Exploring gravitational theories beyond Horndeski

Abstract

We have recently proposed a new class of gravitational scalar-tensor theories free from Ostrogradski instabilities, in arXiv:1404.6495. As they generalize Horndeski theories, or "generalized" galileons, we call them G${}^3$. These theories possess a simple formulation when the time hypersurfaces are chosen to coincide with the uniform scalar field hypersurfaces. We confirm that they contain only three propagating degrees of freedom by presenting the details of the Hamiltonian formulation. We examine the coupling between these theories and matter. Moreover, we investigate how they transform under a disformal redefinition of the metric. Remarkably, these theories are preserved by disformal transformations that depend on the scalar field gradient, which also allow to map subfamilies of G${}^3$ into Horndeski theories.

33 pages, added comments and corrected typos as in JCAP version

References in corpus (15)

• Covariant Galileon
• Generalized Galileons: All scalar models whose curved background extensions maintain second-order field equations and stress tensors
• Imperfect Dark Energy from Kinetic Gravity Braiding
• Starting the Universe: Stable Violation of the Null Energy Condition and Non-standard Cosmologies
• Avoiding Dark Energy with 1/R Modifications of Gravity
• Maximal freedom at minimum cost: linear large-scale structure in general modifications of gravity
• Models of non-relativistic quantum gravity: the good, the bad and the healthy
• The Effective Theory of Quintessence: the w<-1 Side Unveiled
• Unifying framework for scalar-tensor theories of gravity
• Hamiltonian structure of scalar-tensor theories beyond Horndeski
• Effective field theory of modified gravity with two scalar fields: dark energy and dark matter
• The effective field theory of inflation/dark energy and the Horndeski theory
• Cosmology in generalized Horndeski theories with second-order equations of motion
• Who You Gonna Call? Runaway Ghosts, Higher Derivatives and Time-Dependence in EFTs
• Non-Gaussian inflationary shapes in $G^3$ theories beyond Horndeski

Cited by in corpus (78)

• Dark Energy after GW170817: dead ends and the road ahead
• Implications of the Neutron Star Merger GW170817 for Cosmological Scalar-Tensor Theories
• Healthy theories beyond Horndeski
• Horndeski theory and beyond: a review
• Degenerate higher order scalar-tensor theories beyond Horndeski up to cubic order
• Mimetic gravity: a review of recent developments and applications to cosmology and astrophysics
• Galileon Gravity in Light of ISW, CMB, BAO and $H_0$ data
• Vainshtein mechanism after GW170817
• On the consistency of universally non-minimally coupled $f(R,T,R_{\mu \nu }{T}^{\mu \nu })$ theories
• Modified gravity inside astrophysical bodies
• Selected topics in scalar-tensor theories and beyond
• Stability of Geodesically Complete Cosmologies
• Horndeski theories self-tuning to a de Sitter vacuum
• Cosmological self-tuning and local solutions in generalized Horndeski theories
• Vainshtein regime in Scalar-Tensor gravity: constraints on DHOST theories
• Fundamental theorem on gauge fixing at the action level
• Hairy black holes in DHOST theories: Exploring disformal transformation as a solution-generating method
• Towards Strong Field Tests of Beyond Horndeski Gravity Theories
• A comparison of Einstein-Boltzmann solvers for testing General Relativity
• Shaken, not stirred: kinetic mixing in scalar-tensor theories of gravity
• Unveiling the Dynamics of the Universe
• Disformal invariance of cosmological perturbations in a generalized class of Horndeski theories
• Anisotropic cosmological solutions in massive vector theories
• Optimising growth of structure constraints on modified gravity
• Weakening Gravity on Redshift-Survey Scales with Kinetic Matter Mixing
• Effective field theory for gravitational radiation in scalar-tensor gravity
• Parametrizing modified gravity for cosmological surveys
• A no-hair theorem for stars in Horndeski theories
• Observational signatures of the theories beyond Horndeski
• Gravitational lensing by a Horndeski black hole
• Spontaneous scalarization of black holes in the Horndeski theory
• Cosmological black holes and white holes with time-dependent mass
• Exploring degeneracies in modified gravity with weak lensing
• On the stability conditions for theories of modified gravity in presence of matter fields
• On the screening mechanism in DHOST theories evading gravitational wave constraints
• Higher order derivative coupling to gravity and its cosmological implications
• Cosmological models in modified gravity theories with extended nonminimal derivative couplings
• Diagnostic of Horndeski Theories
• New constraints on cosmological modified gravity theories from anisotropic three-point correlation functions of BOSS DR12 galaxies
• Quantum Corrections in Galileons from Matter Loops
• Stellar Pulsations in Beyond Horndeski Gravity Theories
• Spin-orbit effects for compact binaries in scalar-tensor gravity
• Spatially covariant gravity: Perturbative analysis and field transformations
• Topological black hole in the theory with nonminimal derivative coupling with power-law Maxwell field and its thermodynamics
• A geometrical approach to degenerate scalar-tensor theories
• Higher derivative scalar-tensor theory and spatially covariant gravity: the correspondence
• Forecasts for Low Spin Black Hole Spectroscopy in Horndeski Gravity
• 50 Years of Horndeski Gravity: Past, Present and Future
• Inflationary gravitational waves in the effective field theory of modified gravity
• Disforming to Conformal Symmetry
• Perturbative unitarity and NEC violation in genesis cosmology
• Horndeski stars
• No need for dark matter in galaxy clusters within Galileon theory
• Constraining DHOST theories with linear growth of matter density fluctuations
• Superluminality in DHOST theory with extra scalar
• CMB lensing bi-spectrum: assessing analytical predictions against full-sky lensing simulations
• Quadratic DHOST theories revisited
• Tackling non-linearities with the effective field theory of dark energy and modified gravity
• Superluminality in beyond Horndeski theory with extra scalar field
• Disformal mappings of spherical DHOST geometries
• Neutron stars in degenerate higher-order scalar-tensor theories
• Absence of solid angle deficit singularities in beyond-generalized Proca theories
• Generalising the matter coupling in massive gravity: a search for new interactions
• On the Coupling of Generalized Proca Fields to Degenerate Scalar-Tensor Theories
• Potential-driven Inflation with Disformal Coupling to Gravity
• On covariant expansion of the gravitational Stückelberg trick
• Generalized Horndeski-Like Einstein Gauss-Bonnet Inflation with Massless Primordial Gravitons
• The effective field theory of dark energy diagnostic of linear Horndeski theories after GW170817 and GRB170817A
• Vainshtein mechanism in massive gravity nonlinear sigma models
• Higher-Order Spectra of Weak Lensing Convergence Maps in Parameterized Theories of Modified Gravity
• An effective description of dark energy: from theory to phenomenology
• New time-dependent solutions of viable Horndeski gravity
• Gravitational wave interactions in ${\Lambda }_3$ models of dark energy
• Cosmological perturbations in the spatially covariant gravity with a dynamical lapse function
• New effective theories of gravitation and their phenomenological consequences
• The Black Hole Window on Cosmic Inflation
• Scale-dependence in DHOST inflation
• Weakly Broken Galileon Symmetry in Cosmology