Pith. sign in

REVIEW 2 major objections 6 minor 32 references

The paper argues that, under the pre-fixed-field treatment, the gravitational-wave phase is a nearly blind channel to variation of the gravitational constant, and it quantifies the detector improvement needed before that channel opens.

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 ↗

Using LIGO/Virgo/KAGRA data, the phase correction from a varying gravitational constant is undetectable today, and constraints would improve only as the square root of the distance-times-SNR product.

T0 review reviewed 2026-08-05 challenge →

load-bearing objection Useful null result on GW phase constraints for G-variation, but the 2n-orders forecast is built on a shaky mean∝Δ step and an inconsistent anchor. the 2 major comments →

arxiv 2508.21746 v1 pith:X3UBBJPJ submitted 2025-08-29 gr-qc

The effect of the gravitational constant variation on the phase of gravitational waves

Jiachen An , Bing Sun , Zhoujian Cao This is my paper
classification gr-qc
keywords gravitational constant variationgravitational wave phase correctionpre-fixed fieldFisher matrixcompact binary coalescenceelectromagnetic counterpartmatched filteringeffective gravitational constant
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 reading

This paper tries to establish that the phase of a gravitational wave is, at current and foreseeable sensitivity, essentially uninformative about a slowly varying gravitational constant. Treating the variation as a pre-fixed field, the waveform's amplitude changes at first order in G'/G but its phase changes only at second order, so the phase shift is tiny. Applying the phase-corrected waveform to the loudest binary black hole event leaves the posterior for G'/G exactly what the prior was; for a binary neutron star event with an independently measured distance, including the phase correction changes the constraint almost not at all. A Fisher-matrix forecast then says that reaching |G'/G| < 10^{-n}/yr from the phase requires the product of signal-to-noise ratio and luminosity distance to grow by 2n orders of magnitude. The result matters because it says the phase-based route to testing whether gravity's coupling changes will remain silent for a long time, unless the constant is dynamical rather than pre-fixed.

Core claim

Under the pre-fixed-field picture, the leading phase correction to a gravitational wave is quadratic in G'/G: the frequency-domain waveform acquires the factor exp(-i Xi D_L /(4 pi f)) with Xi = (3/4)(G'/G)^2, while the amplitude correction is linear and degenerate with luminosity distance. Because current bounds put |G'/G| near 10^-14/s, this phase factor is minuscule at around 100 Hz. Analyzing the loudest catalog black-hole event yields a G'/G posterior identical to its uniform prior, and adding the phase correction to a neutron-star merger whose distance is known from electromagnetic observations changes the inferred constraint negligibly. The Fisher-matrix forecast gives Delta(G'/G) pro

What carries the argument

The central object is the phase factor exp(-i Xi D_L/(4 pi f)) in the corrected waveform, with Xi = (3/4)(G'/G)^2; it is the second-order-in-G'/G imprint that the paper tests against data. The Fisher matrix built from derivatives of this waveform converts that tiny phase into the measurement-error scaling Delta(G'/G) proportional to 1/(rho D_L |G'/G|); the paper's noise-driven mean-value approximation then turns it into the forecast Delta(G'/G) proportional to 1/sqrt(rho D_L).

Load-bearing premise

The forecast that each 10^{-n}/yr target costs 2n orders of rho D_L assumes the measured central value of G'/G is pure noise and scales with the measurement error; when the posterior is instead pinned to the prior, as the paper's own loud black-hole event shows, that scaling is not calibrated.

What would settle it

Inject simulated signals with a known nonzero G'/G (say 10^-9/yr) and a known distance into detector noise, recover G'/G from many realizations at different values of the signal-to-noise ratio and distance, and check whether the credible-interval width shrinks as (rho D_L)^(-1/2) or as (rho D_L)^(-1). If the width follows the latter, the paper's forecast is wrong; if a zero-injected signal still yields an exactly flat posterior for the loudest event, the noise-driven-mean premise is not met.

