A new covariant foliation-based construction of scalar-tensor theories up to four derivatives of the scalar field that extends DHOST and U-DHOST without unitary gauge and propagates three degrees of freedom.
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Degenerate higher derivative theories beyond Horndeski: evading the Ostrogradski instability
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abstract
Theories with higher order time derivatives generically suffer from ghost-like instabilities, known as Ostrogradski instabilities. This fate can be avoided by considering "degenerate" Lagrangians, whose kinetic matrix cannot be inverted, thus leading to constraints between canonical variables and a reduced number of physical degrees of freedom. In this work, we derive in a systematic way the degeneracy conditions for scalar-tensor theories that depend quadratically on second order derivatives of a scalar field. We thus obtain a classification of all degenerate theories within this class of scalar-tensor theories. The quartic Horndeski Lagrangian and its extension beyond Horndeski belong to these degenerate cases. We also identify new families of scalar-tensor theories with the intriguing property that they are degenerate despite the nondegeneracy of the purely scalar part of their Lagrangian.
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representative citing papers
Derives primary degeneracy matrix conditions, antisymmetric consistency conditions from constraint preservation, and a final rank condition sufficient to ensure quadratic multi-field higher-derivative scalar-tensor theories propagate only 2+N degrees of freedom without extra Ostrogradsky modes.
Extends the stochastic inflation formalism to a wide class of scalar-tensor theories by mapping EFT of dark energy coefficients to stochastic equations of motion.
A metric-affine version of quadratic DHOST theories is derived and reduced to a one-function family that satisfies degeneracy conditions and light-speed gravitational wave propagation.
Requiring stealth Schwarzschild and de Sitter solutions in quadratic/cubic scalar-tensor theories eliminates odd-parity deviations from GR when all solutions are required, while allowing some deviations and non-trivial GW speeds in less restrictive cases.
A master screening equation is derived for luminal Horndeski gravity that recovers Vainshtein and Chameleon mechanisms and introduces Phaedrus screening with screening radius scaling linearly with source mass.
The Paneitz operator in 4D belongs to extended mimetic gravity and is constrained by gravitational wave propagation speed.
Bumblebee gravity enhances primordial black hole abundance through three mechanisms, but the model harbors a ghost instability and a tachyonic instability that make it cosmologically unviable.
Radial perturbations of black holes with primary hair in DHOST theories are rewritten as a flat radial wave equation whose positive self-adjoint extension guarantees stability of the monopole mode.
Exact Schwarzschild and Kerr geometries in a disformally related frame yield secondary disformal scalar hair on black holes in a projectively invariant scalar-torsion theory.
Derives the cubic scalar-scalar-tensor interaction action for perturbations in quadratic DHOST theories on cosmological backgrounds.
The Coherence Principle supplies a falsifiable prior for Bayesian model selection by converting compatibility with a theory's validated grammar into prior weights via a maximum-entropy exponential controlled by one parameter.
Using simulated binary black hole mergers and neutral hydrogen maps, the radio sirens method constrains H0 to 8% precision with 3000 high-SNR events, offering a 90% improvement over standard dark siren analyses.
An effective constrained scalar-Gauss-Bonnet inflation model yields n_s ≃ 0.958 and r ≃ 2.7×10^{-4} while the exact theory has no propagating scalar degree of freedom.
In scalar-vector-tensor gravity, the vector-curvature coupling alters neutron star mass-radius curves and radial oscillation frequencies while preserving the coincidence of maximum mass with the onset of radial instability.
Dynamical systems analysis of a Palatini k-essence model identifies fixed points for quasi-de-Sitter epochs, scaling solutions, and quintessence phases connected by heteroclinic orbits in flat FLRW cosmology.
Numerical simulations show ghost-normal scalar systems can remain dynamically bounded for long times when initial data is ultraviolet-dominated and low-amplitude, with some nonlinear potentials creating transient metastable states.
Neutron stars with primary scalar hair in a DHOST subfamily are more compact than GR predictions and develop singularities above a critical scalar charge threshold.
Refines two-field DHOST bouncing model to match observed f_NL and keep strong-coupling scale above background energy, claiming full viability at linear and non-linear levels.
In DHOST theories consistent with GW observations, deviations from GR suppress high-redshift galaxy cluster abundance relative to ΛCDM when using spherical collapse and analytic mass functions matched to eROSITA data.
Reconstruction of EFT background functions from cosmic chronometer Hubble data allows model-independent tests of dark energy evolution in scalar-tensor theories.
A review thesis covering Mukhanov parametrization, general scalar-tensor theories, and new slow-roll techniques for canonical and noncanonical inflation observables.
citing papers explorer
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Covariant scalar-tensor theories beyond second derivatives
A new covariant foliation-based construction of scalar-tensor theories up to four derivatives of the scalar field that extends DHOST and U-DHOST without unitary gauge and propagates three degrees of freedom.
-
Removing Ostrogradsky modes in multi-field higher-order scalar-tensor theories
Derives primary degeneracy matrix conditions, antisymmetric consistency conditions from constraint preservation, and a final rank condition sufficient to ensure quadratic multi-field higher-derivative scalar-tensor theories propagate only 2+N degrees of freedom without extra Ostrogradsky modes.
