Pith. sign in

REVIEW 2 major objections 5 minor 1 cited by

Primordial gravitational waves in DHOST inflation

T0 review · 2 major / 5 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 Tiny shift-symmetry-breaking terms in DHOST inflation flatten the tensor spectrum, violating the single-field consistency relation and putting a constant gravitational-wave background within reach of a future mHz detector.

desk verdict Solid DHOST inflation extension, but the mHz detection claim is an uncomputed extrapolation. read the letter →

arxiv 2501.13210 v2 pith:VAP3F7FB submitted 2025-01-22 astro-ph.CO gr-qc

Philippe Brax , Andrei Lazanu This is my paper · ORCID
classification astro-ph.COgr-qc
keywords DHOSTinflationprimordialgravitationalwavestensorpowerspectrumconsistencyrelationshiftsymmetrybreakingmHzinterferometersinflationaryperturbationsPlanckconstraints
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

This paper claims that a class of DHOST theories, gravitational theories with a scalar field that avoid ghost instabilities, can inflate the early universe with an exactly de Sitter background while generating small deviations from scale invariance through tiny shift-symmetry-breaking terms added to the coefficient of the Ricci scalar. The result is a tensor power spectrum that is almost perfectly flat, with a tensor spectral index $n_T \approx 4 \times 10^{-8}$ and a tensor-to-scalar ratio $r(k_*) = 0.0148$, which strongly violates the single-field consistency relation $r = -8 n_T$. If the claim is right, the gravitational-wave density parameter $\Omega_{\rm GW} h^2$ remains constant across frequencies, at $5.18 \times 10^{-17}$, and a future space-based mHz interferometer could detect it and tell this model apart from slow-roll inflation. The paper also finds that the running of the scalar spectral index is positive, opposite to what most single-field models predict.

What carries the argument

The central object is the shift-symmetry-breaking perturbation in $F_2(\phi,X)$, the coefficient of the Ricci scalar, taking the form $F_2(X) \to F_2(X) - \left(\frac{m_{\rm phys}^2}{2}\phi^2 + \frac{\lambda_{\rm phys}}{4!}\phi^4\right)$. With the background solution $\phi = c - t$ (so $X = -1$), the functions $f_i$ and their derivatives are constant, and the model's parameters can be expressed through the $\alpha_i$ and $\beta_i$ coefficients. The shift-breaking terms modify the coefficients $A$ and $B$ in the second-order action for both scalar and tensor perturbations, and the power spectra are obtained by quantising the Mukhanov-Sasaki variable from a Bunch-Davies vacuum. This machinery is what decouples the background expansion (set by the shift-invariant part of the action) from the generation of perturbations (set by the tiny shift-breaking parameters), which is the root of the consistency-relation violation.

What would settle it

Solve the model's Mukhanov-Sasaki equation at the high-$k$ modes corresponding to mHz gravitational waves ($k \sim 10^6$ to $10^{15}\,{\rm Mpc}^{-1}$) and check whether $\Omega_{\rm GW} h^2$ remains constant at $5.18 \times 10^{-17}$; if the tensor spectrum tilts or the small couplings stop being perturbative at those scales, the claimed detectability fails.

Watch

Extended reading notes

Core claim

The central discovery is that breaking the shift symmetry of a DHOST action in the $F_2$ function, by adding small $\phi^2$ and $\phi^4$ pieces to the coefficient of the Ricci scalar, leaves the de Sitter background intact while making the scalar and tensor perturbations acquire their observed tilts. For the fiducial parameters the model matches Planck's scalar spectral index, running, and amplitude constraints and gives $r(k_*) = 0.0147879$ with $n_T \approx 4 \times 10^{-8}$, so that $r \gg 8|n_T|$, a strong violation of the consistency relation of single-field inflation. Because the tensor spectrum is so flat, the gravitational-wave density parameter is constant, $\Omega_{\rm GW} h^2 = 5.18 \times 10^{-17}$, and the paper argues this lies within the detectable range of the proposed $\mu$ARES space-based interferometer in the mHz band.

Load-bearing premise

The detection prospect rests on the tensor spectrum staying almost perfectly flat at much higher frequencies than the paper actually computes, with the tiny symmetry-breaking couplings remaining perturbative even as the background field grows with time.

