Pith. sign in

REVIEW 3 major objections 4 minor 118 references

This paper claims that a single parameterization of gravitational-wave propagation, extended to early-universe corrections, can capture the observable effects of any non-minimal matter–curvature coupling, and it demonstrates the mapping for

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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

T0 review · deepseek-v4-flash

2026-08-04 07:21 UTC pith:YC4B7VDP

load-bearing objection Useful extension of the GW-propagation parameterization with solid model mappings, but the early-universe bound from GW170817 in Eq. (5.91) does not actually follow from the observation. the 3 major comments →

arxiv 2510.25895 v2 pith:YC4B7VDP submitted 2025-10-29 gr-qc astro-ph.COhep-th

Beyond general relativity: gravitational waves in non-minimally coupled theories

Stephon Alexander , Tatsuya Daniel , Tucker Manton This is my paper
classification gr-qc astro-ph.COhep-th MSC 83C3583D0583F05 PACS 04.30.-w04.50.Kd95.35.+d
keywords gravitational wavesnon-minimal couplingsparity violationbirefringencedark matterKalb-RamondChern-SimonsGW170817
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper tries to establish that the observable effects of non-minimal couplings between matter and spacetime curvature on gravitational-wave propagation can be organized into a single, model-independent parameterization, now extended to include early-universe corrections of order H^2 and H'. It shows that three different dark-matter theories — Kalb-Ramond fields, axion-dilaton-Chern-Simons-Gauss-Bonnet, and U(1) vector fields — each map onto this parameterization, and it uses the GW170817 speed measurement to place order-of-magnitude constraints on their parameters, including an upper bound on the Kalb-Ramond mass near 10^11 GeV. If correct, this gives a practical way to use current and future gravitational-wave observations to test dark-matter models that couple non-minimally to gravity.

Core claim

The central claim is that the propagation of gravitational waves through backgrounds with non-minimally coupled matter is described, at linear order and under slowly-varying matter fields, by the parameterized equation (3.10)-(3.11) with parity-even and parity-odd coefficients; the new H^2 and H' terms extend the known parameterization into the early universe. The paper maps three explicit Lagrangians onto this scheme, reads off amplitude and velocity birefringence plus modified dispersion relations, and derives constraints from the GW170817 bound: |δ_1| < 6×10^-15, a Kalb-Ramond mass bound m_B ≲ 10^11 GeV for order-one couplings, and an early-universe bound |φ'| ≲ 10^-15 m_p^2 at H ~ Λ_E.

What carries the argument

The key object is the parameterized propagation equation for left- and right-handed GW strains, h'' + (2H + C_O^(1)+C_E^(1))h' + k^2(1+C_O^(0)+C_E^(0))h=0, where the eight coefficient families {α,β,γ,δ,μ,ν,ρ,σ} are organized by parity (even/odd) and by momentum power, with separate cutoffs for each parity. The companion solution (3.14) expresses the strain corrections as exponentials of redshift integrals and effective distances, so that any Lagrangian of the form (3.9) reduces to a small set of algebraic coefficients, which can then be directly compared with observations.

Load-bearing premise

The closed-form solution (3.14) and the early-universe bound (5.91) assume that matter fields vary slowly, so their derivatives can be replaced by present-day constants; the paper itself concedes this assumption may break down in realistic early-universe scenarios.

What would settle it

Numerically solve the propagation equations (3.10) for a concrete rolling axion background with a time-dependent φ'(η) typical of inflation, and compare the waveform to the analytic solution (3.14) evaluated at φ'_0; a significant mismatch would show the parameterization does not capture early-universe effects as claimed. Alternatively, a future measurement of a circular polarization in the stochastic GW background that cannot be represented by the parity-odd coefficients of this parameterization would refute the completeness of the scheme.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Any non-minimal coupling within the class (3.9) can be constrained by the same waveform and speed tests, without re-deriving the propagation equations.
  • The GW170817 speed bound translates directly into a Kalb-Ramond mass bound m_B ≲ 10^11 GeV for order-one couplings, ruling out a simple static Kalb-Ramond configuration as a dominant dark-matter component.
  • The early-universe constraint |φ'| ≲ 10^-15 m_p^2 at H ~ Λ_E delimits how large Chern-Simons-Gauss-Bonnet corrections can be at the edge of EFT validity.
  • Parity-odd couplings produce a distinctive signature: one circular polarization is attenuated while the other is amplified, plus a helicity-dependent phase velocity.
  • The U(1) dimension-six model is quartic-Planck suppressed, so its effects are unobservable in current detectors, yet the parameterization still organizes them for future use.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The slowly-varying assumption is least reliable precisely where the new H^2 and H' terms matter — during inflation and reheating — so a numerical integration for rapidly rolling fields could reveal that early-universe effects are significantly larger than the closed-form solution suggests.
  • A net circular polarization in the stochastic gravitational-wave background would directly test the parity-odd sector of these models; the coefficient mapping in this paper provides a ready translation from such a future measurement to model parameters.
  • The paper notes that teleparallel/Nieh-Yan parity violation cannot be mapped into this parameterization, implying an even more general scheme is needed to cover all beyond-GR theories; a natural test is to search for H-independent parity-violating terms in GW propagation.
  • If future detectors improve the GW speed bound by an order of magnitude, the same formulas would immediately sharpen the Kalb-Ramond mass and axion derivative bounds, potentially reaching the parameter space of viable dark-matter candidates.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper extends a previously proposed model-independent parameterization of parity-even and parity-odd modifications to gravitational-wave propagation, adding terms of order H^2 and H'. It gives a closed-form solution for the GW strains under the assumption that matter fields are slowly varying, and then maps three specific dark-matter models onto the parameterization: Kalb-Ramond two-form dark matter (dimension-four operators), axion-dilaton Chern-Simons-Gauss-Bonnet theory (dimension-five operators), and a U(1) dark-photon model (dimension-six operators). The paper also uses the GW170817 speed bound to constrain combinations of model parameters, including an early-universe bound on the scalar-field derivative in the axion-dilaton model.