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

If this is right

  • Phase-based gravitational-wave constraints on G'/G will stay at the prior level until the product of signal-to-noise ratio and luminosity distance improves by orders of magnitude.
  • For sources with independently known distances, the phase correction can be omitted from waveform templates when constraining G variation unless the characteristic frequency falls below about 10^-16 Hz.
  • The linear amplitude correction is fully degenerate with luminosity distance for unresolved sources, so it cannot provide a phase-independent constraint on G variation.
  • A target accuracy of 10^{-n}/yr requires a 2n-order increase in rho D_L, so each tenfold gain in measurement accuracy costs a hundredfold gain in detection reach.
  • If the effective gravitational constant is instead a dynamical field, a first-order dipole phase appears and the constraint story must be reworked, as the paper's caution notes.

Where Pith is reading between the lines

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

  • Beyond the paper: the scaling forecast depends on the mean measured G'/G being noise-driven and growing like the error; the paper's own loud-event result, where the posterior equals the prior, is the regime where that assumption fails, so the true required gain could be larger than 2n orders.
  • Beyond the paper: reported upper bounds on G'/G from the phase channel in the pre-fixed-field picture should be read as prior-driven statements rather than data-driven measurements until rho D_L grows by the forecast amounts.
  • Beyond the paper: if a dynamical-field dipole phase is ever observed, the phase channel would become first-order in G'/G and could become informative much sooner; the pre-fixed-field forecast is the conservative limiting case.
Share X Bluesky LinkedIn Reddit HN

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

2 major / 6 minor

Summary. The paper analyzes whether the phase correction induced by a time-varying effective gravitational constant, treated as a pre-fixed field, is observable in current LIGO-Virgo-KAGRA gravitational wave data. The authors argue that the amplitude correction is degenerate with luminosity distance and that the phase correction is second order in G'/G. They apply the corrected waveform to GW200129 and GW170817, finding that the phase correction negligibly improves constraints. A Fisher matrix analysis is then used to forecast when the phase correction will matter, leading to the claim that reaching an accuracy |G'/G| < 10^{-n}/yr requires ρ D_L to increase by 2n orders relative to the current state of the art. For events with an independent luminosity distance, the phase correction is said to be negligible because (G'/G) 3/(8π f_GW) ~ 10^{-17}.

Significance. If the central forecast were rigorously derived, the paper would provide a useful practical message: current and near-future gravitational wave detectors cannot constrain a pre-fixed-field G variation through the phase channel, and events with electromagnetic counterparts are better handled through the amplitude/luminosity-distance channel. The direct data analysis portion is transparent and uses public LVK data, and the rough mapping between the LVK δφ2 bound and G'/G in Eq. (17) is a useful cross-check. The paper is also honest in stating the pre-fixed-field assumption in the final caution. However, the main forecast in the abstract rests on a single proportionality assumption that is not justified, and the numerical anchor used for the forecast is not consistently defined. These issues are load-bearing because the abstract's headline prediction depends on them.