Editorial extensions

If this is right

  • A future measurement that finds $r \approx -8 n_T$ would contradict this model; the paper predicts $r(k_*) = 0.0148$ with $n_T \approx 4 \times 10^{-8}$.
  • The gravitational-wave density parameter is predicted to be frequency-independent at $\Omega_{\rm GW} h^2 \approx 5.2 \times 10^{-17}$ in the mHz band, in contrast to slow-roll models where it decays with frequency, so the shape of the background alone can discriminate the two.
  • The model predicts a positive running of the scalar spectral index, $\alpha_s \approx 0.0011$, opposite to the negative running expected in most single-field slow-roll models, testable with future CMB data.
  • The tiny shift-symmetry-breaking couplings ($\lambda \approx -1.1 \times 10^{-30}$, $m^2 \approx -1 \times 10^{-21}$) keep the perturbative treatment valid at the scales where the paper checks it, but their smallness is not explained.
  • The model yields $N_* \approx 59.8$ e-foldings between pivot-scale horizon exit and the end of inflation, assuming inflation ends by a sudden change of physics.

Reading between the lines

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

  • If the flat tensor spectrum persists at the much higher wavenumbers ($k \sim 10^6$ to $10^{15}\,{\rm Mpc}^{-1}$) that source mHz gravitational waves, the model predicts a nearly white stochastic background in $\Omega_{\rm GW}$; but the paper only computes the spectrum on CMB scales, so this is an untested extrapolation.
  • The same mechanism of decoupling the background from perturbation generation could be realised in other shift-symmetric scalar-tensor theories, making a flat tensor spectrum a more general signature than this particular DHOST construction; the paper does not explore that generality.
  • A future detection of a positive scalar spectral-index running would be a strong discriminator against single-field slow-roll, but current Planck uncertainties are too large to distinguish the sign; high-resolution CMB experiments could settle it.
  • The extreme smallness of the symmetry-breaking couplings resembles the cosmological-constant fine-tuning problem, and explaining it might require a symmetry or anthropic argument; the paper leaves this open.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 5 minor

Summary. The paper studies DHOST inflationary models whose background is a de Sitter phase generated by shift-symmetric operators, with the shift symmetry broken in the F2 sector by small φ^2 and φ^4 terms. The authors derive the scalar and tensor power spectra using a Mukhanov-Sasaki quantization procedure, fit the model parameters to the Planck 2018 scalar spectral observables, and report a tensor-to-scalar ratio r(k*)=0.0147879 with a nearly scale-invariant tensor spectrum (n_T ~ 4×10^-8), thereby strongly violating the single-field consistency relation. They then use the constant tensor spectrum to predict a gravitational-wave density parameter Ω_GW h^2 = 5.18×10^-17 in the mHz band and argue that this is within reach of the proposed μARES interferometer.

Significance. If the mHz extrapolation is valid, the paper provides a concrete counterexample to the single-field consistency relation in a well-defined DHOST framework, with explicit spectra that are compatible with Planck scalar constraints. The computations are substantial, the fiducial model is clearly specified, and the appendix gives the perturbed scalar and tensor coefficients. The main caveat is that the central detectability claim rests on an uncomputed extrapolation of the tensor spectrum from CMB scales to mHz scales, and the extremely small couplings λ ~ 10^-30 and m^2 ~ 10^-21 are tuned without a dynamical explanation. The paper is therefore interesting and publishable in principle, but the mHz prediction needs additional support.

