Pith. sign in

REVIEW 2 major objections 3 minor 1 cited by

Gravitomagnetic tidal response of relativistic stars in partially screened scalar-tensor theories

T0 review · 2 major / 3 minor · reviewed 2026-08-10 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read In DHOST scalar-tensor theories, partial failure of Vainshtein screening inside matter leaves a roughly ten-times-parameter imprint on the gravitomagnetic tidal Love numbers of relativistic stars, growing with multipole and compactness.

desk verdict First gravitomagnetic Love numbers for DHOST stars with partial Vainshtein breaking, but the headline scaling inherits a known convention ambiguity that needs a clear caveat; worth refereeing with major revision. read the letter →

arxiv 2501.10659 v2 pith:HS5KMJ72 submitted 2025-01-18 gr-qc

Tsutomu Kobayashi This is my paper · ORCID
classification gr-qc PACS 04.50.Kd04.40.Dg
keywords gravitomagnetictidalLovenumbersDHOSTtheoriesVainshteinscreeningscalar-tensorgravityneutronstardeformabilityodd-parityperturbationscompactstarsmodified
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper aims to show that the Vainshtein screening mechanism, though complete outside a star, is only partially effective inside matter in scalar-tensor theories beyond Horndeski, and that this internal leak is visible in the star's tidal response. It computes the gravitomagnetic (odd-parity) tidal Love numbers of static relativistic stars in a concrete class of DHOST theories and finds deviations from general relativity of order ten times the modified-gravity parameters $\alpha_H$ and $\beta_1$. The deviations increase with multipole order and with compactness, so more compact stars and higher multipoles should be better probes. The paper also argues that $\alpha_H$ and $\beta_1$ do not fully characterize the strong-field tidal response, since a third parameter of the model affects the Love numbers at large compactness.

What carries the argument

The argument is carried by the zero-frequency odd-parity perturbation equation for the metric component $h_0$, Eq. (64): $h_0'' - (P/r)h_0' - (Q/r^2)h_0=0$, with $P=r(\nu'/2+\lambda'/2 - f_X X'/f)$ and $Q=e^\lambda[\ell(\ell+1)-2(1-e^{-\lambda})]-2P$, where primes denote radial derivatives and $f_X=\partial f/\partial X$. At the center the regular solution satisfies $\kappa(0)=\ell+1$ for $\kappa=rh_0'/h_0$; integrating Eq. (71) to the surface and matching to the analytic GR exterior solution (67) yields the rescaled Love number $\tilde{k}_\ell$. Modified gravity enters in two ways: the background metric functions $\nu,\lambda$ carry the DHOST-modified stellar structure, and the new term $f_X X'/f$ modifies the perturbation equation itself relative to GR. The external solution reduces to Schwarzschild with $X=1/2$, so the screening outside the star is complete.

What would settle it

Compute the same gravitomagnetic Love numbers with the alternative fluid convention ($U=0$ from the outset, as discussed in the paper); if the GR baseline becomes zero while the DHOST Love numbers remain nonzero, the paper's relative-deviation story is convention-driven rather than observable. Alternatively, a high-signal-to-noise gravitational-wave measurement of the tidal deformability of a compact binary that matches GR to much better than the predicted $\mathcal{O}(10)\,\alpha_H,\beta_1$ shift would rule out the large-deviation part of the parameter space.

Watch

Extended reading notes

Core claim

The central result is that in quadratic DHOST theories with gravitational-wave speed equal to $c$, the gravitomagnetic Love numbers $\tilde{k}_\ell$ of an irrotational fluid star deviate from their GR values by roughly $(\tilde{k}_\ell-\tilde{k}_\ell^{\rm GR})/\tilde{k}_\ell^{\rm GR}\sim -\mathcal{O}(10)\,\alpha_H$, with $\beta_1$ acting similarly; higher multipoles $\ell$ and larger compactness $C=\mu/R$ enlarge the relative difference, and positive (negative) $\alpha_H,\beta_1$ decrease (increase) $|\tilde{k}_\ell|$. The deviations have two sources: the modified interior metric of the star and the nonvanishing gradient $X'$ of the scalar kinetic term, which enters the perturbation equation directly. Outside the star the metric is exactly Schwarzschild, so complete Vainshtein screening hides the modification in the exterior; the signal lives in the interior tidal response. Away from the weak-field limit the two standard parameters are not enough: changing the model parameter $q$ at fixed $\alpha_H,\beta_1$ changes the Love numbers once the star is sufficiently compact.