major comments (2)
  1. [Section IV, Eqs. (31)-(32)] The transition from Δ(G'/G) ∝ 1/(ρ D_L |G'/G|) to Δ(G'/G) ∝ 1/√(ρ D_L) via 'we can approximate that the mean value (G'/G) ∝ Δ(G'/G)' is the load-bearing step for the abstract's 2n-orders forecast. For a fixed true value q, Eq. (31) is the standard Fisher scaling σ_q ∝ 1/(ρ D_L |q|). Setting |q| ≈ σ_q is the detection-threshold condition q_min = N σ_q, not a generic relation between a measured central value and its error. The paper's own Section III example (GW200129 posterior equal to its prior) is the opposite regime, where the central value is prior-dominated and does not fluctuate at the 1σ level. The square-root scaling in Eq. (32) is therefore not derived as a measurement-accuracy scaling. It may be salvageable as a sensitivity-limit statement, but that requires an explicit derivation (e.g., q_min = N/(ρ D_L q_min)) and a clear statement that the forecast is about detectability, not
  2. [Section IV, anchor calibration] The text states 'Our data analysis result for binary black hole done in the above section tells us that the current measurement accuracy is about Δ G'/G ∼ 10^{-7}/sec.' But the Section III GW200129 analysis reports a posterior that is the adopted prior, uniform over |G'/G| < 10^{-14}/sec. A posterior equal to the prior means the data add no information; the 'measurement accuracy' is neither 10^{-7}/sec nor 10^{-14}/sec. The 10^{-7}/sec figure appears to come from the rough δφ2 bound in Eq. (17), not from the posterior. Calibrating Eq. (32) with a prior-dominated null result conflates prior width with measurement accuracy and makes the numerical forecast uncalibrated. The authors should either run the BBH analysis with a broad prior to extract a likelihood width, or explicitly state that Eq. (17) is the anchor and justify why that is the appropriate 'current accuracy' for the phase channe
minor comments (6)
  1. [Section II, after Eq. (9)] The sentence 'This means that binary black hole events which have no electromagnetic counterpart can not be used to constrain the variation of the effective gravitational constant' is contradicted by Section III, where GW200129 (a BBH without EM counterpart) is used with the phase correction. The intended meaning is that the amplitude correction alone is degenerate with D_L; please rephrase to avoid this apparent contradiction.
  2. [Section IV] The approximations '10^{-7}/sec ∼ 1/yr' and '10^{-14}/sec ∼ 10^{-7}/yr' rely on the rough identification 1 yr ≈ 10^7 s. State this explicitly so the numerical conversions are not misleading.
  3. [Figure 1] The legend text contains typos: 'with phase modification' appears as 'ith phase modification', 'without' as 'witho t', and 'previous result' as 'previo s res lt'. The y-axis label '1e8' is also unclear.
  4. [Section IV, Eq. (35)] The symbol f_GW is used in Eq. (35) but only defined as 'the characteristic frequency of the detected gravitational wave' a few lines later. Define it before first use.
  5. [Eq. (13)] The sign convention for δφ2 is not discussed. Since Eq. (14) takes an absolute value, the sign of δφ2 is irrelevant for the bound, but the mapping from the LIGO-Virgo-KAGRA δφ2 convention to Eq. (13) should be stated explicitly.
  6. [General] General typographical issues: 'gravita tional', 'affine', 'L VK' spacing, 'blocked matrix' should be 'block matrix', and reference [28] should be formatted consistently with the journal style.

Circularity Check

1 steps flagged

The 2n-order forecast reduces to the assumed mean-value-proportional-to-error relation; the rest of the paper is anchored to external LVK constraints.

specific steps
  1. self definitional [Section IV, between Eqs. (31) and (32)]
    "But for real data, a variety of noise will result in a Gaussian distribution of G′/G with the center deviating from the origin, and therefore the real measurement accuracy of G′/G will not diverge. Considering such real data analysis fact, we can approximate that the mean value (G′/G) ∝ Δ G′/G. Then Eq. (31) becomes Δ G′/G ∝ 1/√(ρDL)."

    Eq. (31) is Δq ∝ 1/(ρDL|q|). Inserting the assumption |q| ∝ Δq gives Δq ∝ 1/√(ρDL). Conversely, given Eq. (31), the square-root law implies |q| ∝ 1/(ρDLΔq) ∝ 1/√(ρDL) ∝ Δq; so the assumption and the predicted scaling are equivalent. The 2n-order forecast (abstract, Section IV) is therefore not an independent Fisher result; it is the assumed mean-proportional-to-error relation restated. The paper's own GW200129 analysis (posterior identical to the chosen uniform prior, mean at prior center) is the prior-dominated regime, contradicting the 'center deviating from origin' premise used to justify the assumption. The forecast is a detection-threshold self-consistency scaling, not a measurement-accuracy scaling.