major comments (2)
  1. [Section 3, Fig. 2 and Eq. (30)] The constant Ω_GW h^2 = 5.18×10^-17 is obtained by taking the tensor power spectrum to remain essentially scale-invariant from CMB scales (k ~ 0.05 Mpc^-1) to mHz frequencies (k ~ 6×10^11 Mpc^-1). However, Fig. 1 only displays spectra over k ∈ [10^-4, 10^-1] Mpc^-1, and the paper does not compute P_T(k) at the high-k, late-time horizon crossings relevant for mHz detectors. Since the shift-symmetry-breaking corrections in Eqs. (A7) and (A8) depend on φ at horizon crossing, which evolves as φ(k) = const - (1/h_dS) ln k, the size of these corrections changes by many orders of magnitude over the extrapolated range. The authors should either extend the numerical computation of P_T and n_T to mHz scales or provide an analytic bound on n_T at high k derived from the explicit expressions in Appendix A. This is load-bearing for the μARES detectability statement in the conclusions.
  2. [Section 2, after Eq. (29)] The perturbativity argument states that "Due to the large values of the coefficients K^2_λ and K^2_m2, λ≲O(10^-30) and m^2≲O(10^-18) ensure that the perturbative regime is indeed valid," but the coefficients K^2_λ and K^2_m2 are never displayed, and the statement appears to be checked only over the CMB k-range shown in Fig. 1. At mHz horizon crossings, φ is roughly 6×10^5 times larger than at CMB scales for the fiducial h_dS = 5×10^-5, so the same coefficients must be re-evaluated there. The paper should state the range of k for which the perturbative treatment is claimed to hold and verify that the high-k part of Fig. 2 is within that range.
minor comments (5)
  1. [Section 2, Eq. (20)] There is a stray closing parenthesis in the definition of α_s(k): "d log k)" should read "d log k."
  2. [Section 2, Eq. (10) and surrounding text] The value N* = 59.78 is quoted without a derivation of the end of inflation or a reheating mechanism; the model is presented as a truncated effective theory, and it would be helpful to state the assumptions used to estimate N*.
  3. [Section 2, Eq. (26)-(27)] The formulas for c̄_s^2 and r are cited from earlier work, but the notation (e.g., β_H, c̄_s) is introduced only in passing; a short definition or reference to the specific equations in Brax & Lazanu (2021) would improve readability.
  4. [Figure 1] The panel labels for α_s and β_s are difficult to read, and the captions abbreviate "the running of its running" without naming α_s and β_s in the same order as the panels; please make the caption-to-panel correspondence explicit.
  5. [Conclusions] The statement that the model is "within the detectable range" of μARES is stronger than the body text, where the amplitude is described as "very close to the sensitivity threshold"; please use consistent wording and quantify the signal-to-noise ratio or sensitivity margin.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular derivation: tensor flatness is computed from the F2 perturbation, not fitted; self-citations are scaffolding.

full rationale

The derivation chain is not circular. The DHOST background and quantization formalism are taken from the authors' earlier work (Brax & Lazanu 2021), and the unperturbed shift-symmetric action is stated to give a scale-invariant scalar spectrum; this is a parameter-free prior result that motivates, but does not constitute, the new claim. The new physics is the F2 shift-symmetry breaking of Eq. (4), with two free parameters m^2 and λ. These are fixed by requiring compatibility with the Planck scalar spectral index, running, amplitude, and the tensor-to-scalar upper bound ("By choosing the model parameters ... we obtain a model that is compatible with the above cited constraints"), i.e., they are inputs. The flat tensor spectrum, n_T ≈ 4e-8, the strong violation r ≫ 8|n_T|, and the constant Ω_GW h^2 = 5.18e-17 are then computed from the Mukhanov-Sasaki system (Eqs. 28-30 and Appendix A), not imposed. The paper candidly labels the parameter choice as not unique and the tuning as unexplained. The mHz detectability claim depends on an extrapolation of Fig. 1 (k in [1e-4, 1e-1] Mpc^-1) to mHz scales, which is a regime-of-validity concern rather than a circular reduction: no mHz datum or fitted mHz quantity is fed back into the derivation. The self-citations are scaffolding for the formalism; they do not smuggle in the tensor flatness or the consistency-relation violation. Therefore no circular step is identified; score 2 reflects only the presence of minor, non-load-bearing self-citations.

