pith. sign in

arxiv: 2510.21521 · v2 · submitted 2025-10-24 · 🌌 astro-ph.CO · gr-qc· hep-ph

Synergy between CSST and third-generation gravitational-wave detectors: Inferring cosmological parameters using cross-correlation of dark sirens and galaxies

Ya-Nan Du , Ji-Yu Song , Yichao Li , Shang-Jie Jin , Ling-Feng Wang , Jing-Fei Zhang , Xin Zhang This is my paper

Pith reviewed 2026-05-18 04:44 UTC · model grok-4.3

classification 🌌 astro-ph.CO gr-qchep-ph
keywords gravitational wavesdark sirenscross-correlationcosmological parametersHubble constantCSSTthird-generation detectorslarge-scale structure
0
0 comments X

The pith

Cross-correlating dark sirens from third-generation detectors with CSST galaxies constrains the Hubble constant to 1.04% precision.

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

This paper examines how future third-generation gravitational-wave detectors can work together with the China Space Station Telescope's photometric galaxy survey. Gravitational-wave events provide direct luminosity distances but lack redshifts due to mass degeneracy; cross-correlating them with galaxies statistically links distances to redshift shells. The resulting forecasts indicate that this approach can measure the Hubble constant to 1.04% precision and the matter density parameter to 2.04% precision. The same correlations also yield constraints on the clustering bias of the gravitational-wave sources themselves. These results point to a practical route for cosmological inference that treats gravitational-wave events as tracers of large-scale structure alongside galaxies.

Core claim

By cross-correlating the luminosity distances of dark sirens detected by third-generation ground-based gravitational-wave detectors with the photometric redshifts of galaxies in the CSST survey, the authors establish a correspondence between distance and redshift shells that enables cosmological parameter inference, achieving constraint precisions of 1.04% on the Hubble constant and 2.04% on the matter density parameter while also bounding the gravitational-wave source clustering bias.

What carries the argument

Cross-correlation between gravitational-wave luminosity distances and galaxy photometric redshifts to map dark sirens onto redshift shells

If this is right

  • Delivers percent-level constraints on the Hubble constant and matter density parameter from the cross-correlation signal.
  • Provides a measurement of the gravitational-wave source clustering bias that can help distinguish formation channels.
  • Establishes a statistical method to assign redshifts to dark sirens without requiring electromagnetic counterparts for individual events.
  • Demonstrates that the combination of CSST photometry and third-generation detectors offers a viable new probe of large-scale structure.

Where Pith is reading between the lines

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

  • If the assumptions hold, the technique could serve as an independent check on the current Hubble tension when combined with other distance-ladder or CMB measurements.
  • The same cross-correlation framework could be applied to other upcoming galaxy surveys or detector networks to test robustness across different data sets.
  • Measuring the bias parameter in real data would offer a direct observational handle on whether gravitational-wave sources preferentially trace star-forming or passive galaxies.

Load-bearing premise

The forecasts depend on assumed fiducial models for the redshift distribution of gravitational-wave sources, their clustering bias, and the photometric redshift accuracy of the CSST survey.

What would settle it

Future data from 3G detectors and CSST that yields a Hubble constant constraint precision significantly worse than 1.04% or a measured clustering bias inconsistent with the assumed fiducial value would falsify the projected performance.

Figures

Figures reproduced from arXiv: 2510.21521 by Jing-Fei Zhang, Ji-Yu Song, Ling-Feng Wang, Shang-Jie Jin, Xin Zhang, Ya-Nan Du, Yichao Li.

Figure 1
Figure 1. Figure 1: Angular power spectra and noise contributions. [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: SNRs for the auto-correlation of the CSST photometric galaxy sample (left), the auto-correlation of GW source [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Number density distributions as a function of redshift. The left panel shows galaxies from the CSST survey, while [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Cumulative distribution functions of the relative luminosity distance error ∆ [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Constraints on cosmological and GW clustering bias parameters derived from the individual analyses of the galaxy [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Constraint precisions of H0, Ωm, ns, and As as a function of the number of bins obtained by using the CSST photometric galaxy sample combined with the 10-year GW sample of ET2CE. H0 c b ns As 0 1 2 3 4 5 p /p ( % ) 2.18 2.07 3.62 2.12 4.15 1.44 2.07 2.98 1.86 3.21 1.04 2.04 2.73 1.73 2.76 1 yr 5 yr 10 yr [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Constraint precisions of H0, Ωm, ns, and As ob￾tained by using the CSST photometric galaxy sample com￾bined with the GW sample of ET2CE, considering different GW observation durations. of ET2CE and combining the galaxy auto-correlation, the GW–galaxy cross-correlation, and the GW auto￾correlation spectra, we constrain H0, Ωm, ns, and As to 1.04%, 1.77%, 1.73%, and 2.76%, respectively. When increasing the n… view at source ↗
read the original abstract

