Gravity? Constraining Horndeski with Sigma and Mu
• Modified gravity inside astrophysical bodies
• On the local well-posedness of Lovelock and Horndeski theories
• Testing Gravity Using Dwarf Stars
• Extended vector-tensor theories
• "Shadowy" modes in Higher-Order Scalar-Tensor theories
• Stability of Geodesically Complete Cosmologies
• A covariant Lagrangian for stable nonsingular bounce
• Effective action approach to cosmological perturbations in dark energy and modified gravity
• Ostrogradsky in Theories with Multiple Fields
• Self-accelerating universe in scalar-tensor theories after GW170817
• White Dwarf Critical Tests for Modified Gravity
• Weakly Broken Galileon Symmetry
• Counting the degrees of freedom of generalized Galileons
• Slowly rotating black hole solutions in Horndeski gravity
• Extended mimetic gravity: Hamiltonian analysis and gradient instabilities
• Stability of a black hole and the speed of gravity waves within self-tuning cosmological models
• Neutron stars in Horndeski gravity
• Hamiltonian structure of scalar-tensor theories beyond Horndeski
• Cosmological bounce and Genesis beyond Horndeski
• Testing Gravity Using Galaxy Clusters: New Constraints on Beyond Horndeski Theories
• Cosmological Constraints on Horndeski Gravity in Light of GW170817
• Effective Theory of Dark Energy at Redshift Survey Scales
• Exorcising the Ostrogradsky ghost in coupled systems
• Mimetic gravity as DHOST theories
• Cosmological self-tuning and local solutions in generalized Horndeski theories
• No Slip Gravity
• Large-scale structure phenomenology of viable Horndeski theories
• Towards Strong Field Tests of Beyond Horndeski Gravity Theories
• Partial accretion in the propeller stage of low mass X-ray binary Aql X--1
• White dwarfs and revelations
• Higher Derivative Field Theories: Degeneracy Conditions and Classes
• Ghost-free theory with third-order time derivatives
• Dark Energy and Modified Gravity in the Effective Field Theory of Large-Scale Structure
• Phenomenology of dark energy: general features of large-scale perturbations
• Ghost-free theories with arbitrary higher-order time derivatives
• Testing general scalar-tensor gravity and massive gravity with cluster lensing
• Dark energy scenario consistent with GW170817 in theories beyond Horndeski gravity
• Bounce beyond Horndeski with GR asymptotics and $\gamma$-crossing
• Challenges in Connecting Modified Gravity Theory and Observations
• Signatures of Horndeski gravity on the Dark Matter Bispectrum
• Relativistic stars in degenerate higher-order scalar-tensor theories after GW170817
• On the hyperbolicity of the most general Horndeski theory
• Weakening Gravity on Redshift-Survey Scales with Kinetic Matter Mixing
• Reconstructing Horndeski theories from phenomenological modified gravity and dark energy models on cosmological scales
• Space-time slicing in Horndeski theories and its implications for non-singular bouncing solutions
• Phenomenology of Large Scale Structure in scalar-tensor theories: joint prior covariance of $w_{\text{DE}}$, $\Sigma$ and $\mu$ in Horndeski
• Parametrizing modified gravity for cosmological surveys
• Hiding neutrino mass in modified gravity cosmologies
• Doppelgänger dark energy: modified gravity with non-universal couplings after GW170817
• Cosmological evolution in DHOST theories
• Observational signatures of the theories beyond Horndeski
• Compact objects in scalar-tensor theories after GW170817
• Behind Horndeski: Structurally Robust Higher Derivative EFTs
• Matter bispectrum beyond Horndeski
• Diagnostic of Horndeski Theories
• Investigating scalar-tensor-gravity with statistics of the cosmic large-scale structure
• Cosmology with a successful Vainshtein screening in theories beyond Horndeski
• The sound of DHOST
• Cosmic structures and gravitational waves in ghost-free scalar-tensor theories of gravity

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• Black holes with primary scalar hair
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• Invertible disformal transformations with higher derivatives
• Intermittent null energy condition violations during inflation and primordial gravitational waves
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• Cosmological tests of the osculating Barthel-Kropina dark energy model
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• Genesis with general relativity asymptotics in beyond Horndeski theory
• Dark energy and accelerating cosmological evolution from osculating Barthel-Kropina geometry
• Generalized Regge-Wheeler Equation from Effective Field Theory of Black Hole Perturbations with a Timelike Scalar Profile
• Minimally modified gravity with an auxiliary constraint: a Hamiltonian construction
• Gravitational waves and geometrical optics in scalar-tensor theories
• Perturbations and quasi-normal modes of black holes with time-dependent scalar hair in shift-symmetric scalar-tensor theories
• On the screening mechanism in DHOST theories evading gravitational wave constraints
• Reconsidering the Ostrogradsky theorem: Higher-derivatives Lagrangians, Ghosts and Degeneracy
• Pre-inflation and Trans-Planckian Censorship
• Degeneracy, matter coupling, and disformal transformations in scalar-tensor theories
• Black holes with a nonconstant kinetic term in degenerate higher-order scalar tensor theories
• Anisotropic cosmological models in Horndeski gravity
