Effective field theory of degenerate higher-order inflation

Motohashi, Hayato; Hu, Wayne

doi:10.48550/arxiv.2002.07967

Cited by 3 publications

(3 citation statements)

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“…In general, for the EFT to cover a wide class of theories of modified gravity, one needs a further generalization of the EFT action to include additional terms [37][38][39][40][41][42][43]. In particular, Horndeski theory generates a peculiar interaction between curvature and lapse, and general DHOST theories include time derivative of lapse.…”

Section: Simple Estimates Of Strong Coupling Scalesmentioning

confidence: 99%

Weakly-coupled stealth solution in scordatura degenerate theory

Motohashi

Mukohyama

2020

J. Cosmol. Astropart. Phys.

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162

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In scalar-tensor theories we revisit the issue of strong coupling of perturbations around stealth solutions, i.e. backgrounds with the same forms of the metric as in General Relativity but with non-trivial configurations of the scalar field. The simplest among them is a stealth Minkowski (or de Sitter) solution with a constant, timelike derivative of the scalar field, i.e. ghost condensation. In the decoupling limit the effective field theory (EFT) describing perturbations around the stealth Minkowski (or de Sitter) solution shows the universal dispersion relation of the form ω 2 = αk 4 /M 2 , where M is a mass scale characterizing the background scalar field and α is a dimensionless constant. Provided that α is positive and of order unity, a simple scaling argument shows that the EFT is weakly coupled all the way up to M . On the other hand, if the structure of the underlining theory forces the perturbations to follow second-order equations of motion then α = 0 and the dispersion relation loses dependence on the spatial momentum. This not only explains the origin of the strong coupling problem that was recently pointed out in a class of degenerate theories but also provides a hint for a possible solution of the problem. We then argue that a controlled detuning of the degeneracy condition, which we call scordatura, renders the perturbations weakly coupled without changing the properties of the stealth solutions of degenerate theories at astrophysical scales.

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Section: Simple Estimates Of Strong Coupling Scalesmentioning

confidence: 99%

Weakly-coupled stealth solution in scordatura degenerate theory

Motohashi

Mukohyama

2020

J. Cosmol. Astropart. Phys.

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162

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“…Not only there exist many "no-go" theorems, extending the no-hair theorem of General Relativity (GR) which kill the hope of having new solutions, but also the equations of modified theories of gravity are, most of the time, much more complicated than the Einstein equations, even for symmetry reduced spacetimes. Nevertheless, it was possible to circumvent these difficulties and new black hole (analytical and numerical) solutions have emerged these last years, in particular, in the context of Degenerate Higher Order Scalar Tensor (DHOST) theories [1][2][3][4][5][6][7] which provide the most general class of viable scalar-tensor theories to date evading the Ostrogradsky ghosts [8][9][10] (see also [11] where DHOST theories have been extended to the so-called U-DHOST theories, and [12] for further generalization). However, most of these solutions are stealth spherically symmetric black holes [13][14][15][16][17][18][19][20][21].…”

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confidence: 99%

On Rotating Black Holes in DHOST Theories

Achour,

Liu,

Motohashi

et al. 2020

Preprint

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“…For example, the SCG [19,20] contains only the extrinsic curvature as the kinetic terms and thus is trivially degenerate. SCG with the a dynamical lapse function has also been investigated in [38][39][40] (see also [41]). However, the general covariance is explicitly broken in SCG.…”

Section: Theory Triangle: Relations Among Different Formulationsmentioning

confidence: 99%

Covariant 3+1 correspondence of the spatially covariant gravity and the degeneracy conditions

Hu,

Gao

2021

Preprint

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A necessary condition for a generally covariant scalar-tensor theory to be ghostfree is that it contains no extra degrees of freedom in the unitary gauge, in which the Lagrangian corresponds to the spatially covariant gravity. Comparing with analysing the scalar-tensor theory directly, it is simpler to map the spatially covariant gravity to the generally covariant scalar-tensor theory using the gauge recovering procedures. In order to ensure the resulting scalar-tensor theory to be ghostfree absolutely, i.e., no matter if the unitary gauge is accessible, a further covariant degeneracy/constraint analysis is required. We develop a method of covariant 3+1 correspondence, which map the spatially covariant gravity to the scalar-tensor theory in 3+1 decomposed form without fixing any coordinates. Then the degeneracy conditions to remove the extra degrees of freedom can be found easily. As an illustration of this approach, we show how the Horndeski theory is recovered from the spatially covariant gravity. This approach can be used to find more general ghostfree scalar-tensor theory.

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Effective field theory of degenerate higher-order inflation

Cited by 3 publications

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Weakly-coupled stealth solution in scordatura degenerate theory

Weakly-coupled stealth solution in scordatura degenerate theory

On Rotating Black Holes in DHOST Theories

Covariant 3+1 correspondence of the spatially covariant gravity and the degeneracy conditions

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