full rationale

The paper's data-analysis sections are largely self-contained: the GW170817 comparison with and without the phase correction uses standard LVK data and external EM distance/sky priors, and the conclusion that the phase correction is negligible for EM-counterpart events follows from the external LVK bound |δϕ2|≲0.1 combined with fGW∼100 Hz. The waveform correction is taken from the authors' previous works [26,27], but that is ordinary citation of prior derivation rather than circular argument; the prior |DLG′/G|<20 is an explicit assumption, and the GW200129 posterior equal to that prior is honestly reported as a null result, not as an independent measurement. The central circularity is confined to Section IV: Eq. (32) is obtained by assuming the mean value of G′/G is proportional to its own measurement error. Since Eq. (31) already relates the error inversely to |q|, this assumption is mathematically equivalent to the square-root scaling that the paper then 'derives.' The abstract's headline forecast—that ρDL must grow by 2n orders to improve the accuracy by n orders—therefore reduces to that assumption by construction. The paper's own GW200129 result, where the posterior is identical to the chosen prior, is the opposite regime and does not support the assumed proportionality. The final caution about the pre-fixed-field model is a scope limitation, not a circularity, but it further limits the generality of the forecast. Excluding the Eq. (32) step, the remaining claims have independent empirical anchors.

Axiom & Free-Parameter Ledger

4 free parameters · 5 axioms · 0 invented entities

Everything the central forecast rests on: the waveform is carried from the authors' own [26,27]; the prior on G'/G is self-chosen via |DL G'/G| < 20; the externally supplied pieces are LVK's |δϕ2| ≲ 0.1, the GW170817 EM distance and sky priors, and the GWOSC data; and the unproven statistical step is the 'mean ∝ Δ' proportionality. These inputs, not new entities, are the load-bearing cost of the paper.

free parameters (4)
  • Prior width of G'/G = 10^-14/sec ≈ 3×10^-7/yr (uniform)
    Chosen from the authors' previous works via |DL G'/G| < 20 (Section III); because the GW200129 posterior equals the prior, this input is the entire reported BBH constraint.
  • Current measurement accuracy anchor = 10^-7/sec (claimed)
    Section IV uses this to phrase the 2n-orders forecast; it comes from the rough δϕ2 mapping (17), not from the Section III posterior, and is inconsistent with it by about seven orders of magnitude.
  • Reference frequency for the δϕ2 mapping = f ≈ 1/M
    Eq. (13) equates the phase correction at f = 1/M to the 1PN coefficient term; different choices of this reference frequency shift the rough bound (17).
  • Proportionality constant in 'mean ∝ Δ' = unspecified, order unity
    Eq. (32) inherits this undetermined constant; only the scaling exponent is quoted, so the absolute normalization of the forecast is not fixed.
axioms (5)
  • domain assumption The effective gravitational constant is a pre-fixed field on spacetime, so no dipole radiation appears at O(G'/G).
    Invoked in the Introduction ('we still take the effective gravitational constant as a pre-fixed field in the current paper') and repeated in the final caution, which admits the conclusions change if G is dynamical as in [8,25].
  • domain assumption Variation along the propagation path is slow: ∫Ξdζ ≈ ΞDL and Ξd - Ξs ≈ 0.
    Eqs. (7)-(8) in Section II; this drops the (1 + A(Mf)^-2) amplitude factor and reduces the phase to ΞDL/4πf.
  • ad hoc to paper The mean of the measured G'/G is proportional to its measurement error, Δ.
    Section IV, sentence between Eqs. (31) and (32); this is the load-bearing step converting quadratic degeneracy into the square-root scaling. It is asserted without derivation and conflicts with the Section III prior-dominated BBH posterior.
  • domain assumption LVK's GWTC-3 bound |δϕ2| ≲ 0.1 can be mapped onto the f^-1 phase correction via Eq. (13).
    Eqs. (13)-(16); the phase correction has a different frequency dependence than the 1PN term, so the mapping is an order-of-magnitude proxy evaluated at f = 1/M.
  • standard math Block inversion and perturbative expansion of the Fisher matrix in (G'/G) is valid.
    Appendix A, Eqs. (A1)-(A25); standard linear algebra, the mathematics itself appears sound.