Load-bearing premise

The reported size of the deviations rests on the choice of the irrotational-fluid, zero-frequency convention for gravitomagnetic Love numbers; if the alternative convention for the fluid motion is the physically observable one, the general-relativity baseline changes, possibly to zero, and the claimed ten-times-parameter shifts would not hold as stated.

Editorial extensions

If this is right

  • For fixed DHOST parameters, the relative deviation of the gravitomagnetic Love number from GR grows with multipole order and compactness, so higher-multipole tidal moments and more compact stars give stronger tests of the theory.
  • Positive values of $\alpha_H$ and $\beta_1$ decrease $|\tilde{k}_\ell|$ and negative values increase it, by roughly the same order, so the sign of a measured Love-number shift can help orient the allowed parameter region.
  • The exterior metric in this theory class is Schwarzschild, so the partial-screening signal is carried by the tidal response itself rather than by the leading exterior geometry; Love numbers are the right observable.
  • Within the paper's adopted observational ranges for $\alpha_H$ and $\beta_1$, the predicted relative shifts are potentially of order unity, large enough to matter for gravitational-wave tidal measurements.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper, the same calculation should be repeated with the alternative fluid convention (the one the paper cites but does not use); if that convention is the physical one, the GR baseline for gravitomagnetic Love numbers can change, possibly to zero, and the ten-times-parameter deviations would need re-evaluation.
  • Beyond the paper, the partial-screening effect should also shift the gravitoelectric (even-parity) Love numbers that dominate binary-inspiral phasing; the paper defers them for technical reasons, so a full observational test needs that sector.
  • Beyond the paper, extending the polytropic models to realistic neutron-star equations of state, including the low-index cases the paper excludes because of surface-matching discontinuities, would test whether the $\sim\mathcal{O}(10)\,\alpha_H,\beta_1$ scaling is robust in astrophysical settings.
  • Beyond the paper, the $q$-dependence at large compactness implies that future tidal measurements should be fitted with at least three theory parameters (for example $\alpha_H$, $\beta_1$, and a shape parameter of the scalar interaction), not just the two standard ones.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 3 minor

Summary. The paper studies gravitomagnetic (odd-parity) tidal Love numbers of nonrotating relativistic stars in quadratic DHOST theories with partial Vainshtein screening. It reviews the TOV background, derives an odd-parity master equation and a zero-frequency second-order equation for the metric perturbation h0 (Eqs. (63)-(66)), and then integrates this equation numerically for energy-polytrope stars in the concrete DHOST model of Eqs. (74)-(75). The main numerical findings are that the relative deviations of the Love numbers from their GR values are roughly O(10) × αH, β1, that these deviations grow with multipole order and compactness, and that a third parameter q produces effects not captured by αH and β1 once the weak-field regime is left. The paper concludes that αH and β1 alone are insufficient to characterize the strong-field tidal response.

Significance. If the convention issue discussed below is properly addressed, the paper would provide one of the first quantitative studies of tidal response in theories with partial Vainshtein breaking. The reduction of the odd-parity perturbation system to a single zero-frequency equation for h0 is a useful technical step, and the systematic scan over αH, β1, q, and compactness gives a concrete picture of how modified-gravity parameters enter the tidal response. The paper is also honest about the technical difficulty of the even-parity sector. However, the headline quantitative claim is formulated in terms of gravitomagnetic Love numbers, which are known to be convention-dependent for nonrotating bodies; the manuscript does not establish that the chosen irrotational-fluid convention corresponds to an observable tidal response. No code, data files, or numerical accuracy estimates are provided, which limits reproducibility of the quantitative results.

