Horndeski theory and beyond: a review

Kobayashi, Tsutomu

doi:10.1088/1361-6633/ab2429

Cited by 539 publications

(424 citation statements)

References 316 publications

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“…In the context of analytical mechanics, a simple example of degenerate higher-derivative system is given by [4,10,11]…”

Section: The Dhost Theoriesmentioning

confidence: 99%

“…Although generically the EL equations in such theories contain higher derivative terms, the appearance of Ostrogradsky ghosts [2] can be avoided using certain degeneracy conditions [3]. Degenerate higher-order scalar-tensor (DHOST) theories [4-9] (see also [10,11]) provide the most general framework of scalar-tensor theories which are free from Ostrogradsky instabilities [2], and hence the system contains only three degrees of freedom (DOFs), namely, two tensorial and one scalar polarizations (See § II for details). Applications of DHOST theories to cosmological and astrophysical problems have been investigated in Refs.…”

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confidence: 99%

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Black holes with a nonconstant kinetic term in degenerate higher-order scalar tensor theories

Minamitsuji

Edholm

2020

Phys. Rev. D

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We investigate static and spherically symmetric black hole (BH) solutions in shift-symmetric quadratic-order degenerate higher-order scalar-tensor (DHOST) theories. We allow a nonconstant kinetic term X = g µν ∂µφ∂ν φ for the scalar field φ and assume that φ is, like the spacetime, a pure function of the radial coordinate r, namely φ = φ(r). First, we find analytic static and spherically symmetric vacuum solutions in the so-called Class Ia DHOST theories, which include the quartic Horndeski theories as a subclass. We consider several explicit models in this class and apply our scheme to find the exact vacuum BH solutions. BH solutions obtained in our analysis are neither Schwarzschild or Schwarzschild (anti-) de Sitter. We show that a part of the BH solutions obtained in our analysis are free of ghost and Laplacian instabilities and are also mode stable against the oddparity perturbations. Finally, we argue the case that the scalar field has a linear time dependence φ = qt + ψ(r) and show several simple examples of nontrivial BH solutions with a nonconstant kinetic term obtained analytically and numerically. I. INTRODUCTIONScalar-tensor theories have provided the unified mathematical description of modified gravity theories [1]. In classic scalar-tensor theories, whose Lagrangian density depends on the metric g µν , the scalar field φ, and its first-order derivative φ µ := ∇ µ φ, L = L(g µν , φ, φ µ ), the Euler-Lagrange (EL) equations are given by the second-order differential equations. However, the Lagrangian density of modern scalar-tensor theories may also contain the second-order derivatives of the scalar field φ µν := ∇ µ ∇ ν φ. Although generically the EL equations in such theories contain higher derivative terms, the appearance of Ostrogradsky ghosts [2] can be avoided using certain degeneracy conditions [3]. Degenerate higher-order scalar-tensor (DHOST) theories [4-9] (see also [10,11]) provide the most general framework of scalar-tensor theories which are free from Ostrogradsky instabilities [2], and hence the system contains only three degrees of freedom (DOFs), namely, two tensorial and one scalar polarizations (See § II for details). Applications of DHOST theories to cosmological and astrophysical problems have been investigated in Refs. [9,[12][13][14][15].The application of modern scalar-tensor theories to BH physics has attracted great interest. Besides the Schwarzschild or Kerr solutions in General Relativity (GR) with or without a constant scalar field [16,17], i.e. GR BH solutions, they also allow BH solutions which are absent in GR. A typical nontrivial BH solution is the stealth Schwarzschild solution [18,19] obtained in shift-symmetric Horndeski theories with the assumptions of a linearly time-dependent scalar field φ = qt + ψ(r) and a constant kinetic term X = const, where t and r are the time and radial coordinates of the static and spherically symmetric spacetime and X := g µν φ µ φ ν represents the canonical kinetic term of the scalar field. In stealth solutions, the spacetime geometry ...

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“…In the context of analytical mechanics, a simple example of degenerate higher-derivative system is given by [4,10,11]…”

Section: The Dhost Theoriesmentioning

confidence: 99%

mentioning

confidence: 99%

Black holes with a nonconstant kinetic term in degenerate higher-order scalar tensor theories

Minamitsuji

Edholm

2020

Phys. Rev. D

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“…The second reason is that nonlinear modifications of gravity have been introduced in attempts to address the discovery of dark matter, dark energy, solve the flatness and horizon problems of early universe cosmology, and resolve the issues of the initial cosmological singularity and singularities formed during gravitational collapse. EdGB is an important and representative member of a class of modified gravity theories, Horndeski theories, that have been invoked to solve these various issues within classical GR (for a recent review on Horndeski theories see [26]), and it thus is interesting to see if the theory is mathematically sensible as a classical field theory.…”

Section: Introductionmentioning

confidence: 99%

Scalarized black hole dynamics in Einstein-dilaton-Gauss-Bonnet gravity

Ripley

Pretorius

2020

Phys. Rev. D

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We report on a numerical investigation of the stability of scalarized black holes in Einstein dilaton Gauss-Bonnet (EdGB) gravity in the full dynamical theory, though restricted to spherical symmetry. We find evidence that for sufficiently small curvature-couplings the resulting scalarized black hole solutions are nonlinearly stable. For such small couplings, we show that an elliptic region forms inside these EdGB black hole spacetimes (prior to any curvature singularity), and give evidence that this region remains censored from asymptotic view. However, for coupling values "superextremal" relative to a given black hole mass, an elliptic region forms exterior to the horizon, implying the exterior Cauchy problem is ill-posed in this regime. *

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“…In [19], it is shown that (7) has a wide range of cosmological solutions, that may be relevant for the primordial universe, because it may be responsible, for instance, for a cosmological bounce. There is a debate concerning the relation between G 5 theories and gravitational waves, but it was already explored in several papers (see [8] and [20], for instance) and, for (7) in particular, it was addressed in detail in [19]. Taking into account that debate, one has to consider (7) as a contribution to the canonical Lagrangian for the minimal coupling in order to study stages of the evolution of the universe after inflation [19].…”

Section: Introductionmentioning

confidence: 99%

Quantum Cosmology of Fab Four John Theory with Conformable Fractional Derivative

et al. 2020

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We study a quantization via fractional derivative of a nonminimal derivative coupling cosmological theory, namely, the Fab Four John theory. Its Hamiltonian version presents the issue of fractional powers in the momenta. That problem is solved here by the application of the so-called conformable fractional derivative. This leads to a Wheeler-DeWitt equation of second order, showing that a Bohm-de Broglie interpretation can be constructed. That combination of fractional quantization and Bohmian interpretation provides us a new quantization method, in which the quantum potential is the criterion to say if a quantum solution is acceptable or not to be further studied. We show that a wide range of solutions for the scale factor is possible. Among all of those, a bouncing solution analogous to the perfect fluid cosmology seems to deserve special attention. *

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Horndeski theory and beyond: a review

Cited by 539 publications

References 316 publications

Black holes with a nonconstant kinetic term in degenerate higher-order scalar tensor theories

Black holes with a nonconstant kinetic term in degenerate higher-order scalar tensor theories

Scalarized black hole dynamics in Einstein-dilaton-Gauss-Bonnet gravity

Quantum Cosmology of Fab Four John Theory with Conformable Fractional Derivative

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