Significance. If the derivations were fully correct, the paper would provide a useful bridge between a model-agnostic propagation parameterization and several non-minimally coupled dark-matter theories, with concrete GW observables. The authors are appropriately transparent about the slowly-varying-field assumption and about the need for numerical integration when it fails. The WKB-style derivation in Appendix A is standard in structure, and the three model mappings are valuable. However, the explicit redshift-integrated solution contains conversion errors for the new H^2 and H' terms, and the GW170817 bound is extrapolated to early times without justification. These issues are load-bearing for the paper's claimed early-universe results, though the dispersion relations and the late-time constraints on delta1 and gamma1 are likely still sound.

major comments (3)
  1. [Sec. 3 and Appendix A, Eqs. (3.14), (1.99)-(1.102)] The conversion from conformal-time integrals to redshift integrals for the new mu, rho, nu, sigma terms is incorrect. For example, the exact conversion for the mu0 term is the integral of H_conf^2 / a d(eta) = integral over z of H_cos(z')/(1+z') dz', where H_conf is the conformal Hubble parameter and H_cos is the cosmic Hubble parameter, not the integral over z of H_cos dz' as written in Eq. (1.99). Similarly, the integral of H_conf' / a d(eta) equals H_cos(0) - H_cos(z)/(1+z), not (1+z) times the integral of H_cos_z/(1+z) dz, and the integral of H_conf^2 d(eta) equals the integral over z of H_cos(z')/(1+z')^2 dz', not the integral of H_cos dz. These errors propagate into the model-specific solutions (4.49), (4.66), and (4.81). The closed-form solution (3.14) is therefore not valid as written at arbitrary redshift; it is at best a small-redshift approximation.
  2. [Sec. 5, Eqs. (5.85)-(5.91)] Equation (5.91) does not follow from the GW170817 bound. The bound (5.85) constrains the group velocity of GW170817, which propagated only through the late universe (z ~ 0.01). Evaluating the same inequality at H ~ Lambda_E assumes that the beyond-GR coefficients are constant across cosmic history, which the paper explicitly does not assume (see Sec. 6 and footnote 9). Thus |phi'| less than about 10^-15 m_p^2 is not an observational consequence of GW170817. The late-time constraints on delta1 and gamma1 are unaffected, but the claimed early-universe bound should be removed or substantially reframed.
  3. [Sec. 3.1 and Sec. 6] The paper's own caveats undermine the early-universe applicability of the central solution. Footnote 9 states that the slowly-varying assumption 'possibly breaks down in realistic early-universe scenarios,' and Sec. 6 concedes that the H^2/k^2 and H'/k^2 corrections 'have importance in the early universe, when matter fields are not necessarily slowly varying.' Since the new terms are precisely intended to capture early-universe effects, the slowly-varying assumption is load-bearing exactly where the claimed novelty lies. The authors should either restrict the closed-form solution to late times or provide a controlled expansion that remains valid during early-universe rolling.
minor comments (4)
  1. [Appendix A, Eq. (1.103)] The amplitude exponent in Eq. (1.103) has a plus sign in front of the first exponential, whereas the main-text solution (3.14) has a minus sign. Since the minus sign is the physically correct one (and is consistent with the alpha0 friction example), the appendix appears to contain a sign typo.
  2. [Sec. 3, notation] The notation H is used for the conformal Hubble parameter in the equations of motion but for the cosmic Hubble parameter in the redshift integrals in Eq. (3.14). This is a frequent source of confusion and should be fixed by using e.g. H_conf and H_cos.
  3. [Sec. 4.3, Eq. (4.77)] The approximation d/deta B^2 approximately equals H B^2 assumes that the dimensionless B-tilde^2 is nearly constant, not just that the fields are slowly varying. This should be stated explicitly.
  4. [Sec. 4.4, Table 1] The table is hard to read because the column headers are not aligned with the row check marks in the text version. A formatted table with explicit nonzero coefficients would improve clarity.

Circularity Check

0 steps flagged

No circular reduction found: the extended parameterization and model mappings are explicit derivations, and the GW170817 constraints are external. Self-citations are present but not load-bearing.

full rationale

The derivation chain is self-contained. Equations (3.10)-(3.11) are written out explicitly as a parameterization, and the solution (3.14) is derived from them in Appendix A under the stated slow-variation and WKB assumptions; the new O(H^2) and O(H') terms are not obtained by fitting anything to GW data. The mappings in Section 4 are computed from the respective Lagrangians (Kalb-Ramond, axion-dilaton-Chern-Simons-Gauss-Bonnet, and U(1) vector field), with the nonzero coefficients in Table 1 identified by substitution into (3.11). There is no step in which a parameter is fitted to a subset of data and then reported as a prediction of a closely related quantity. The GW170817 bound (5.85) is an external observational input, not an output of the model, and the late-time constraints (5.87)-(5.89) are elementary substitutions. The early-universe bound (5.91) is obtained by evaluating (5.90) at H ~ Lambda_E; whether it is physically justified to apply the GW170817-derived group-velocity inequality at that epoch is a validity/correctness concern, not a circularity. The paper openly cites prior work by overlapping authors ([2], [33], [121]), but these citations are not load-bearing: the prior parameterization is reproduced in Eq. (2.7), the Kalb-Ramond constant-background configuration is an explicitly adopted ansatz (also attributed to [111,113]), and the [2] bound on phi' is used only for context, not to derive the paper's new results. Footnote 9 and Section 6 acknowledge the slow-variation limitation, which further shows the assumptions are stated rather than smuggled in. Therefore, no circular step is exhibited in the sense required by the review criteria.