• Tidal effects up to next-to-next-to leading post-Newtonian order in massless scalar-tensor theories
• General formulation of cosmological perturbations in scalar-tensor dark energy coupled to dark matter
• Black hole hairs in scalar-tensor gravity and the lack thereof
• Gravitational transitions via the explicitly broken symmetron screening mechanism
• New constraints on cosmological modified gravity theories from anisotropic three-point correlation functions of BOSS DR12 galaxies
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• Invertible disformal transformations with arbitrary higher-order derivatives
• Perturbations of a rotating black hole in DHOST theories
• Disformal Transition of a Black Hole to a Wormhole in Scalar-Tensor Horndeski Theory
• Higher derivative scalar-tensor theory and spatially covariant gravity: the correspondence
• Horndeski genesis: consistency of classical theory
• 50 Years of Horndeski Gravity: Past, Present and Future
• Subluminal cosmological bounce beyond Horndeski
• Disformal transformation of stationary and axisymmetric solutions in modified gravity
• Positivity in the effective field theory of cosmological perturbations
• Constraints on the growth rate using the observed galaxy power spectrum
• Spatially covariant gravity with two degrees of freedom: perturbative analysis
• More on the first-order thermodynamics of scalar-tensor and Horndeski gravity
• Consistency of higher derivative couplings to matter fields in scalar-tensor gravity
• Alleviating $H_0$ tension in scalar-tensor and bi-scalar-tensor theories
• Constraining the growth rate by combining multiple future surveys
• Detecting Dark Energy Fluctuations with Gravitational Waves
• MG-MAMPOSSt: A code to test modifications of gravity with the dynamics of galaxy clusters
• Disforming to Conformal Symmetry
• Reconstruction of mimetic gravity in a non-singular bouncing universe from quantum gravity
• Limiting curvature mimetic gravity for group field theory condensates
• The first variation of the matter energy-momentum tensor with respect to the metric, and its implications on modified gravity theories
• Solar System tests and chameleon effect in f (R) gravity
• On the effective metric of axial black hole perturbations in DHOST gravity
• Compressed baryon acoustic oscillation analysis is robust to modified-gravity models
• Testing gravity theories with cosmic microwave background in the degenerate higher-order scalar-tensor theory
• Sudden singularities in generalized hybrid metric-Palatini cosmologies
• Ostrogradsky mode in scalar-tensor theories with higher-order derivative couplings to matter
• Modified gravity in the interior of population II stars
• Perturbative unitarity and NEC violation in genesis cosmology
• Approximately stealth black hole in higher-order scalar-tensor theories
• Fifth forces and broken scale symmetries in the Jordan frame
• Unified $f(R)$ gravity at local scales
• Thermodynamics of black holes featuring primary scalar hair
• Constraining modified gravity from tidal phenomena in binary stars
• Odd-parity perturbations of the wormhole-like geometries and quasi-normal modes in Einstein-Æther theory
• Addressing Cosmological Tensions by Non-Local Gravity
• Disformal map and Petrov classification in modified gravity
• Constraining DHOST theories with linear growth of matter density fluctuations
• Covariant 3+1 correspondence of the spatially covariant gravity and the degeneracy conditions
• Higher derivative scalar-tensor theory from the spatially covariant gravity: a linear algebraic analysis
• CMB constraints on DHOST theories
• Superluminality in DHOST theory with extra scalar
• Past-directed scalar field gradients and scalar-tensor thermodynamics
• Small Anisotropy in Stellar Objects in Modified Theories of Gravity
• Relativistic Khronon Theory in agreement with Modified Newtonian Dynamics and Large-Scale Cosmology
• Neutron Stars in Modified Teleparallel Gravity
• Multi-fluid cosmology in Einstein gravity: analytical solutions
• White dwarfs in regularized 4D Einstein-Gauss-Bonnet gravity
• Multi-component DHOST analysis in galaxy clusters
• Shape of Dark Energy: Constraining Its Evolution with a General Parametrization
• Constraining Palatini-Horndeski theory with gravitational waves after GW170817
• Quadratic DHOST theories revisited
• Superluminality in beyond Horndeski theory with extra scalar field
• Noncompactified Kaluza--Klein Gravity
• Early evolution of fully convective stars in scalar-tensor gravity
• Observational constraints on varying fundamental constants in a minimal CPC model
• UV sensitive one-loop matter power spectrum in degenerate higher-order scalar-tensor theories
• Stable cosmological solutions in Horndeski theory
• Length-preserving biconnection gravity and its cosmological implications
• Stable non-singular cosmologies in beyond Horndeski theory and disformal transformations
• Interacting Models of Dark Energy and Dark Matter in Einstein scalar Gauss Bonnet Gravity
• Dissipative quintessence, and its cosmological implications
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• Neutron stars in degenerate higher-order scalar-tensor theories
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• Higher Derivative Scalar Tensor Theory in Unitary Gauge
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