Assumptions & free parameters 8 free parameters · 6 assumptions · 0 invented entities

The model is a tuned construction: eight dimensionless parameters are chosen to match Planck scalar data, the background is taken to be exactly de Sitter with a linear field profile, and the perturbative treatment of the tiny symmetry-breaking couplings is assumed. No new particles or forces are introduced; the action is a restricted subset of DHOST theories.

free parameters (8)
  • α_H = 1.04
    Chosen along with α_B and β_K to set the scalar sound speed to c (Eq. 26) and to satisfy the tensor-to-scalar ratio bound while matching Planck scalar constraints.
  • α_B = 1
    Set to 1 for simplicity; the authors state other O(1) values could give similar results.
  • β_K = 3.97343
    Fitted to reproduce the observed scalar spectral index and its running.
  • c = 1
    Integration constant of the linear background field solution φ = c - t; sets the field amplitude and the value of x = -1.
  • h_dS = 0.000050
    Fitted to obtain the observed scalar perturbation amplitude A_s.
  • f2 = 4.34
    Fitted to obtain the observed scalar amplitude and a tensor-to-scalar ratio below the current bound.
  • λ = -1.1e-30
    Quartic shift-symmetry breaking parameter; fitted to match n_s and the running.
  • m^2 = -1e-21
    Quadratic shift-symmetry breaking parameter; fitted to match n_s and the running.
assumptions (6)
  • domain assumption The action (3) is the most general stable DHOST action with functions of X only.
    Imported from Crisostomi & Koyama 2018 and related no-ghost analyses; the paper does not rederive it.
  • domain assumption The background is an exact de Sitter solution with constant h_dS.
    Eqs (12)-(13); the inflationary phase is assumed to be exactly de Sitter with no slow-roll corrections.
  • ad hoc to paper The scalar field background is the linear solution φ = c - t.
    Eq (14); chosen for simplicity and gives constant x = -1; other solutions could change the phenomenology.
  • domain assumption The F2-breaking perturbation (4) is small enough for first-order perturbative treatment.
    The paper gives order-of-magnitude estimates (λ≲1e-30, m^2≲1e-18) but does not prove convergence at all scales.
  • standard math Mukhanov-Sasaki quantization with a Bunch-Davies vacuum yields the power spectra.
    Standard cosmological perturbation theory; cited to Peter & Uzan 2013.
  • domain assumption Eq (30) for Ω_GW with standard radiation-dominated transfer function applies.
    From Clarke et al. 2020; assumes standard thermal history after inflation and no non-standard reheating.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Primordial gravitational waves in DHOST inflation." pith.science (2026). https://pith.science/paper/VAP3F7FB

@misc{pith2026250113210,
  author       = {Pith},
  title        = {Pith review of: Primordial gravitational waves in DHOST inflation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VAP3F7FB}},
  note         = {Machine review of arXiv:2501.13210}
}
read the original abstract

We consider DHOST inflationary models with a shift symmetry leading to a de Sitter space-time at the background cosmological level. Deviations from scale invariance of the scalar and tensor perturbations follow from the breaking of the shift symmetry by quadratic and quartic operators. These models show a strong violation of the consistency relation of single-field inflationary models with a very flat spectrum of tensor perturbations. This opens up the prospects of future detection of primordial gravitational waves by mHz experiments.

Figures

Figures reproduced from arXiv: 2501.13210 by the authors.

Figure 1
Figure 1. Model compatible with the Planck 2018 data: from top to bottom and left to right, the scalar power spectrum, the scalar spectral index 𝑛𝑠, its running 𝛼𝑠, the running of its running 𝛽𝑠, the tensor power spectrum, the tensor spectral index, the tensor-to-scalar ratio 𝑟, and the value of 𝑟 8|𝑛𝑇 | for a DHOST model with 𝛼𝐻 = 1.04, 𝛼𝐵 = 1, 𝛽𝐾 = 3.97343, 𝑐 = 1, ℎdS = 0.000050, 𝑓2 = 4.34 and the perturbation variables as … view at source ↗
Figure 2
Figure 2. Gravitational wave density parameter for the slow-roll and DHOST model together with the power law integrated sensitivity curves for 𝜇ARES from Ref. Roshan & White (2025). we showed that the DHOST model has a constant density, while for the slow-roll model this has a lower amplitude and is slowly decay￾ing. The amplitude of the DHOST model is within the detectable range of the future 𝜇ARES space-based interferometer… view at source ↗

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. Spherical collapse in DHOST theories and EFT of dark energy

    astro-ph.CO 2025-04 conditional novelty 7.0 of 10

    Spherical collapse in DHOST theories fails for the beyond-Horndeski parameter β1 above about 10^-7 because the scalar-field gradient becomes imaginary, and the halo mass function is suppressed relative to ΛCDM.