Axiom & Free-Parameter Ledger

3 free parameters · 5 axioms · 0 invented entities

No new particles, forces, or dimensions are invented. The Kalb-Ramond field, axion, dilaton, and U(1) vector are all pre-existing fields, and the non-minimal operators are standard EFT couplings. The free parameters are background field values and field derivatives that the constraint analysis bounds; they are not fitted to make the derivation work, though the slowly-varying-field axiom is a strong modeling choice.

free parameters (3)
  • Ṽ_e, Ṽ_m (Kalb-Ramond background components)
    Dimensionless constant components of the KR 2-form background in Eq. (4.45), held constant via a symmetry-breaking potential. They are input background values, not fitted; the GW170817 constraint (5.88) bounds their combination, and the figures use Ṽ_e = Ṽ_m = 3 for illustration.
  • ϕ′_0, φ′_0 (axion-dilaton scalar derivatives)
    Derivatives of the axion and dilaton fields, assumed slowly varying and approximated by their current values in Appendix A. They are the physical parameters constrained by Eqs. (5.90)–(5.91), not fitted to produce the parameterization.
  • B̃² (dark photon magnetic background)
    Dimensionless magnetic-field combination introduced in Eq. (4.76) and assumed nearly constant. It is an input parameter, not fitted; the figure uses B̃² = 2 for illustration.
axioms (5)
  • domain assumption GW perturbations obey the linearized TT propagation form (2.5)/(3.10) with no additional source terms or higher-derivative structures.
    This is the foundation of the entire parameterization. The authors themselves note in Sec. 6 that some theories, e.g. teleparallel gravity with the Nieh-Yan term, cannot be mapped into this form.
  • ad hoc to paper Matter fields are slowly varying; second derivatives and (dB/dη)² terms are neglected.
    Required for the closed-form solution (3.14) and the constraint (5.91). Footnote 9 concedes the assumption may break down in realistic early-universe scenarios.
  • standard math WKB approximations: δθ ≪ θ̄, θ″ ≪ (θ′)², δθ″ ≪ θ̄ δθ′.
    Used in Appendix A to linearize the phase equation and derive the generic waveform correction.
  • domain assumption The EFT operator expansion is truncated at the stated dimensions, and coupling constants ξ_i are assumed O(1) when converting bounds into mass scales.
    Used in Sec. 5, e.g. √|6ξ1 − ξ2| ∼ 1 to turn Eq. (5.88) into m_B ≲ 10¹¹ GeV.
  • domain assumption FLRW background with the standard ΛCDM Hubble expansion H(z) = H₀√(Ω_m,0(1+z)³ + Ω_r,0(1+z)⁴ + Ω_Λ,0).
    Used in the redshift integrals of Eq. (3.14) and the constraints.

pith-pipeline@v1.3.0-alltime-deepseek · 26834 in / 14320 out tokens · 138171 ms · 2026-08-04T07:21:55.662029+00:00 · methodology

0 comments
read the original abstract

Non-minimal couplings between matter and curvature tensors arise in many different contexts. Such couplings modify solutions of general relativity (GR) and therefore can be probed in various astrophysical systems. A particularly interesting scenario arises if dark matter experiences non-minimal couplings, as dark matter densities are expected to spike in the vicinity of binary black hole mergers. This gives a novel setting for simultaneously studying dark matter and (beyond) GR physics via observations of gravitational waves (GWs). In this work, we explore effects of various non-minimal couplings on GWs by working with a model-independent parameterization for left- and right-handed GW strains. We extend the parameterization proposed in \cite{Jenks:2023pmk,Daniel:2024lev} to include early-universe effects, and we write down the generic solution assuming slowly-varying matter fields. We then systematically apply our results to three models: Kalb-Ramond dark matter with dimension-four operators, axion-dilaton-Chern-Simons-Gauss-Bonnet dimension-five operators, and dimension-six couplings to a (dark) vector field.

Figures

Figures reproduced from arXiv: 2510.25895 by Stephon Alexander, Tatsuya Daniel, Tucker Manton.

Figure 1
Figure 1. Figure 1: Example modification to a binary black hole waveform for [PITH_FULL_IMAGE:figures/full_fig_p018_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Example modification to a binary black hole waveform for [PITH_FULL_IMAGE:figures/full_fig_p019_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Example modification to a binary black hole waveform for [PITH_FULL_IMAGE:figures/full_fig_p019_3.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

118 extracted references · 4 canonical work pages

  1. [1]

    Parametrized parity violation in gravitational wave propagation,

    L. Jenks, L. Choi, M. Lagos, and N. Yunes, “Parametrized parity violation in gravitational wave propagation,”Phys. Rev. D108no. 4, (2023) 044023, arXiv:2305.10478 [gr-qc]

    Pith/arXiv arXiv 2023

  2. [2]

    Gravitational waves in chern-simons-gauss-bonnet gravity,

    T. Daniel, L. Jenks, and S. Alexander, “Gravitational waves in chern-simons-gauss-bonnet gravity,”Phys. Rev. D109(Jun, 2024) 124012. https://link.aps.org/doi/10.1103/PhysRevD.109.124012. [3]LIGO Scientific, VirgoCollaboration, B. P. Abbottet al., “GWTC-1: A Gravitational-Wave Transient Catalog of Compact Binary Mergers Observed by LIGO and Virgo during th...