major comments (2)
  1. [Sec. III, Eq. (54) and following; Figs. 2 and Eq. (79)] The gravitomagnetic Love numbers are computed in the irrotational-fluid prescription, in which the zero-frequency limit is taken after imposing U = -(ρ+p)h0 from Eq. (58). Ref. [50], cited by the paper at Eq. (54), shows that magnetic-type Love numbers of nonrotating bodies are convention-dependent within the odd-parity sector: if one instead sets U = 0 from the beginning, the source term in Eq. (60) becomes r^2(ρ+p)h0 rather than zero, and the GR baseline can be different (vanishing in some conventions). The relative differences in Fig. 2 and the estimate (79) are normalized by the nonzero GR baseline in the irrotational convention, so the central quantitative claim and the abstract's detectability statement are tied to this convention. The manuscript does not justify that the irrotational-fluid choice is the physically relevant response of a nonrotating star to an external odd-parity tidal field, nor does it show that the U = 0 convention yields the same conclusions. Please provide such a justification or reformulate the claims as convention-dependent and soften the abstract accordingly.
  2. [Sec. III, Eq. (64)] The central reduction from the master equation (63) to the zero-frequency equation for h0 is stated with the phrase "it can be shown" and is not demonstrated. This equation, together with the definitions of P and Q in Eqs. (65)-(66), generates all numerical results in the paper; a reader cannot verify the handling of the boundary/source terms in Eq. (60) without rederiving the reduction by hand. Please include the derivation in an appendix or as a supplementary calculation.
minor comments (3)
  1. [Sec. V] The numerical results are produced with NDSolve, but no error tolerances, convergence tests, or data files are reported. For a quantitative claim such as Eq. (79), an accuracy statement or a release of the numerical data would make the results reproducible and easier to assess.
  2. [Abstract and Sec. VI] The abstract says that partial breaking of Vainshtein screening can be detected through the tidal response, but the paper itself notes that the even-parity (gravitoelectric) Love numbers have a larger contribution to the gravitational-wave phase than the odd-parity ones computed here. This wording overstates what the odd-parity calculation alone establishes.
  3. [Sec. II C] There are a few typographical issues, for example "suitable νc does not necessarily exit" should read "exist," and the section heading in the conclusions is missing a period. These do not affect the physics.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the gravitomagnetic Love-number deviations are obtained by solving the derived odd-parity perturbation equation, with the DHOST parameters appearing as free inputs rather than fitted targets.

full rationale

The derivation chain is not circular. The model parameters αH, β1, and q are used to specify the action through Eqs. (73)-(75); they are inputs, and the Love numbers k̃ℓ are outputs obtained by integrating Eq. (71) with boundary condition (72) and matching to the external solution via Eq. (70). Nothing in the extraction is fitted to the Love-number output, and Eq. (79) is a numerical observation from the computed curves rather than an imposed relation. The background TOV equations are taken from Ref. [39], but they are explicitly reproduced in Appendix A, and the weak-field limit is cross-checked against Refs. [24,33-35]; these prior results are parameter-free derivations within stated assumptions and do not contain the Love-number result, so citing them is not self-citation load-bearing. The use of the irrotational-fluid convention of Refs. [5,48] is a stated physical convention, and the paper itself cites Ref. [50] for the existence of an alternative U=0 convention. That convention-dependence is a substantive caveat about which baseline should be called the physical gravitomagnetic response, but it does not make the computation circular: the same convention is applied to both the GR and DHOST calculations, and no parameter is adjusted to produce the reported relative differences. The claim that αH and β1 are insufficient away from the weak-field limit is demonstrated by varying q at fixed αH and β1 and observing a growing spread with compactness, which is a computed consequence rather than an input.

