Horndeski Theory Research Articles

Recent Developments in Degenerate Higher Order Scalar Tensor Theories

AbstractDegenerate Higher Order Scalar Tensor (DHOST) theories are the most general scalar‐tensor theories whose Lagrangian depends on the metric tensor and a single scalar field and its derivatives up to second order. They propagate only one scalar degree of freedom, without being plagued by Ostrogradsky instabilities. This is achieved through certain degeneracies of the functions forming their Lagrangian. They generalize the Horndeski and beyond‐Horndeski theories. Originally proposed to describe the late‐time acceleration of the expansion of the universe, generalizing the cosmological constant, they can also be used to build models of the early universe, to describe inflation or alternatives to standard inflation. In the late universe, they modify the standard Vainstein screening mechanism from Horndeski theories (which can have observable consequences) and are suited to build black hole models, featuring non‐stealth Kerr black hole solutions. In this work, their phenomenology is reviewed, looking at their basic properties, their parameterizations and classifications, focusing on solutions in the early and the late universe and at cosmological and astrophysical constraints.

Complete stability for spherically symmetric backgrounds in beyond Horndeski theory

Complete stability for spherically symmetric backgrounds in beyond Horndeski theory

Reviving Horndeski after GW170817 by Kaluza-Klein compactifications

The application of Horndeski theory/Galileons for late time cosmology is heavily constrained by the strict coincidence in the speed of propagation of gravitational and electromagnetic waves. These constraints presuppose that the minimally coupled photon is not modified, not even at the scales where General Relativity (GR) may need modification. We find that the 4D Galileon obtained from a Kaluza-Klein compactification of its higher dimensional version is a natural simultaneous modification of GR and electromagnetism with automatically “luminal” gravitational waves. This property follows without any fine tuning of Galileon potentials for a larger class of theories than previously thought. In particular, the G4 potential is not constrained by the speed test and G5 may also be present. In other words, some Galileon models that have been ruled out since the event GW170817 are, in fact, not necessarily constrained if they arise in 4D from compactifications of their higher dimensional Galileon counterparts. Besides their compelling luminality, the resulting vector Galileons are naturally U(1) gauge invariant. We also argue that the Vainshtein screening that allows to recover GR predictions for solar system tests is also at work for electrodynamics in the dense region of laboratory tests.

A simple prediction of the nonlinear matter power spectrum in Brans–Dicke gravity from linear theory

Brans–Dicke (BD), one of the first proposed scalar-tensor theories of gravity, effectively makes the gravitational constant of general relativity (GR) time-dependent. Constraints on the BD parameter ω serve as a benchmark for testing GR, which is recovered in the limit ω → ∞. Current small-scale astrophysical constraints ω ≳ 105 are much tighter than large-scale cosmological constraints ω ≳ 103, but the two decouple if the true theory of gravity features screening. On the largest cosmological scales, BD approximates the most general second-order scalar–tensor (Horndeski) theory, so constraints here have wider implications. These constraints will improve with upcoming large-scale structure and cosmic microwave background surveys. To constrain BD with weak gravitational lensing, one needs its nonlinear matter power spectrum PBD. By comparing the boost B = PBD/PGR from linear theory and nonlinear N-body simulations, we show that the nonlinear boost can simply be predicted from linear theory if the BD and GR universes are parameterized in a way that makes their early cosmological evolution and quasilinear power today similar. In particular, they need the same H0/√Geff(a = 0) and σ8, where Geff is the (effective) gravitational strength. Our prediction is 1% accurate for ω ≥ 100, z ≤ 3, and k ≤ 1 h/Mpc; and 2% up to k ≤ 5 h/Mpc. It also holds for GBD that do not match Newton’s constant today, so one can study GR with different gravitational constants GGR by sending ω → ∞. We provide a code that computes B with the linear Einstein-Boltzmann solver HI_CLASS and multiplies it by the nonlinear PGR from EUCLIDEMULATOR2 to predict PBD.