    Pith/arXiv arXiv 2024

  3. [6]

    Is cosmological data suggesting a nonminimal coupling between matter and gravity?,

    M. Barroso Varela and O. Bertolami, “Is cosmological data suggesting a nonminimal coupling between matter and gravity?,”Phys. Dark Univ.48(2025) 101861, arXiv:2412.09348 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  4. [7]

    Nonminimal superheavy dark matter,

    S. Verner, “Nonminimal superheavy dark matter,”JCAP05(2025) 060, arXiv:2408.11889 [hep-ph]

    Pith/arXiv arXiv 2025

  5. [8]

    Cosmology with a non-minimally coupled dark matter fluid i. background evolution,

    S. Silveravalle, A. Lapi, F. Benetti, and S. Liberati, “Cosmology with a non-minimally coupled dark matter fluid i. background evolution,” 2025. https://arxiv.org/abs/2507.16614

    Pith/arXiv arXiv 2025

  6. [9]

    The Confrontation between General Relativity and Experiment,

    C. M. Will, “The Confrontation between General Relativity and Experiment,”Living Rev. Rel.17(2014) 4,arXiv:1403.7377 [gr-qc]

    Pith/arXiv arXiv 2014

  7. [10]

    Testing general relativity with pulsar timing,

    I. H. Stairs, “Testing general relativity with pulsar timing,”Living Rev. Rel.6(2003) 5,arXiv:astro-ph/0307536

    Pith/arXiv arXiv 2003

  8. [11]

    Testing gravity with realistic gravitational waveforms in Pulsar Timing Arrays,

    W. Hu, Q. Liang, M.-X. Lin, and M. Trodden, “Testing gravity with realistic gravitational waveforms in Pulsar Timing Arrays,”JCAP12(2024) 054, arXiv:2408.11774 [astro-ph.CO]. 25 [12]LIGO Scientific, VIRGO, KAGRACollaboration, R. Abbottet al., “Tests of General Relativity with GWTC-3,”arXiv:2112.06861 [gr-qc]

    Pith/arXiv arXiv 2024

  9. [13]

    Gravitational collapse and space-time singularities,

    R. Penrose, “Gravitational collapse and space-time singularities,”Phys. Rev. Lett.14 (1965) 57–59

    1965

  10. [14]

    Quantum gravity: A Progress report,

    S. Carlip, “Quantum gravity: A Progress report,”Rept. Prog. Phys.64(2001) 885, arXiv:gr-qc/0108040

    Pith/arXiv arXiv 2001

  11. [15]

    Dark spiky primordial black holes,

    A. Ireland, “Dark spiky primordial black holes,”Phys. Rev. D111no. 2, (2025) 023513,arXiv:2406.07624 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  12. [16]

    Evolution of the DM distribution function in the density spikes around PBHs,

    Y. N. Eroshenko, “Evolution of the DM distribution function in the density spikes around PBHs,”JCAP08(2024) 019,arXiv:2407.10225 [astro-ph.CO]

    Pith/arXiv arXiv 2024

  13. [17]

    Probing dark-matter effects with gravitational waves using the parametrized post-Einsteinian framework,

    E. Wilcox, D. A. Nichols, and K. Yagi, “Probing dark-matter effects with gravitational waves using the parametrized post-Einsteinian framework,”Phys. Rev. D110no. 12, (2024) 124009,arXiv:2409.10846 [gr-qc]

    Pith/arXiv arXiv 2024

  14. [18]

    Effect of ultralight dark matter on compact binary mergers,

    K. Chakravarti, S. Acharya, S. Chakraborty, and S. Sarkar, “Effect of ultralight dark matter on compact binary mergers,”arXiv:2503.19660 [gr-qc]

    arXiv

  15. [19]

    Ringing of a black hole in a dark matter halo,

    D. Liu, Y. Yang, S. Wu, Y. Xing, Z. Xu, and Z.-W. Long, “Ringing of a black hole in a dark matter halo,”Phys. Rev. D104no. 10, (2021) 104042,arXiv:2104.04332 [gr-qc]

    Pith/arXiv arXiv 2021

  16. [20]

    Gravitational ringing and superradiant instabilities of the Kerr-like black holes in a dark matter halo,

    D. Liu, Y. Yang, A. ¨Ovg¨ un, Z.-W. Long, and Z. Xu, “Gravitational ringing and superradiant instabilities of the Kerr-like black holes in a dark matter halo,”Eur. Phys. J. C83no. 7, (2023) 565,arXiv:2204.11563 [gr-qc]

    Pith/arXiv arXiv 2023

  17. [21]

    Modeling the black holes surrounded by a dark matter halo in the galactic center of M87,

    D. Liu, Y. Yang, Z. Xu, and Z.-W. Long, “Modeling the black holes surrounded by a dark matter halo in the galactic center of M87,”Eur. Phys. J. C84no. 2, (2024) 136,arXiv:2307.13553 [gr-qc]

    Pith/arXiv arXiv 2024

  18. [22]

    Probing the black holes in a dark matter halo of M87 using gravitational wave echoes,

    D. Liu, Y. Yang, and Z.-W. Long, “Probing the black holes in a dark matter halo of M87 using gravitational wave echoes,”Eur. Phys. J. C84no. 8, (2024) 871, arXiv:2312.07074 [gr-qc]

    Pith/arXiv arXiv 2024

  19. [23]

    Quasinormal modes of Schwarzschild-like black hole surrounded by the pseudo-isothermal dark matter halo,

    Y. Liu, B. Mu, J. Tao, and Y. Weng, “Quasinormal modes of Schwarzschild-like black hole surrounded by the pseudo-isothermal dark matter halo,”Nucl. Phys. B1010 (2025) 116787,arXiv:2409.20333 [gr-qc]

    Pith/arXiv arXiv 2025

  20. [24]

    Probing black holes in a dark matter spike of M87 using quasinormal modes,

    D. Liu, Y. Yang, and Z.-W. Long, “Probing black holes in a dark matter spike of M87 using quasinormal modes,”Eur. Phys. J. C84no. 7, (2024) 731, arXiv:2401.09182 [gr-qc]. 26

    Pith/arXiv arXiv 2024

  21. [25]