Reference graph

Works this paper leans on

37 extracted references · 14 canonical work pages · cited by 1 Pith paper

  1. [1]

    P., et al., 2016, @doi [Phys

    Abbott B. P., et al., 2016, @doi [Phys. Rev. Lett.] 10.1103/PhysRevLett.116.061102 , 116, 061102

    doi:10.1103/physrevlett.116.061102 2016

  2. [2]

    Abbott R., et al., 2021a, @doi [Phys. Rev. D] 10.1103/PhysRevD.104.022004 , 104, 022004

    doi:10.1103/physrevd.104.022004

  3. [3]

    Abbott R., et al., 2021b, @doi [Phys. Rev. Lett.] 10.1103/PhysRevLett.126.241102 , 126, 241102

    doi:10.1103/physrevlett.126.241102

  4. [4]

    Ade P. A. R., et al., 2018, @doi [Phys. Rev. Lett.] 10.1103/PhysRevLett.121.221301 , 121, 221301

    doi:10.1103/physrevlett.121.221301 2018

  5. [5]

    Astrophys.] 10.1051/0004-6361/201833887 , 641, A10

    Akrami Y., et al., 2020, @doi [Astron. Astrophys.] 10.1051/0004-6361/201833887 , 641, A10

    doi:10.1051/0004-6361/201833887 2020

  6. [6]

    Bellini E., Sawicki I., 2014, @doi [JCAP] 10.1088/1475-7516/2014/07/050 , 07, 050

    doi:10.1088/1475-7516/2014/07/050 2014

  7. [7]

    Ben Achour J., Crisostomi M., Koyama K., Langlois D., Noui K., Tasinato G., 2016a, @doi [JHEP] 10.1007/JHEP12(2016)100 , 12, 100

    work page doi:10.1007/jhep12(2016)100 2016

  8. [8]

    Ben Achour J., Langlois D., Noui K., 2016b, @doi [Phys. Rev. D] 10.1103/PhysRevD.93.124005 , 93, 124005

    work page doi:10.1103/physrevd.93.124005

Show all 37 references
  1. [9]

    J., Montani G., 2021, @doi [Phys

    Bombacigno F., Boudet S., Olmo G. J., Montani G., 2021, @doi [Phys. Rev. D] 10.1103/PhysRevD.103.124031 , 103, 124031

    2021 doi

  2. [10]

    Brax P., Lazanu A., 2021, @doi [JCAP] 10.1088/1475-7516/2021/08/061 , 08, 061

    2021 doi

  3. [11]

    Brax P., Lazanu A., 2022, @doi [JCAP] 10.1088/1475-7516/2022/01/026 , 01, 026

    2022 doi

  4. [12]

    J., Copeland E

    Clarke T. J., Copeland E. J., Moss A., 2020, @doi [JCAP] 10.1088/1475-7516/2020/10/002 , 10, 002

    2020 doi

  5. [13]

    Crisostomi M., Koyama K., 2018, @doi [Phys. Rev. D] 10.1103/PhysRevD.97.084004 , 97, 084004

    2018 doi

  6. [14]

    Crisostomi M., Koyama K., Tasinato G., 2016, @doi [JCAP] 10.1088/1475-7516/2016/04/044 , 04, 044

    2016 doi

  7. [15]

    A., 2019a, @doi [JCAP] 10.1088/1475-7516/2019/01/030 , 01, 030

    Crisostomi M., Koyama K., Langlois D., Noui K., Steer D. A., 2019a, @doi [JCAP] 10.1088/1475-7516/2019/01/030 , 01, 030

    2019 doi

  8. [16]

    Crisostomi M., Lewandowski M., Vernizzi F., 2019b, @doi [Phys. Rev. D] 10.1103/PhysRevD.100.024025 , 100, 024025

    doi

  9. [17]

    Galloni G., Bartolo N., Matarrese S., Migliaccio M., Ricciardone A., Vittorio N., 2023, @doi [JCAP] 10.1088/1475-7516/2023/04/062 , 04, 062

    2023 doi

  10. [18]

    Gleyzes J., Langlois D., Piazza F., Vernizzi F., 2015a, @doi [JCAP] 10.1088/1475-7516/2015/02/018 , 02, 018