Polarized image of a synchrotron emitting ring around a static hairy black hole in Horndeski theory

In this paper, we investigate the polarization images of a synchrotron-emitting fluid ring surrounding a static hairy black hole within the framework of Horndeski’s theory. Our findings indicate that the characteristics of these polarization images are predominantly influenced by the hairy parameter, alongside the magnetic field near the black hole, the fluid’s velocity, and the observer’s inclination angle. Specifically, the hairy parameter primarily affects the polarized intensity and the apparent radius of the ring in the images. Conversely, the impacts of the magnetic field, fluid velocity, and inclination angle on the polarization images are found to be independent of the hairy parameter and closely resemble those observed in the context of Schwarzschild black holes. Additionally, the polarization direction is significantly influenced by the magnetic field orientation, while the inclination angle crucially determines the apparent flatness of the images. Variations in the fluid velocity direction also markedly affect the trend in polarized intensity. Furthermore, we explore how these parameters influence the Stokes Q-U\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Q-U$$\\end{document} loops, revealing distinct behaviors in response to changes in the aforementioned variables. This comprehensive analysis enhances our understanding of the intricate dynamics and observational signatures of black holes within alternative gravitational theories.

Isotropization of the magnetic universe in Horndeski theory with G 3(X,ϕ) and G 5(X)

We study the isotropization process of Bianchi-I space-times in Horndeski theory with and . A global unidirectional electromagnetic field interacts with a scalar field according to the law . In Horndeski theory, the anisotropy can develop in different ways. The proposed reconstruction method allows us to build models with acceptable anisotropy behavior. To analyze space-time anisotropy, we use the relations ( ), where are metric functions, and .

Healthy Horndeski cosmologies with torsion

We show that the full Horndeski theory with both curvature and torsion can support nonsingular, stable and subluminal cosmological solutions at all times. Thus, with torsion, the usual No-Go theorem that holds in a curved spacetime is avoided. In particular, it is essential to include the nonminimal derivative couplings of the ℒ5 part of the Horndeski action (Gμν ∇ μ ∇ νϕ, and (∇2 ϕ)3). Without the latter a No-Go already impedes the eternal subluminality of nonsingular, stable cosmologies.

Infrared sensitivity of cosmological probes in Horndeski theory

Infrared sensitivity of cosmological probes in Horndeski theory

Magnetic Bianchi-I cosmology in the Horndeski theory

In this paper, we study the evolution of Bianchi-I spacetimes within the framework of the Horndeski theory with [Formula: see text]. The spacetimes are filled a global unidirectional electromagnetic field interacting with a scalar field. We consider the minimal interaction and the non-minimal interaction by the law [Formula: see text]. The Horndeski theory allows anisotropy to grow over time, so the question arises of regulating the anisotropic level in this theory. Using the designer method, we build models in which the anisotropic level tends to a small value as the Universe expands. One of the results is a model with a anisotropic bounce.

Parameter constraints on traversable wormholes within beyond Horndeski theories through quasiperiodic oscillations

compact astrophysical objects such as black holes and wormholes, as well as testing gravity theories, are important issues in relativistic astrophysics. In this sense, theoretical and observational studies of quasiperiodic oscillations (QPOs) observed in (micro)quasars become helpful in exploring their central object, which can be a black hole or a wormhole. In the present work, we study the throat properties of traversable wormholes beyond Horndeski theory. Also, we investigate the circular motion of test particles orbiting the wormhole. We analyze the test particle’s effective potential and angular momentum for circular orbits. Frequencies of radial and vertical oscillations of the particles around stable circular orbits have also been studied and applied in explaining the quasiperiodic oscillations mechanism in the relativistic precession (RP) model. Finally, we obtain constraint values for the parameters of beyond Horndeski gravity and the mass of the wormhole candidates using QPOs observed in the microquasars GRO J1655-40, GRS 1915+105 & XTE J1550-564 and at the center of Milky Way galaxy through Monte-Carlo-Markovian-chain (MCMC) analyses. Published by the American Physical Society 2024

Holographic renormalization of Horndeski gravity

We study the renormalization of a particular sector of Horndeski theory. In particular, we focus on the nonminimal coupling of a scalar field to the Gauss-Bonnet term and its kinetic coupling to the Einstein tensor. Adopting a power expansion on the scalar function that couples the Gauss-Bonnet term, we find specific conditions on their coefficients such that the action and charges are finite. To accomplish the latter, we add a finite set of intrinsic boundary terms. The contribution of the nonminimal coupling generates an effective scalar mass, allowing us to recover a modified Breitenlohner-Freedman bound. Furthermore, we compute the holographic 1-point functions and Ward identities associated with the scalar field and the metric. We constrain the parameter space of the theory by taking into account the preservation of scaling symmetry at the boundary.