    Black holes surrounded by dark matter spike: spacetime metrics and gravitational wave ringdown waveforms,

    D. Liu, “Black holes surrounded by dark matter spike: spacetime metrics and gravitational wave ringdown waveforms,”arXiv:2501.12213 [gr-qc]

    Pith/arXiv arXiv

  22. [26]

    Black hole surrounded by the pseudo-isothermal dark matter halo,

    Y. Yang, D. Liu, A. ¨Ovg¨ un, G. Lambiase, and Z.-W. Long, “Black hole surrounded by the pseudo-isothermal dark matter halo,”Eur. Phys. J. C84no. 1, (2024) 63, arXiv:2308.05544 [gr-qc]

    Pith/arXiv arXiv 2024

  23. [27]

    Gravitational wave emission in binary neutron star early post-merger within a dark environment,

    D. Su´ arez-Fontanella, D. Barba-Gonz´ alez, C. Albertus, and M.´A. P´ erez-Garc ´ ıa, “Gravitational wave emission in binary neutron star early post-merger within a dark environment,”Phys. Lett. B862(2025) 139358,arXiv:2408.05226 [gr-qc]

    Pith/arXiv arXiv 2025

  24. [28]

    Constraining dark-sector effects using gravitational waves from compact binary inspirals,

    C. B. Owen, A. Tucker, Y. Kahn, and N. Yunes, “Constraining dark-sector effects using gravitational waves from compact binary inspirals,”Phys. Rev. D111no. 12, (2025) 124042,arXiv:2503.04916 [gr-qc]

    Pith/arXiv arXiv 2025

  25. [29]

    Gravitational waveforms from periodic orbits around a Schwarzschild black hole embedded in a Dehnen-type dark matter halo,

    M. Alloqulov, T. Xamidov, S. Shaymatov, and B. Ahmedov, “Gravitational waveforms from periodic orbits around a Schwarzschild black hole embedded in a Dehnen-type dark matter halo,”Eur. Phys. J. C85no. 7, (2025) 798, arXiv:2504.05236 [gr-qc]

    Pith/arXiv arXiv 2025

  26. [30]

    Gravitational waves of quasi-circular, inspiraling black hole binaries in an ultralight vector dark-matter environment,

    T. F. Chase, D. L´ opez Nacir, and N. Yunes, “Gravitational waves of quasi-circular, inspiraling black hole binaries in an ultralight vector dark-matter environment,” arXiv:2505.21383 [astro-ph.CO]

    arXiv

  27. [31]

    Probing self-interacting dark matter via gravitational-wave background from eccentric supermassive black hole mergers,

    M.-C. Chen and Y. Tang, “Probing self-interacting dark matter via gravitational-wave background from eccentric supermassive black hole mergers,” Phys. Rev. D112no. 4, (2025) 043033,arXiv:2505.09219 [astro-ph.GA]

    Pith/arXiv arXiv 2025

  28. [32]

    Probing Dark Matter Spike with Gravitational Waves from Early EMRIs in the Milky Way Center,

    C. Feng, Y. Tang, and Y.-L. Wu, “Probing Dark Matter Spike with Gravitational Waves from Early EMRIs in the Milky Way Center,”arXiv:2506.02937 [astro-ph.GA]

    Pith/arXiv arXiv

  29. [33]

    Kalb-Ramond field and gravitational parity violation,

    T. Manton and S. Alexander, “Kalb-Ramond field and gravitational parity violation,”Phys. Rev. D110no. 4, (2024) 044067,arXiv:2401.14452 [gr-qc]

    arXiv 2024

  30. [34]

    Observational constraints on the nonlinear regime of gravity with a parametrized beyond-GR gravitational waveform model,

    D. Watarai, A. Nishizawa, H. Takeda, H. Imafuku, and K. Cannon, “Observational constraints on the nonlinear regime of gravity with a parametrized beyond-GR gravitational waveform model,”arXiv:2509.17592 [gr-qc]

    arXiv

  31. [35]

    The Final parsec problem,

    M. Milosavljevic and D. Merritt, “The Final parsec problem,”AIP Conf. Proc.686 no. 1, (2003) 201–210,arXiv:astro-ph/0212270

    Pith/arXiv arXiv 2003

  32. [36]

    Fundamental Theoretical Bias in Gravitational Wave Astrophysics and the Parameterized Post-Einsteinian Framework,

    N. Yunes and F. Pretorius, “Fundamental Theoretical Bias in Gravitational Wave Astrophysics and the Parameterized Post-Einsteinian Framework,”Phys. Rev. D80 (2009) 122003,arXiv:0909.3328 [gr-qc]. 27

    Pith/arXiv arXiv 2009

  33. [37]

    Gravitational Wave Tests of General Relativity with the Parameterized Post-Einsteinian Framework,

    N. Cornish, L. Sampson, N. Yunes, and F. Pretorius, “Gravitational Wave Tests of General Relativity with the Parameterized Post-Einsteinian Framework,”Phys. Rev. D84(2011) 062003,arXiv:1105.2088 [gr-qc]

    Pith/arXiv arXiv 2011

  34. [38]

    Neural post-Einsteinian framework for efficient theory-agnostic tests of general relativity with gravitational waves,

    Y. Xie, D. Chatterjee, G. Narayan, and N. Yunes, “Neural post-Einsteinian framework for efficient theory-agnostic tests of general relativity with gravitational waves,”Phys. Rev. D110no. 2, (2024) 024036,arXiv:2403.18936 [gr-qc]

    Pith/arXiv arXiv 2024

  35. [39]

    Search for exotic gravitational wave signals beyond general relativity using deep learning,

    Y.-X. Wang, X. Wei, C.-Y. Li, T.-Y. Sun, S.-J. Jin, H. Wang, J.-L. Cui, J.-F. Zhang, and X. Zhang, “Search for exotic gravitational wave signals beyond general relativity using deep learning,”Phys. Rev. D112no. 2, (2025) 024030,arXiv:2410.20129 [gr-qc]