    2015 doi

  11. [19]

    Gleyzes J., Langlois D., Vernizzi F., 2015b, @doi [Int. J. Mod. Phys. D] 10.1142/S021827181443010X , 23, 1443010

    doi

  12. [20]

    Gleyzes J., Langlois D., Piazza F., Vernizzi F., 2015c, @doi [Phys. Rev. Lett.] 10.1103/PhysRevLett.114.211101 , 114, 211101

    doi

  13. [21]

    A., Motohashi H., Mukohyama S., 2021, @doi [JCAP] 10.1088/1475-7516/2021/03/081 , 03, 081

    Gorji M. A., Motohashi H., Mukohyama S., 2021, @doi [JCAP] 10.1088/1475-7516/2021/03/081 , 03, 081

    2021 doi

  14. [22]

    W., 1974, @doi [International Journal of Theoretical Physics] 10.1007/BF01807638 , https://ui.adsabs.harvard.edu/abs/1974IJTP...10..363H 10, 363

    Horndeski G. W., 1974, @doi [International Journal of Theoretical Physics] 10.1007/BF01807638 , https://ui.adsabs.harvard.edu/abs/1974IJTP...10..363H 10, 363

    1974 doi

  15. [23]

    Kobayashi T., 2019, @doi [Rept. Prog. Phys.] 10.1088/1361-6633/ab2429 , 82, 086901

    2019 doi

  16. [24]

    Langlois D., 2019, @doi [Int. J. Mod. Phys. D] 10.1142/S0218271819420069 , 28, 1942006

    2019 doi

  17. [25]

    Langlois D., Noui K., 2016, @doi [JCAP] 10.1088/1475-7516/2016/02/034 , 02, 034

    2016 doi

  18. [26]

    Langlois D., Mancarella M., Noui K., Vernizzi F., 2017, @doi [JCAP] 10.1088/1475-7516/2017/05/033 , 05, 033

    2017 doi

  19. [27]

    Lazanu A., 2025, @doi [Annalen der Physik] 10.1002/andp.202400263 , 537, 2400263

    2025 doi

  20. [28]

    Martin J., Ringeval C., Vennin V., 2024, @doi [EPL] 10.1209/0295-5075/ad847c , 148, 29002

    2024 doi

  21. [29]

    Motohashi H., Hu W., 2017, @doi [Phys. Rev. D] 10.1103/PhysRevD.96.023502 , 96, 023502

    2017 doi

  22. [30]

    Oxford Graduate Texts, Oxford University Press

    Peter P., Uzan J.-P., 2013, Primordial Cosmology . Oxford Graduate Texts, Oxford University Press

    2013

  23. [31]

    Roshan R., White G., 2025, @doi [Rev. Mod. Phys.] 10.1103/RevModPhys.97.015001 , 97, 015001

    2025 doi

  24. [32]

    Schmitz K., Schr\"oder T., 2024, @doi [Phys. Rev. D] 10.1103/PhysRevD.110.063549 , 110, 063549

    2024 doi

  25. [33]

    Astron.] 10.1007/s10686-021-09709-9 , 51, 1333

    Sesana A., et al., 2021, @doi [Exper. Astron.] 10.1007/s10686-021-09709-9 , 51, 1333

    2021 doi

  26. [34]

    R., 2024, @doi [JCAP] 10.1088/1475-7516/2024/04/071 , 04, 071

    Sohn W., Lazanu A., Brax P., Fergusson J. R., 2024, @doi [JCAP] 10.1088/1475-7516/2024/04/071 , 04, 071

    2024 doi

  27. [35]

    Astrophys.] 10.1051/0004-6361/202039585 , 647, A128

    Tristram M., et al., 2021, @doi [Astron. Astrophys.] 10.1051/0004-6361/202039585 , 647, A128

    2021 doi

  28. [36]

    Tristram M., et al., 2022, @doi [Phys. Rev. D] 10.1103/PhysRevD.105.083524 , 105, 083524

    2022 doi

  29. [37]

    Zumalac\'arregui M., Garc\' a-Bellido J., 2014, @doi [Phys. Rev. D] 10.1103/PhysRevD.89.064046 , 89, 064046

    2014 doi

Pith tools

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