reviewed 2026-08-05 · how reviews work

0 comments
Cite this review

Pith. "Pith review of The effect of the gravitational constant variation on the phase of gravitational waves." pith.science (2026). https://pith.science/paper/X3UBBJPJ

@misc{pith2026250821746,
  author       = {Pith},
  title        = {Pith review of: The effect of the gravitational constant variation on the phase of gravitational waves},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/X3UBBJPJ}},
  note         = {Machine review of arXiv:2508.21746}
}
Share X Bluesky LinkedIn Reddit HN
abstract

We have previously investigated the effect of the gravitational constant variation on the gravitational wave propagation. Pure theoretical analysis indicates that the leading order effect of the gravitational constant variation corrects the amplitude of gravitational waves, and the second order effect corrects the phase of gravitational waves. As the matched filtering technique is used by gravitational wave data analysis, the phase is more important than the amplitude. In the current paper we use LIGO-VIRGO-KAGRA data to constrain the gravitational constant variation. Our findings indicate that we need to wait until the distance of the detected gravitational wave events and/or the signal-to-noise ratio increases by $2n$ orders compared to the current detection state, and then we can use phase correction to get constraint $|\frac{G'}{G}|<10^{-n}$/yr for gravitational wave events without electromagnetic counterparts. For gravitational wave events with electromagnetic counterparts which provide the information of source's luminosity distance, the phase correction can almost always be neglected to constrain $\frac{G'}{G}$.

Figures

Figures reproduced from arXiv: 2508.21746 by Bing Sun, Jiachen An, Zhoujian Cao.

Figure 1
Figure 1. Figure 1: FIG. 1. Posterior distribution of [PITH_FULL_IMAGE:figures/full_fig_p004_1.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

32 extracted references · 25 canonical work pages · 7 internal anchors

  1. [1]

    P. A. M. Dirac, The cosmological constants, Nature 139, 323 (1937)

    work page 1937

  2. [2]

    Goldman, J

    T. Goldman, J. Perez-Mercader, F. Cooper, and M. M. Nieto, The dark matter problem and quantum gravity, Physics Letters B 281, 219 (1992)

    work page 1992

  3. [3]

    J. W. Moffat, Gravitational theory, galaxy rotation curves and cosmology without dark matter, Journal of Cosmology and Astroparticle Physics 2005 (5), 003, arXiv:astro-ph/0412195 [astro-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  4. [4]

    S. Ray, U. Mukhopadhyay, and S. B. D. Choudhury, Dark Energy Models with a Time-Dependent Gravita- tional Constant, International Journal of Modern Physics D 16, 1791 (2007), arXiv:astro-ph/0510549 [astro-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  5. [5]

    Marra and L

    V. Marra and L. Perivolaropoulos, Rapid transition of Geff at zt ≃ 0.01 as a possible solution of the hubble and growth tensions, Phys. Rev. D 104, L021303 (2021)

    work page 2021

  6. [6]

    Banik, H

    I. Banik, H. Desmond, and N. Samaras, Strong con- straints on a sharp change in G as a solution to the Hubble tension, arXiv e-prints , arXiv:2411.15301 (2024), arXiv:2411.15301 [astro-ph.CO]

    Pith/arXiv arXiv 2024

  7. [7]

    W. J. Marciano, Time variation of the fundamental ”con- stants” and kaluza-klein theories, Phys. Rev. Lett. 52, 489 (1984)

    work page 1984

  8. [8]

    Z. Wang, J. Zhao, Z. An, L. Shao, and Z. Cao, Simulta- neous bounds on the gravitational dipole radiation and varying gravitational constant from compact binary in- spirals, Physics Letters B 834, 137416 (2022)

    work page 2022

  9. [9]