    Pith/arXiv arXiv 2025

  36. [40]

    Chern-Simons Modified General Relativity,

    S. Alexander and N. Yunes, “Chern-Simons Modified General Relativity,”Phys. Rept.480(2009) 1–55,arXiv:0907.2562 [hep-th]

    Pith/arXiv arXiv 2009

  37. [41]

    A Horizon Study for Cosmic Explorer: Science, Observatories, and Community,

    M. Evanset al., “A Horizon Study for Cosmic Explorer: Science, Observatories, and Community,”arXiv:2109.09882 [astro-ph.IM]

    Pith/arXiv arXiv

  38. [42]

    Science Case for the Einstein Telescope,

    M. Maggioreet al., “Science Case for the Einstein Telescope,”JCAP03(2020) 050, arXiv:1912.02622 [astro-ph.CO]

    Pith/arXiv arXiv 2020

  39. [43]

    Gravitational-Wave Tests of General Relativity with Ground-Based Detectors and Pulsar-Timing Arrays,

    N. Yunes, X. Siemens, and K. Yagi, “Gravitational-Wave Tests of General Relativity with Ground-Based Detectors and Pulsar-Timing Arrays,”arXiv:2408.05240 [gr-qc]

    Pith/arXiv arXiv

  40. [44]

    Measuring the circular polarization of gravitational waves with pulsar timing arrays,

    N. M. J. Cruz, A. Malhotra, G. Tasinato, and I. Zavala, “Measuring the circular polarization of gravitational waves with pulsar timing arrays,”Phys. Rev. D110 no. 10, (2024) 103505,arXiv:2406.04957 [astro-ph.CO]. [45]LISACollaboration, P. A. Seoaneet al., “Astrophysics with the Laser Interferometer Space Antenna,”Living Rev. Rel.26no. 1, (2023) 2,arXiv:22...

    Pith/arXiv arXiv 2024

  41. [46]

    The Taiji Program in Space for gravitational wave physics and the nature of gravity,

    W.-R. Hu and Y.-L. Wu, “The Taiji Program in Space for gravitational wave physics and the nature of gravity,”Natl. Sci. Rev.4no. 5, (2017) 685–686

    2017

  42. [47]

    Alternative LISA-TAIJI networks: Detectability of parity violation in stochastic gravitational wave background,

    J. Chen, C. Liu, Y.-L. Zhang, and G. Wang, “Alternative LISA-TAIJI networks: Detectability of parity violation in stochastic gravitational wave background,”Phys. Rev. D111no. 8, (2025) 084026,arXiv:2412.18420 [gr-qc]

    Pith/arXiv arXiv 2025

  43. [48]

    Primordial gravitational waves in parity-violating symmetric teleparallel gravity,

    R. Zhai, C. Fu, X. Fu, P. Wu, and H. Yu, “Primordial gravitational waves in parity-violating symmetric teleparallel gravity,” 2025. https://arxiv.org/abs/2508.06984. 28

    arXiv 2025

  44. [49]

    Circularly polarized gravitational wave background search with a network of space-borne triangular detectors,

    J. Chen, C. Liu, and Y.-L. Zhang, “Circularly polarized gravitational wave background search with a network of space-borne triangular detectors,”JCAP05 (2025) 050,arXiv:2410.18916 [gr-qc]

    Pith/arXiv arXiv 2025

  45. [50]

    Detectability of the chiral gravitational wave background from audible axions with the LISA-Taiji network,

    H. Su, B. Xu, J. Chen, C. Liu, and Y.-L. Zhang, “Detectability of the chiral gravitational wave background from audible axions with the LISA-Taiji network,” Commun. Theor. Phys.77(2025) 115403,arXiv:2503.20778 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  46. [51]

    Spatial distribution of the large-scale structure: An unsupervised search for parity violation,

    S. Hewson, W. J. Handley, and C. G. Lester, “Spatial distribution of the large-scale structure: An unsupervised search for parity violation,”Phys. Rev. D111no. 12, (2025) 123528,arXiv:2410.16030 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  47. [52]

    Can Baryon Acoustic Oscillations Illuminate the Parity-Violating Galaxy 4PCF?,

    J. Hou, Z. Slepian, and D. Jamieson, “Can Baryon Acoustic Oscillations Illuminate the Parity-Violating Galaxy 4PCF?,”arXiv:2410.05230 [astro-ph.CO]

    Pith/arXiv arXiv

  48. [53]

    Breaking parity: the case of the trispectrum from chiral scalar-tensor theories of gravity,

    T. Moretti, N. Bartolo, and A. Greco, “Breaking parity: the case of the trispectrum from chiral scalar-tensor theories of gravity,”JCAP07(2025) 051, arXiv:2410.11801 [astro-ph.CO]

    arXiv 2025

  49. [54]

    Full Parity-Violating Trispectrum in Axion Inflation: Reduction to Low-D Integrals,

    M. Reinhard, Z. Slepian, J. Hou, and A. Greco, “Full Parity-Violating Trispectrum in Axion Inflation: Reduction to Low-D Integrals,”arXiv:2412.16037 [astro-ph.CO]

    Pith/arXiv arXiv

  50. [55]

    Systematic Analysis of Parity-Violating Modes,

    H.-M. Zhu and U.-L. Pen, “Systematic Analysis of Parity-Violating Modes,”Phys. Rev. Lett.135no. 11, (2025) 111003,arXiv:2409.11400 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  51. [56]

    Anatomy of Parity-violating Trispectra in Galaxy Surveys,

    Y. Bao, L.-T. Wang, Z.-Z. Xianyu, and Y.-M. Zhong, “Anatomy of Parity-violating Trispectra in Galaxy Surveys,”arXiv:2504.02931 [astro-ph.CO]

    arXiv

  52. [57]