Assumptions & free parameters 5 free parameters · 7 assumptions · 0 invented entities

No invented entities appear. The free parameters are theory and EoS parameters scanned to demonstrate parametric dependence; they are not fitted to the Love-number results. The most consequential modeling assumptions are the polytropic EoS with n>1 and the irrotational-fluid convention for gravitomagnetic Love numbers.

free parameters (5)
  • alpha_H
    Dimensionless DHOST parameter defined by Eq. (35); scanned over negative and positive values (+/-1e-3, +/-1e-2, +/-5e-3) to produce Figs. 1, 2, 3, 5; not fitted to data.
  • beta_1
    Dimensionless DHOST parameter from Eq. (35); set to 0 in most figures and varied in Fig. 5; not fitted.
  • q
    Exponent in the model function f(X) = f0 + f1 X^q (Eq. 73); q=1 in most runs and q variation explored in Fig. 4 to demonstrate strong-field sensitivity; chosen by hand.
  • b (central-density measure)
    Dimensionless central-density parameter defined in Eq. (77); scans the sequence of equilibrium configurations and controls compactness C = mu/R.
  • polytropic index n
    Energy polytrope index p = K rho^{1+1/n}; restricted to n=2 and n=3/2 because n<=1 leads to rho'(R) != 0 and breaks smooth matching (Sec. IV B).
assumptions (7)
  • domain assumption The action is restricted to the quadratic DHOST subset satisfying the degeneracy conditions and c_T=1 (A1=0), with F0 and F1 terms neglected in the Vainshtein regime.
    Invoked in Sec. II A, Eqs. (1)-(5), following Refs. [28,33-35,39].
  • domain assumption Shift symmetry of the scalar field is assumed, so f and A_I depend only on X.
    Stated in Sec. II A; motivates the ansatz phi = t + psi(r).
  • domain assumption The background is static, spherically symmetric, with the metric (9) and scalar ansatz (10).
    Eqs. (9)-(10), Sec. II B.
  • domain assumption Matter is a perfect fluid minimally coupled to gravity with the EoS p = p(rho).
    Sec. II B.
  • ad hoc to paper The equation of state is an energy polytrope with n>1.
    Sec. IV B; chosen because n<=1 yields rho'(R) != 0, preventing the smooth surface matching required by the DHOST field equations.
  • ad hoc to paper The gravitomagnetic Love numbers are defined in the irrotational-fluid, zero-frequency-limit convention of Refs. [5,48].
    Sec. III, after Eq. (54); the alternative U=0 convention discussed in Ref. [50] is not analyzed.
  • domain assumption Complete Vainshtein screening outside the star, giving the exterior Schwarzschild solution and X=1/2.
    Sec. II C, Eqs. (17)-(19), based on Refs. [24,33-35].

how reviews work

0 comments
Cite this review

Pith. "Pith review of Gravitomagnetic tidal response of relativistic stars in partially screened scalar-tensor theories." pith.science (2026). https://pith.science/paper/HS5KMJ72

@misc{pith2026250110659,
  author       = {Pith},
  title        = {Pith review of: Gravitomagnetic tidal response of relativistic stars in partially screened scalar-tensor theories},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HS5KMJ72}},
  note         = {Machine review of arXiv:2501.10659}
}
read the original abstract

In scalar-tensor theories beyond Horndeski, the Vainshtein screening mechanism is only partially effective inside astrophysical bodies. We investigate the potential to detect this partial breaking of Vainshtein screening through the tidal response of fluid bodies. We calculate the gravitomagnetic tidal Love numbers in a specific model of degenerate higher-order scalar-tensor gravity and analyze how deviations from general relativity depend on parameters governing the breaking of Vainshtein screening in the weak-gravity regime. For fixed parameter values, the relative deviations increase with higher multipoles and larger compactness. However, we demonstrate that these parameters alone are insufficient to fully characterize the tidal response of relativistic bodies in scalar-tensor theories beyond Horndeski.

Figures

Figures reproduced from arXiv: 2501.10659 by the authors.

Figure 1
Figure 1. FIG. 1. Gravitomagnetic Love numbers [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Relative differences between the [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Gravitomagnetic Love numbers in DHOST theories versus compactness (left) and their relative differences compared [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Gravitomagnetic Love numbers in DHOST theories [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Tidal Love Numbers of Neutron Stars in Horndeski Theories

    gr-qc 2025-01 accept novelty 7.0 of 10

    In scalar-tensor theories, the 1/r^3 term used to extract neutron star tidal Love numbers contains a Love-number-independent contamination, computed here for minimally coupled and DEF scalar fields.