    Yang, B.-F

    S.-Q. Yang, B.-F. Zhan, Q.-L. Wang, C.-G. Shao, L.- C. Tu, W.-H. Tan, and J. Luo, Test of the gravitational inverse square law at millimeter ranges, Phys. Rev. Lett. 108, 081101 (2012)

    work page 2012

  10. [10]

    J. Ke, J. Luo, C.-G. Shao, Y.-J. Tan, W.-H. Tan, and S.-Q. Yang, Combined test of the gravitational inverse- square law at the centimeter range, Phys. Rev. Lett.126, 211101 (2021)

    work page 2021

  11. [11]

    Chin and R

    C.-w. Chin and R. Stothers, Limit on the secular change of the gravitational constant based on studies of solar evolution, Phys. Rev. Lett. 36, 833 (1976)

    work page 1976

  12. [12]

    L. V. Morrison, Rotation of the Earth from AD 1663- 1972 and the Constancy of G, Nature 241, 519 (1973)

    work page 1972

  13. [13]

    P. D. Sisterna and H. Vucetich, Cosmology, oscillating physics, and oscillating biology, Phys. Rev. Lett. 72, 454 (1994)

    work page 1994

  14. [14]

    A. H. C´ orsico, L. G. Althaus, E. Garc´ ıa-Berro, and A. D. Romero, An independent constraint on the secular rate of variation of the gravitational constant from pulsating white dwarfs, Journal of Cosmology and Astroparticle Physics 2013 (6), 032, arXiv:1306.1864 [astro-ph.SR]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  15. [15]

    S. E. Thorsett, The gravitational constant, the chan- drasekhar limit, and neutron star masses, Phys. Rev. Lett. 77, 1432 (1996)

    work page 1996

  16. [16]

    Time-Variation of Newton's Constant and the Age of Globular Clusters

    S. degl’Innocenti, G. Fiorentini, G. G. Raffelt, B. Ricci, and A. Weiss, Time-variation of Newton’s constant and the age of globular clusters., Astronomy and Astrophysics 312, 345 (1996), arXiv:astro-ph/9509090 [astro-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 1996

  17. [17]

    Improved BBN Constraints on the Variation of the Gravitational Constant

    J. Alvey, N. Sabti, M. Escudero, and M. Fairbairn, Im- proved BBN constraints on the variation of the gravi- tational constant, European Physical Journal C 80, 148 (2020), arXiv:1910.10730 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2020

  18. [18]

    E. P. Bellinger and J. Christensen-Dalsgaard, Astero- seismic Constraints on the Cosmic-time Variation of the Gravitational Constant from an Ancient Main-sequence Star, The Astrophysical Journal Letters 887, L1 (2019), arXiv:1909.06378 [astro-ph.SR]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  19. [19]

    Hofmann and J

    F. Hofmann and J. M¨ uller, Relativistic tests with lunar laser ranging, Classical and Quantum Gravity35, 035015 (2018)

    work page 2018

  20. [20]

    Genova, E

    A. Genova, E. Mazarico, S. Goossens, F. G. Lemoine, G. A. Neumann, D. E. Smith, and M. T. Zuber, Solar sys- tem expansion and strong equivalence principle as seen by the NASA MESSENGER mission, Nature Communi- cations 9, 289 (2018)

    work page 2018

  21. [21]

    W. W. Zhu, G. Desvignes, N. Wex, R. N. Caballero, D. J. Champion, P. B. Demorest, J. A. Ellis, G. H. Janssen, M. Kramer, A. Krieger, L. Lentati, D. J. Nice, S. M. Ransom, I. H. Stairs, B. W. Stappers, J. P. W. Verbiest, Z. Arzoumanian, C. G. Bassa, M. Burgay, I. Cognard, K. Crowter, T. Dolch, R. D. Ferdman, E. Fonseca, M. E. Gonzalez, E. Graikou, L. Guill...