    Post-Newtonian parameters of ghost-free parity-violating gravities,

    J. Qiao, T. Zhu, G. Li, and W. Zhao, “Post-Newtonian parameters of ghost-free parity-violating gravities,”JCAP04no. 04, (2022) 054,arXiv:2110.09033 [gr-qc]

    Pith/arXiv arXiv 2022

  53. [58]

    Tests of gravitational wave propagation with LIGO-Virgo catalog,

    X.-L. Wang, S.-C. Yang, and W.-B. Han, “Tests of gravitational wave propagation with LIGO-Virgo catalog,”arXiv:2404.14684 [gr-qc]

    Pith/arXiv arXiv

  54. [59]

    Lorentz violation with gravitational waves: Constraints from NANOGrav and IPTA data,

    A. Allahyari, M. Davari, and D. F. Mota, “Lorentz violation with gravitational waves: Constraints from NANOGrav and IPTA data,”JHEAp49(2026) 100448, arXiv:2505.22736 [astro-ph.CO]

    Pith/arXiv arXiv 2026

  55. [60]

    Primordial gravitational waves from spontaneous Lorentz symmetry breaking,

    M. Khodadi, G. Lambiase, L. Mastrototaro, and T. K. Poddar, “Primordial gravitational waves from spontaneous Lorentz symmetry breaking,”Phys. Lett. B 867(2025) 139597,arXiv:2501.14395 [astro-ph.CO]. 29

    Pith/arXiv arXiv 2025

  56. [61]

    Self-consistency of compact objects in Lorentz-violating gravity theories,

    L. A. Lessa, R. B. Magalh˜ aes, and M. M. Ferreira Junior, “Self-consistency of compact objects in Lorentz-violating gravity theories,”Phys. Rev. D112no. 6, (2025) 064031,arXiv:2505.01374 [gr-qc]

    Pith/arXiv arXiv 2025

  57. [62]

    Modified gravitational wave propagations in linearized gravity with Lorentz and diffeomorphism violations and their gravitational wave constraints,

    Q. Wang, J.-M. Yan, T. Zhu, and W. Zhao, “Modified gravitational wave propagations in linearized gravity with Lorentz and diffeomorphism violations and their gravitational wave constraints,”Phys. Rev. D111no. 8, (2025) 084064, arXiv:2501.11956 [gr-qc]

    Pith/arXiv arXiv 2025

  58. [63]

    Constraining parity and Lorentz violations in gravity with future ground- and space-based gravitational wave detectors,

    B.-Y. Zhang, T. Zhu, J.-M. Yan, J.-F. Zhang, and X. Zhang, “Constraining parity and Lorentz violations in gravity with future ground- and space-based gravitational wave detectors,”Phys. Rev. D111no. 10, (2025) 104012,arXiv:2502.04776 [gr-qc]. [64]LIGO ScientificCollaboration, J. Aasiet al., “Advanced LIGO,”Class. Quant. Grav.32(2015) 074001,arXiv:1411.454...

    Pith/arXiv arXiv 2025

  59. [68]

    Self-interacting scalar dark matter around binary black holes,

    J. C. Aurrekoetxea, J. Marsden, K. Clough, and P. G. Ferreira, “Self-interacting scalar dark matter around binary black holes,”Phys. Rev. D110no. 8, (2024) 083011,arXiv:2409.01937 [gr-qc]

    Pith/arXiv arXiv 2024

  60. [69]

    Compact Binary Merger Rate with Modified Gravity in Dark Matter Spikes,

    S. Fakhry, S. Gholamhoseinian, and M. Farhang, “Compact Binary Merger Rate with Modified Gravity in Dark Matter Spikes,”Astrophys. J.976no. 2, (2024) 248, arXiv:2408.11995 [gr-qc]

    Pith/arXiv arXiv 2024

  61. [70]

    Gravitational radiation in generalized Brans–Dicke theory: compact binary systems,

    S. Mahmoudi and S. H. Hendi, “Gravitational radiation in generalized Brans–Dicke theory: compact binary systems,”Eur. Phys. J. C84no. 8, (2024) 836, arXiv:2408.05825 [gr-qc]

    Pith/arXiv arXiv 2024

  62. [71]

    Inner radius and energy conditions of dark matter halos surrounding Schwarzschild black holes,

    Z. Shen, A. Wang, and S. Yin, “Inner radius and energy conditions of dark matter halos surrounding Schwarzschild black holes,”Phys. Lett. B862(2025) 139300, arXiv:2408.05417 [gr-qc]. 30

    Pith/arXiv arXiv 2025

  63. [72]

    Neutron stars and dark matter,

    A. Del Popolo, M. Le Delliou, and M. Deliyergiyev, “Neutron stars and dark matter,” Universe6no. 12, (Nov., 2020) 222. http://dx.doi.org/10.3390/universe6120222

    work page doi:10.3390/universe6120222 2020

  64. [73]

    Electrically charged black holes in gravity with a background Kalb–Ramond field,

    Z.-Q. Duan, J.-Y. Zhao, and K. Yang, “Electrically charged black holes in gravity with a background Kalb–Ramond field,”Eur. Phys. J. C84no. 8, (2024) 798, arXiv:2310.13555 [gr-qc]

    Pith/arXiv arXiv 2024

  65. [74]

    Testing EGB gravity coupled to bumblebee field and black hole parameter estimation with EHT observations,

    M. Afrin, S. G. Ghosh, and A. Wang, “Testing EGB gravity coupled to bumblebee field and black hole parameter estimation with EHT observations,”Phys. Dark Univ. 46(2024) 101642,arXiv:2409.06218 [gr-qc]

    Pith/arXiv arXiv 2024

  66. [75]