Observational appearance and additional photon rings of the asymmetric thin-shell wormhole in Horndeski theory

Observational appearance and additional photon rings of the asymmetric thin-shell wormhole in Horndeski theory

Shadow images of compact objects in beyond Horndeski theory

A beyond Horndeski theory is considered that admits wormholes, black holes and naked singularities. In this theory the shadow images of the black holes and the exotic compact objects (ECOs), illuminated by an optically and geometrically thin disk, are investigated. The results show that the three kinds of objects cast unlike shadow images, in particular, because the different objects possess a different number of light rings. The different boundaries of the accretion disk also affect the images. This may provide further insight into the nature of the shadow images of massive compact objects.

Gravitational redshift constraints on the effective theory of interacting dark energy

Upcoming galaxy surveys provide the necessary sensitivity to measure gravitational redshift, a general relativistic effect that generates a dipole in galaxy clustering data when correlating two distinct populations of galaxies. Here, we study the constraining power of gravitational redshift within the framework of the effective theory of interacting dark energy. This formalism describes linear cosmological perturbations in scalar-tensor theories of gravity with a limited number of free functions, and allows each particle species to be coupled differently to the gravitational sector. In this work, we focus on Horndeski theories with a non-minimal coupling of dark matter to the scalar degree of freedom, yielding a breaking of the weak equivalence principle for this cosmic component, a scenario that is yet untested. We show that the dipole generated by gravitational redshift significantly breaks degeneracies and tightens the constraints on the parameters of the effective theory compared to the standard redshift-space distortion analysis solely based on the even multipoles in the galaxy correlation function, with an improvement of up to ∼ 50% for populations with a galaxy bias difference equal to 1. We make the Python package EF-TIGRE (Effective Field Theory of Interacting dark energy with Gravitational REdshift) developed for this work publicly available (https://github.com/Mik3M4n/EF-TIGRE).

DPSV trick for spherically symmetric backgrounds

We discuss the approach suggested by Deffayet et al. (DPSV) to analysing the linearized perturbations in Horndeski theory in the case of a static, spherically symmetric background. In L3 subclass of Horndeski theories we prove the validity of the DPSV approach by showing that the original method corresponds to a specific gauge choice in the quadratic action for perturbations. We also show that in the case of a spherically symmetric background the DPSV trick does not work in a more general L4 Horndeski theory.

Linear instability of hairy black holes in Horndeski theory* *Supported in part by the National Key Research and Development Program of China (2020YFC2201503), the National Natural Science Foundation of China (12205254, 12275238, 11675143), the Natural Science Foundation of Zhejiang Province, China (LR21A050001, LY20A050002), the Fundamental Research Funds for the Provincial Universities of Zhejiang Province, China (RF-A2019015), and the Science Foundation

Horndeski theory constitutes the most general model of scalar-tensor theories. It has attracted much attention in recent years in relation with black holes, celestial dynamics, stability analysis, etc. It is important to note that, for certain subclasses of Horndeski models, one can obtain analytic solutions for the background fields. This facilitates the investigation of the corresponding stability problems in detail. In particular, we aim to determine the constraints to the model or theory under which the stability conditions can be satisfied. In this study, we focused on a subclass of Horndeski theory and a set of analytic background solutions. In addition, the odd-parity gravitational perturbation and 2nd-order Lagrangian were investigated. Through careful analysis, the instability was identified within the neighborhood of the event horizon. This allows exclusion of a specific geometry for the model. Such an instability is implanted in the structure of the corresponding Lagrangian and is not erased by simply adding numerical constraints on the coupling parameters. As a starting point of our research, the current study provides insights for further exploration of the Horndeski theory.