Reference graph

Works this paper leans on

57 extracted references · 9 canonical work pages · cited by 1 Pith paper

  1. [50]

    P. Pani, L. Gualtieri, T. Abdelsalhin and X. Jim´ enez-Forteza,Magnetic tidal Love numbers clarified, Phys. Rev. D 98 (2018) 124023 [ 1810.01094]. 5

    arXiv 2018

  2. [1]

    Poisson and C.M

    E. Poisson and C.M. Will, Gravity: Newtonian, Post-Newtonian, Relativistic, Cambridge University Press (2014), 10.1017/CBO9781139507486. 1

    doi:10.1017/cbo9781139507486 2014

  3. [2]

    Love, The yielding of the earth to disturbing forces, Proc

    A.E.H. Love, The yielding of the earth to disturbing forces, Proc. Roy. Soc. Lond. A 82 (1909) 73. 1

    work page 1909

  4. [3]

    Flanagan and T

    E.E. Flanagan and T. Hinderer, Constraining neutron star tidal Love numbers with gravitational wave detectors, Phys. Rev. D 77 (2008) 021502 [ 0709.1915]. 1

    arXiv 2008

  5. [4]

    Hinderer, Tidal Love numbers of neutron stars , Astrophys

    T. Hinderer, Tidal Love numbers of neutron stars , Astrophys. J. 677 (2008) 1216 [ 0711.2420]. 1

    arXiv 2008

  6. [5]

    Damour and A

    T. Damour and A. Nagar, Relativistic tidal properties of neutron stars, Phys. Rev. D 80 (2009) 084035 [0906.0096]. 1, 4, 5, 8

    arXiv 2009

  7. [6]

    Binnington and E

    T. Binnington and E. Poisson, Relativistic theory of tidal Love numbers , Phys. Rev. D 80 (2009) 084018 [0906.1366]. 1, 4

    arXiv 2009

  8. [7]

    Hinderer, B.D

    T. Hinderer, B.D. Lackey, R.N. Lang and J.S. Read, Tidal deformability of neutron stars with realistic equations of state and their gravitational wave signatures in binary inspiral , Phys. Rev. D 81 (2010) 123016 [0911.3535]. 1

    arXiv 2010

Show all 57 references
  1. [8]

    LIGO Scientific, Virgocollaboration, GW170817: Measurements of neutron star radii and equation of state, Phys. Rev. Lett. 121 (2018) 161101 [ 1805.11581]. 1

    2018 arXiv

  2. [9]

    Pani and E

    P. Pani and E. Berti, Slowly rotating neutron stars in scalar-tensor theories, Phys. Rev. D 90 (2014) 024025 [1405.4547]. 1

    2014 arXiv

  3. [10]

    Yazadjiev, D.D

    S.S. Yazadjiev, D.D. Doneva and K.D. Kokkotas, Tidal Love numbers of neutron stars in f (R) gravity, Eur. Phys. J. C 78 (2018) 818 [ 1803.09534]

    2018 arXiv

  4. [11]

    Saffer and K

    A. Saffer and K. Yagi, Tidal deformabilities of neutron stars in scalar-Gauss-Bonnet gravity and their applications to multimessenger tests of gravity , Phys. Rev. D 104 (2021) 124052 [ 2110.02997]

    2021 arXiv

  5. [12]

    Brown, Tidal Deformability of Neutron Stars in Scalar-tensor Theories of Gravity , Astrophys

    S.M. Brown, Tidal Deformability of Neutron Stars in Scalar-tensor Theories of Gravity , Astrophys. J. 958 (2023) 125 [ 2210.14025]

    2023 arXiv

  6. [13]

    Creci, T

    G. Creci, T. Hinderer and J. Steinhoff, Tidal properties of neutron stars in scalar-tensor theories of gravity , Phys. Rev. D 108 (2023) 124073 [ 2308.11323]