    Ultra-compact objects of non-minimally coupled dark matter,

    F. Benetti, A. Lapi, S. Silveravalle, and S. Liberati, “Ultra-compact objects of non-minimally coupled dark matter,”JCAP03(2025) 029,arXiv:2412.07533 [gr-qc]

    arXiv 2025

  67. [76]

    Can We Detect Deviations from Einstein’s Gravity in Black Hole Ringdowns?,

    A. Kehagias and A. Riotto, “Can We Detect Deviations from Einstein’s Gravity in Black Hole Ringdowns?,”arXiv:2411.12428 [gr-qc]

    Pith/arXiv arXiv

  68. [77]

    Time dependent black holes and gravitational wave in Einstein–Gauss–Bonnet theory with two scalar fields,

    G. G. L. Nashed, “Time dependent black holes and gravitational wave in Einstein–Gauss–Bonnet theory with two scalar fields,”Eur. Phys. J. C84no. 10, (2024) 1119,arXiv:2411.02439 [gr-qc]

    Pith/arXiv arXiv 2024

  69. [78]

    Quasinormal modes, greybody factors, and Hawking radiation sparsity of black holes influenced by a global monopole charge in Kalb-Ramond gravity,

    A. Baruah, Y. Sekhmani, S. K. Maurya, A. Deshamukhya, and M. K. Jasim, “Quasinormal modes, greybody factors, and Hawking radiation sparsity of black holes influenced by a global monopole charge in Kalb-Ramond gravity,”JCAP08 (2025) 023,arXiv:2502.13496 [gr-qc]

    Pith/arXiv arXiv 2025

  70. [79]

    Exact black hole solutions in gravity with a background Kalb-Ramond field,

    J.-Z. Liu, S.-P. Wu, S.-W. Wei, and Y.-X. Liu, “Exact black hole solutions in gravity with a background Kalb-Ramond field,”arXiv:2505.07404 [gr-qc]

    arXiv

  71. [80]

    Observational signatures and polarized images of rotating charged black holes in Kalb-Ramond Gravity,

    C.-Y. Yang, K.-J. He, X.-X. Zeng, and L.-F. Li, “Observational signatures and polarized images of rotating charged black holes in Kalb-Ramond Gravity,” arXiv:2508.07393 [gr-qc]

    Pith/arXiv arXiv

  72. [81]

    Charged black holes in KR gravity: Weak deflection angle, shadow cast, quasinormal modes and neutrino annihilation,

    R. C. Pantig, A. ¨Ovg¨ un, and´A. Rinc´ on, “Charged black holes in KR gravity: Weak deflection angle, shadow cast, quasinormal modes and neutrino annihilation,”Phys. Dark Univ.49(2025) 102029,arXiv:2505.17947 [gr-qc]

    Pith/arXiv arXiv 2025

  73. [82]

    Dark matter distributions around Schwarzschild-like black holes in bumblebee and Kalb–Ramond models,

    M.-H. Yu and T. Wang, “Dark matter distributions around Schwarzschild-like black holes in bumblebee and Kalb–Ramond models,”Eur. Phys. J. C85no. 8, (2025) 823,arXiv:2503.09104 [gr-qc]

    arXiv 2025

  74. [83]

    Compact stars in Einstein-scalar-Gauss-Bonnet gravity: regular and divergent scalar field configurations,

    R. D. A. Q., J. Chagoya, and A. A. Roque, “Compact stars in Einstein-scalar-Gauss-Bonnet gravity: regular and divergent scalar field configurations,”arXiv:2508.13273 [gr-qc]. 31

    arXiv

  75. [84]

    Gravitational lensing and shadow by a Schwarzschild-like black hole in metric-affine bumblebee gravity,

    X.-J. Gao, “Gravitational lensing and shadow by a Schwarzschild-like black hole in metric-affine bumblebee gravity,”Eur. Phys. J. C84no. 9, (2024) 973, arXiv:2409.12531 [gr-qc]

    Pith/arXiv arXiv 2024

  76. [85]

    Lensing and light rings of parity-odd rotating boson stars,

    Y. Huang, D.-J. Liu, and H. Zhang, “Lensing and light rings of parity-odd rotating boson stars,”Sci. China Phys. Mech. Astron.68no. 8, (2025) 280411, arXiv:2410.20867 [gr-qc]

    Pith/arXiv arXiv 2025

  77. [86]

    Imprints of Dark Photons on Gravitational Wave Polarizations,

    K. Nomura, J. Soda, K. Ueda, and Z. Wang, “Imprints of Dark Photons on Gravitational Wave Polarizations,”arXiv:2409.10471 [gr-qc]

    arXiv

  78. [87]

    Demagnifying gravitational lenses as probes of dark matter structures and nonminimal couplings to gravity,

    H.-Y. Zhang, “Demagnifying gravitational lenses as probes of dark matter structures and nonminimal couplings to gravity,”arXiv:2510.05575 [gr-qc]

    arXiv

  79. [88]

    Generation of the CMB cosmic birefringence through axion-like particles, sterile and active neutrinos,

    S. Mahmoudi, M. Sadegh, J. Khodagholizadeh, I. Motie, S.-S. Xue, and A. Blanchard, “Generation of the CMB cosmic birefringence through axion-like particles, sterile and active neutrinos,”Eur. Phys. J. C84no. 6, (2024) 619, arXiv:2409.18588 [hep-ph]

    Pith/arXiv arXiv 2024

  80. [89]

    CMB Implications of Multi-field Axio-dilaton Cosmology,

    A. Smith, M. Mylova, P. Brax, C. van de Bruck, C. P. Burgess, and A.-C. Davis, “CMB Implications of Multi-field Axio-dilaton Cosmology,”arXiv:2408.10820 [hep-th]

    Pith/arXiv arXiv

Showing first 80 references.