    Pith/arXiv arXiv 2019

  22. [22]

    T. D. Le, A study of space-time variation of the grav- itational constant using high-resolution quasar spectra, General Relativity and Gravitation 53, 37 (2021)

    work page 2021

  23. [23]

    Vijaykumar, S

    A. Vijaykumar, S. J. Kapadia, and P. Ajith, Constraints on the time variation of the gravitational constant using gravitational wave observations of binary neutron stars, Phys. Rev. Lett. 126, 141104 (2021)

    work page 2021

  24. [24]

    W. Zhao, B. S. Wright, and B. Li, Constraining the time variation of Newton’s constant G with gravitational- wave standard sirens and supernovae, Journal of Cos- mology and Astroparticle Physics 2018 (10), 052, arXiv:1804.03066 [astro-ph.CO]

    Pith/arXiv arXiv 2018

  25. [25]

    Yunes, F

    N. Yunes, F. Pretorius, and D. Spergel, Constraining the evolutionary history of newton’s constant with grav- itational wave observations, Phys. Rev. D 81, 064018 (2010)

    work page 2010

  26. [26]

    J. An, Y. Xue, Z. Cao, X. He, and B. Sun, The effect of the gravitational constant variation on the propagation of gravitational waves, Physics Letters B 844, 138108 (2023), arXiv:2307.15382 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  27. [27]

    B. Sun, J. An, and Z. Cao, Constrain the time variation of the gravitational constant via the propagation of grav- itational waves, Physics Letters B 848, 138350 (2024)

    work page 2024

  28. [28]

    Abbott, et al

    The LIGO Scientific Collaboration, the Virgo Collabo- ration, the KAGRA Collaboration, R. Abbott, et al. , Tests of General Relativity with GWTC-3, arXiv e-prints , arXiv:2112.06861 (2021), arXiv:2112.06861 [gr-qc]

    Pith/arXiv arXiv 2021

  29. [29]

    Cantiello, J

    M. Cantiello, J. B. Jensen, J. P. Blakeslee, E. Berger, A. J. Levan, N. R. Tanvir, G. Raimondo, E. Bro- cato, K. D. Alexander, P. K. Blanchard, M. Branchesi, Z. Cano, R. Chornock, S. Covino, P. S. Cowperthwaite, P. D’Avanzo, T. Eftekhari, W. Fong, A. S. Fruchter, A. Grado, J. Hjorth, D. E. Holz, J. D. Lyman, I. Man- del, R. Margutti, M. Nicholl, V. A. Vil...

    Pith/arXiv arXiv 2018

  30. [30]

    Abbott, T

    R. Abbott, T. D. Abbott, F. Acernese, K. Ackley, C. Adams, N. Adhikari, R. X. Adhikari, V. B. Adya, et al. (LIGO Scientific Collaboration, Virgo Collabora- tion, and KAGRA Collaboration), Gwtc-3: Compact bi- nary coalescences observed by ligo and virgo during the second part of the third observing run, Phys. Rev. X 13, 041039 (2023)

    work page 2023

  31. [31]

    B. P. Abbott, R. Abbott, T. D. Abbott, F. Acernese, K. Ackley, C. Adams, et al. , Multi-messenger Observa- tions of a Binary Neutron Star Merger, The Astrophys- ical Journal Letters 848, L12 (2017), arXiv:1710.05833 [astro-ph.HE]

    Pith/arXiv arXiv 2017

  32. [32]

    B. P. Abbott, R. Abbott, T. D. Abbott, F. Acernese, K. Ackley, C. Adams, et al. , Properties of the Binary Neutron Star Merger GW170817, Physical Review X 9, 011001 (2019), arXiv:1805.11579 [gr-qc]

    Pith/arXiv arXiv 2019

This paper was first reviewed by deepseek-v4-flash on August 5, 2026.