    2023 arXiv

  7. [14]

    Diedrichs, S

    R.F. Diedrichs, S. Tsujikawa and K. Yagi, Tidal Love Numbers of Neutron Stars in Horndeski Theories , 2501.07998. 1

    arXiv

  8. [15]

    Babichev and C

    E. Babichev and C. Deffayet, An introduction to the Vainshtein mechanism, Class. Quant. Grav. 30 (2013) 184001 [1304.7240]. 1

    2013 arXiv

  9. [16]

    Horndeski, Second-order scalar-tensor field equations in a four-dimensional space , Int

    G.W. Horndeski, Second-order scalar-tensor field equations in a four-dimensional space , Int. J. Theor. Phys. 10 (1974) 363. 1

    1974

  10. [17]

    Deffayet, X

    C. Deffayet, X. Gao, D.A. Steer and G. Zahariade, From k-essence to generalised Galileons, Phys. Rev. D 84 (2011) 064039 [ 1103.3260]

    2011 arXiv

  11. [18]

    Kobayashi, M

    T. Kobayashi, M. Yamaguchi and J. Yokoyama, Generalized G-inflation: Inflation with the most general second-order field equations, Prog. Theor. Phys. 126 (2011) 511 [ 1105.5723]. 1

    2011 arXiv

  12. [19]

    Kimura, T

    R. Kimura, T. Kobayashi and K. Yamamoto, Vainshtein screening in a cosmological background in the most general second-order scalar-tensor theory , Phys. Rev. D 85 (2012) 024023 [ 1111.6749]. 1

    2012 arXiv

  13. [20]

    Narikawa, T

    T. Narikawa, T. Kobayashi, D. Yamauchi and R. Saito, Testing general scalar-tensor gravity and massive gravity with cluster lensing , Phys. Rev. D 87 (2013) 124006 [1302.2311]

    2013 arXiv

  14. [21]

    Koyama, G

    K. Koyama, G. Niz and G. Tasinato, Effective theory for the Vainshtein mechanism from the Horndeski action, Phys. Rev. D 88 (2013) 021502 [ 1305.0279]. 1

    2013 arXiv

  15. [22]

    Zumalac´ arregui and J

    M. Zumalac´ arregui and J. Garc ´ ıa-Bellido,Transforming gravity: from derivative couplings to matter to second-order scalar-tensor theories beyond the Horndeski Lagrangian, Phys. Rev. D 89 (2014) 064046 [1308.4685]. 1

    2014 arXiv

  16. [23]

    Gleyzes, D

    J. Gleyzes, D. Langlois, F. Piazza and F. Vernizzi, Healthy theories beyond Horndeski , Phys. Rev. Lett. 114 (2015) 211101 [ 1404.6495]. 1

    2015 arXiv

  17. [24]

    Kobayashi, Y

    T. Kobayashi, Y. Watanabe and D. Yamauchi, Breaking of Vainshtein screening in scalar-tensor theories beyond Horndeski, Phys. Rev. D 91 (2015) 064013 [ 1411.4130]. 1, 4, 8

    2015 arXiv

  18. [25]

    Koyama and J

    K. Koyama and J. Sakstein, Astrophysical Probes of the Vainshtein Mechanism: Stars and Galaxies , Phys. Rev. D 91 (2015) 124066 [ 1502.06872]. 1

    2015 arXiv

  19. [26]

    Saito, D

    R. Saito, D. Yamauchi, S. Mizuno, J. Gleyzes and D. Langlois, Modified gravity inside astrophysical bodies, 12 JCAP 06 (2015) 008 [ 1503.01448]. 1

    2015 arXiv

  20. [27]

    Banerjee, D

    P. Banerjee, D. Garain, S. Paul, S.t. Rajibul and T. Sarkar, Constraining modified gravity from tidal phenomena in binary stars , Astrophys. J. 910 (2021) 23 [2006.01646]. 1

    2021 arXiv

  21. [28]