Stability of nonsingular cosmologies in Galileon models with torsion: A no-go theorem for eternal subluminality

Generic models in Galileons or Horndeski theory do not have cosmological solutions that are free of instabilities and singularities in the entire time of evolution. We extend this no-go theorem to a spacetime with torsion. On this more general geometry the no-go argument now holds provided the additional hypothesis that the graviton is also subluminal throughout the entire evolution. Thus, critically different for Galileons’ stability on a torsionful spacetime, an arguably unphysical although arbitrarily short (deep UV) phase occurring at an arbitrary time, when the speed of gravity (cg) is slightly higher than luminal (c), and by at least an amount cg≥2c, can lead to an all-time linearly stable and nonsingular cosmology. As a proof of principle we build a stable model for a cosmological bounce that is almost always subluminal, where the short-lived superluminal phase occurs before the bounce, and that transits to general relativity in the asymptotic past and future. Published by the American Physical Society 2024

No scalar-haired Cauchy horizon theorem in charged Gauss–Bonnet black holes

Recently, a “no inner (Cauchy) horizon theorem” for static black holes with non-trivial scalar hairs has been proved in Einstein–Maxwell–scalar theories and also in Einstein–Maxwell–Horndeski theories with the non-minimal coupling of a charged (complex) scalar field to Einstein tensor. In this paper, we study an extension of the theorem to the static black holes in Einstein–Maxwell–Gauss–Bonnet-scalar theories, or simply, charged Gauss–Bonnet (GB) black holes. We find that no inner horizon with charged scalar hairs is allowed for the planar (k=0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k=0$$\\end{document}) black holes, as in the case without GB term. On the other hand, for the non-planar (k=±1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k=\\pm 1$$\\end{document}) black holes, we find that the haired inner horizon can not be excluded due to GB effect generally, though we can not find a simple condition for its existence. As some explicit examples of the theorem, we study numerical GB black hole solutions with charged scalar hairs and Cauchy horizons in asymptotically anti-de Sitter space, and find good agreements with the theorem. Additionally, in an Appendix, we prove a “no-go theorem” for charged de Sitter black holes (with or without GB terms) with charged scalar hairs in arbitrary dimensions.

Mixed-state entanglement and transport in Einstein–Maxwell–Axion–Horndeski theory

We present a comprehensive study exploring the relationship between transport properties and measures of quantum entanglement in the Einstein–Maxwell–Axion–Horndeski theory. By using holographic duality, we study the entanglement measures, holographic entanglement entropy (HEE) and entanglement wedge cross-section (EWCS), and transport coefficients, for this model and analyze their dependence on free parameters which we classify into action parameters, observable parameters and axion factor. We find contrasting behaviors between HEE and EWCS with respect to observable parameters (charge and temperature), and the axion factor, indicating that they capture different types of quantum correlations. We also find that HEE exhibits positive correlation with both charge and thermal excitations, whereas EWCS exhibits a negative correlation with charge-related conductivities and thermal fluctuations. Furthermore, we find that the Horndeski coupling term, as the modification to standard gravity theory, does not change the qualitative behaviors of the conductivities and the entanglement measures.

Perturbations of massless external fields in a special Horndeski hairy black hole

In this paper, we study the propagations of external fields in a specific black hole solution in Horndeski theory, including the scalar field, electromagnetic field and Dirac field. We extensively explore the quasinormal frequencies, time evolution, greybody factors and emission rates of those massless perturbing fields by solving the corresponding master equations in the specific Horndeski hairy black hole. With the use of both numerical and analytical methods, we disclose the competitive/promotional influences of the Horndeski hair, spin and quantum momentum number of the external fields on those phenomenal physics. Our results show that this specific Horndeski hairy black hole is stable under those perturbations. Moreover, a larger Horndeski hair could enhance the intensity of energy emission rate for Hawking radiation of various particles, indicating that comparing to the Schwarzschild black hole, this specific Horndeski hariy black hole could have longer or shorter lifetime depending on the sign of the Horndeski hair.