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Stochastic scalar-tensor inflation and beyond
Extends the stochastic inflation formalism to a wide class of scalar-tensor theories by mapping EFT of dark energy coefficients to stochastic equations of motion.
-
Degenerate higher-order scalar-tensor theories in metric-affine gravity
A metric-affine version of quadratic DHOST theories is derived and reduced to a one-function family that satisfies degeneracy conditions and light-speed gravitational wave propagation.
-
Inverting no-hair theorems: How requiring General Relativity solutions restricts scalar-tensor theories
Requiring stealth Schwarzschild and de Sitter solutions in quadratic/cubic scalar-tensor theories eliminates odd-parity deviations from GR when all solutions are required, while allowing some deviations and non-trivial GW speeds in less restrictive cases.
-
A Master Equation for Screening in Luminal Horndeski Gravity
A master screening equation is derived for luminal Horndeski gravity that recovers Vainshtein and Chameleon mechanisms and introduces Phaedrus screening with screening radius scaling linearly with source mass.
-
Gravitational wave constraints on the Paneitz operator
The Paneitz operator in 4D belongs to extended mimetic gravity and is constrained by gravitational wave propagation speed.
-
Primordial black hole in Lorentz-violating theories: Insights from Bumblebee gravity
Bumblebee gravity enhances primordial black hole abundance through three mechanisms, but the model harbors a ghost instability and a tachyonic instability that make it cosmologically unviable.
-
Radial Perturbations of Black Holes in DHOST Theories
Radial perturbations of black holes with primary hair in DHOST theories are rewritten as a flat radial wave equation whose positive self-adjoint extension guarantees stability of the monopole mode.
-
Nonrotating and rotating black holes with secondary disformal hair in a ghost-free metric-affine parity-violating scalar-torsion theory
Exact Schwarzschild and Kerr geometries in a disformally related frame yield secondary disformal scalar hair on black holes in a projectively invariant scalar-torsion theory.
-
Scalar-scalar-tensor interaction in DHOST theories
Derives the cubic scalar-scalar-tensor interaction action for perturbations in quadratic DHOST theories on cosmological backgrounds.
-
The Coherence Principle: A Falsifiable Prior for Model Selection from the Grammar of Theories
The Coherence Principle supplies a falsifiable prior for Bayesian model selection by converting compatibility with a theory's validated grammar into prior weights via a maximum-entropy exponential controlled by one parameter.
-
Radio sirens: inferring $H_0$ with binary black holes and neutral hydrogen in the era of the Einstein Telescope and the SKA Observatory
Using simulated binary black hole mergers and neutral hydrogen maps, the radio sirens method constrains H0 to 8% precision with 3000 high-SNR events, offering a 90% improvement over standard dark siren analyses.
-
Effective Constrained Scalar--Gauss--Bonnet Inflation Motivated by $f(R,\mathcal{G})$ Gravity
An effective constrained scalar-Gauss-Bonnet inflation model yields n_s ≃ 0.958 and r ≃ 2.7×10^{-4} while the exact theory has no propagating scalar degree of freedom.
-
Radial Oscillations of Neutron Stars with Vector-Induced Scalar Hair
In scalar-vector-tensor gravity, the vector-curvature coupling alters neutron star mass-radius curves and radial oscillation frequencies while preserving the coincidence of maximum mass with the onset of radial instability.
-
Dynamical system analysis of the cosmological phases in Palatini $k$-essence gravity
Dynamical systems analysis of a Palatini k-essence model identifies fixed points for quasi-de-Sitter epochs, scaling solutions, and quintessence phases connected by heteroclinic orbits in flat FLRW cosmology.
-
Numerical Investigations of Stable Dynamics in the Presence of Ghosts
Numerical simulations show ghost-normal scalar systems can remain dynamically bounded for long times when initial data is ultraviolet-dominated and low-amplitude, with some nonlinear potentials creating transient metastable states.
-
Neutron stars with primary scalar hair
Neutron stars with primary scalar hair in a DHOST subfamily are more compact than GR predictions and develop singularities above a critical scalar charge threshold.
-
Non-Gaussianity and Strong-Coupling Problem in a Two-Field DHOST Bouncing Model
Refines two-field DHOST bouncing model to match observed f_NL and keep strong-coupling scale above background energy, claiming full viability at linear and non-linear levels.
-
Spherical collapse and cluster number counts in DHOST theories that pass the constraints from gravitational waves
In DHOST theories consistent with GW observations, deviations from GR suppress high-redshift galaxy cluster abundance relative to ΛCDM when using spherical collapse and analytic mass functions matched to eROSITA data.
-
EFT of Dark Energy with Cosmic Chronometers: Reconstructing Background EFT Functions
Reconstruction of EFT background functions from cosmic chronometer Hubble data allows model-independent tests of dark energy evolution in scalar-tensor theories.
-
Noncanonical Approaches To Inflation
A review thesis covering Mukhanov parametrization, general scalar-tensor theories, and new slow-roll techniques for canonical and noncanonical inflation observables.
- Scalar emission from binary neutron stars in scalar-tensor theories with kinetic screening