    Langlois and K

    D. Langlois and K. Noui, Degenerate higher derivative theories beyond Horndeski: evading the Ostrogradski instability, JCAP 02 (2016) 034 [ 1510.06930]. 1, 2

    2016 arXiv

  22. [29]

    Crisostomi, K

    M. Crisostomi, K. Koyama and G. Tasinato, Extended Scalar-Tensor Theories of Gravity, JCAP 04 (2016) 044 [1602.03119]

    2016 arXiv

  23. [30]

    Ben Achour, M

    J. Ben Achour, M. Crisostomi, K. Koyama, D. Langlois, K. Noui and G. Tasinato, Degenerate higher order scalar-tensor theories beyond Horndeski up to cubic order, JHEP 12 (2016) 100 [ 1608.08135]. 1

    2016 arXiv

  24. [31]

    Langlois, Dark energy and modified gravity in degenerate higher-order scalar–tensor (DHOST) theories: A review , Int

    D. Langlois, Dark energy and modified gravity in degenerate higher-order scalar–tensor (DHOST) theories: A review , Int. J. Mod. Phys. D 28 (2019) 1942006 [1811.06271]. 1

    2019 arXiv

  25. [32]

    Kobayashi, Horndeski theory and beyond: a review , Rept

    T. Kobayashi, Horndeski theory and beyond: a review , Rept. Prog. Phys. 82 (2019) 086901 [ 1901.07183]. 1

    2019 arXiv

  26. [33]

    Crisostomi and K

    M. Crisostomi and K. Koyama, Vainshtein mechanism after GW170817 , Phys. Rev. D 97 (2018) 021301 [1711.06661]. 1, 2, 4, 8

    2018 arXiv

  27. [34]

    Langlois, R

    D. Langlois, R. Saito, D. Yamauchi and K. Noui, Scalar-tensor theories and modified gravity in the wake of GW170817 , Phys. Rev. D 97 (2018) 061501 [1711.07403]

    2018 arXiv

  28. [35]

    Dima and F

    A. Dima and F. Vernizzi, Vainshtein Screening in Scalar-Tensor Theories before and after GW170817: Constraints on Theories beyond Horndeski , Phys. Rev. D 97 (2018) 101302 [ 1712.04731]. 1, 2, 4, 8

    2018 arXiv

  29. [36]

    Babichev, K

    E. Babichev, K. Koyama, D. Langlois, R. Saito and J. Sakstein, Relativistic Stars in Beyond Horndeski Theories, Class. Quant. Grav. 33 (2016) 235014 [1606.06627]. 1

    2016 arXiv

  30. [37]

    Sakstein, E

    J. Sakstein, E. Babichev, K. Koyama, D. Langlois and R. Saito, Towards Strong Field Tests of Beyond Horndeski Gravity Theories , Phys. Rev. D 95 (2017) 064013 [1612.04263]

    2017 arXiv

  31. [38]

    Chagoya and G

    J. Chagoya and G. Tasinato, Compact objects in scalar-tensor theories after GW170817 , JCAP 08 (2018) 006 [ 1803.07476]

    2018 arXiv

  32. [39]

    Kobayashi and T

    T. Kobayashi and T. Hiramatsu, Relativistic stars in degenerate higher-order scalar-tensor theories after GW170817, Phys. Rev. D 97 (2018) 104012 [1803.10510]. 1, 2, 3, 6, 9

    2018 arXiv

  33. [40]

    LIGO Scientific, Virgocollaboration, GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral , Phys. Rev. Lett. 119 (2017) 161101 [1710.05832]. 2

    2017 arXiv

  34. [41]

    LIGO Scientific, Virgo, Fermi-GBM, INTEGRAL collaboration, Gravitational Waves and Gamma-rays from a Binary Neutron Star Merger: GW170817 and GRB 170817A , Astrophys. J. Lett. 848 (2017) L13 [1710.05834]

    2017 arXiv

  35. [42]

    LIGO Scientific, Virgo, Fermi GBM, INTEGRAL, IceCube, AstroSat Cadmium Zinc Telluride Imager Team, IPN, Insight-Hxmt, ANTARES, Swift, AGILE Team, 1M2H Team, Dark Energy Camera GW-EM, DES, DLT40, GRA WITA, Fermi-LAT, ATCA, ASKAP, Las Cumbres Observatory Group, OzGrav, DWF (Deep...

    2017 arXiv

  36. [43]

    de Rham and A

    C. de Rham and A. Matas, Ostrogradsky in Theories with Multiple Fields , JCAP 06 (2016) 041 [1604.08638]. 2

    2016 arXiv

  37. [44]

    Langlois, M

    D. Langlois, M. Mancarella, K. Noui and F. Vernizzi, Effective Description of Higher-Order Scalar-Tensor Theories, JCAP 05 (2017) 033 [ 1703.03797]. 4

    2017 arXiv

  38. [45]

    Beltran Jimenez, F

    J. Beltran Jimenez, F. Piazza and H. Velten, Evading the Vainshtein Mechanism with Anomalous Gravitational Wave Speed: Constraints on Modified Gravity from Binary Pulsars , Phys. Rev. Lett. 116 (2016) 061101 [ 1507.05047]. 4

    2016 arXiv

  39. [46]

    Saltas, I

    I.D. Saltas, I. Sawicki and I. Lopes, White dwarfs and revelations, JCAP 05 (2018) 028 [ 1803.00541]. 4

    2018 arXiv

  40. [47]

    Saltas and J

    I.D. Saltas and J. Christensen-Dalsgaard, Searching for dark energy with the Sun , Astron. Astrophys. 667 (2022) A115 [ 2205.14134]. 4

    2022 arXiv

  41. [48]

    Landry and E

    P. Landry and E. Poisson, Gravitomagnetic response of an irrotational body to an applied tidal field , Phys. Rev. D 91 (2015) 104026 [ 1504.06606]. 4, 5, 6, 8

    2015 arXiv

  42. [49]

    Regge and J.A

    T. Regge and J.A. Wheeler, Stability of a Schwarzschild singularity, Phys. Rev. 108 (1957) 1063. 4

    1957

  43. [51]

    Takahashi, H

    K. Takahashi, H. Motohashi and M. Minamitsuji, Linear stability analysis of hairy black holes in quadratic degenerate higher-order scalar-tensor theories: Odd-parity perturbations, Phys. Rev. D 100 (2019) 024041 [1904.03554]. 5

    2019 arXiv

  44. [52]

    Tomikawa and T

    K. Tomikawa and T. Kobayashi, Perturbations and quasinormal modes of black holes with time-dependent scalar hair in shift-symmetric scalar-tensor theories , Phys. Rev. D 103 (2021) 084041 [ 2101.03790]. 5

    2021 arXiv

  45. [53]

    Crisostomi and K

    M. Crisostomi and K. Koyama, Self-accelerating universe in scalar-tensor theories after GW170817 , Phys. Rev. D 97 (2018) 084004 [ 1712.06556]. 6

    2018 arXiv

  46. [54]

    Hiramatsu and D

    T. Hiramatsu and D. Yamauchi, Testing gravity theories with cosmic microwave background in the degenerate higher-order scalar-tensor theory, Phys. Rev. D 102 (2020) 083525 [ 2004.09520]

    2020 arXiv

  47. [55]

    Hiramatsu, CMB constraints on DHOST theories , JCAP 10 (2022) 035 [ 2205.11559]

    T. Hiramatsu, CMB constraints on DHOST theories , JCAP 10 (2022) 035 [ 2205.11559]. 6

    2022 arXiv

  48. [56]

    Cisterna, T

    A. Cisterna, T. Delsate and M. Rinaldi, Neutron stars in general second order scalar-tensor theory: The case of nonminimal derivative coupling , Phys. Rev. D 92 (2015) 044050 [ 1504.05189]. 6

    2015 arXiv

  49. [57]

    Takahashi and H

    K. Takahashi and H. Motohashi, Black hole perturbations in DHOST theories: master variables, gradient instability, and strong coupling , JCAP 08 13 (2021) 013 [ 2106.07128]. 9

    2021 arXiv

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.