Gravitational-wave (GW) events are generally believed to originate in galaxies and can thus serve, like galaxies, as tracers of the universe's large-scale structure. In GW observations, waveform analysis provides direct measurements of luminosity distances; however, without relying on a specific cosmological model, the redshifts of GW sources cannot be determined due to the mass-redshift degeneracy. By cross-correlating GW events with galaxies, one can establish a correspondence between luminosity distance and redshift shells, enabling cosmological inference. In this work, we explore the scientific potential of cross-correlating GW sources detected by third-generation (3G) ground-based GW detectors with the photometric redshift survey of the China Space Station Survey Telescope (CSST). We find that the constraint precisions of the Hubble constant and the matter density parameter can reach $1.04\%$ and $2.04\%$, respectively. Additionally, we have also constrained the precision of the GW clustering bias parameter. These results highlight the significant potential of the synergy between CSST and 3G ground-based GW detectors in constraining cosmological models and probing GW source formation channels using cross-correlation of dark sirens and galaxies.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript presents a Fisher-matrix forecast for cosmological parameters derived from the angular cross-power spectrum C_ℓ^{GW-g} between dark sirens detected by third-generation ground-based gravitational-wave observatories and galaxies in the CSST photometric redshift survey. The authors report that this cross-correlation approach yields constraint precisions of 1.04% on the Hubble constant and 2.04% on the matter density parameter, while also constraining the GW clustering bias parameter. The method relies on luminosity distances from GW waveforms combined with photometric redshifts to link distance and redshift shells without requiring electromagnetic counterparts for individual events.

Significance. If the forecasts prove robust, the work would demonstrate a promising multi-messenger route to cosmological inference with dark sirens, offering an independent probe of H0 that could complement other methods. The use of cross-correlation to mitigate the mass-redshift degeneracy is a standard and physically motivated technique. The paper employs conventional forecasting tools, which is a positive aspect, but the quoted precisions rest on specific external model choices whose impact is not fully explored.

major comments (1)
  1. [Abstract and forecast setup] The headline precisions quoted in the abstract (1.04% on H0 and 2.04% on Ωm) are obtained from a Fisher forecast that adopts fixed fiducial forms for the GW source redshift distribution n_GW(z), the clustering bias b_GW(z), and the CSST photometric redshift scatter σ_z/(1+z). The manuscript does not marginalize over these inputs or demonstrate stability of the errors when they are varied within current observational uncertainties. Because the cross-power spectrum amplitude scales linearly with these functions, moderate shifts would alter the forecasted precisions by tens of percent; this is load-bearing for the central claim.
minor comments (2)
  1. [Abstract] The abstract would be clearer if it briefly stated the statistical method (Fisher matrix on the angular cross-power spectrum) rather than only the final numbers.
  2. [Model description] Ensure consistent notation for the GW bias parameter throughout; it is introduced as a free parameter but its redshift dependence (or lack thereof) should be stated explicitly in the model section.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comment, which helps improve the robustness of our forecasts. We respond to the major comment below and outline the revisions we will make.

read point-by-point responses

  1. Referee: [Abstract and forecast setup] The headline precisions quoted in the abstract (1.04% on H0 and 2.04% on Ωm) are obtained from a Fisher forecast that adopts fixed fiducial forms for the GW source redshift distribution n_GW(z), the clustering bias b_GW(z), and the CSST photometric redshift scatter σ_z/(1+z). The manuscript does not marginalize over these inputs or demonstrate stability of the errors when they are varied within current observational uncertainties. Because the cross-power spectrum amplitude scales linearly with these functions, moderate shifts would alter the forecasted precisions by tens of percent; this is load-bearing for the central claim.

    Authors: We thank the referee for pointing out this aspect of the forecast. The quoted precisions are indeed computed for a fixed, observationally motivated fiducial choice of n_GW(z), b_GW(z), and photometric redshift scatter, which is standard in Fisher-matrix studies to establish baseline performance. We agree that the lack of explicit marginalization or sensitivity tests leaves the central claims vulnerable to the referee's concern. In the revised manuscript we will add a dedicated subsection (in Section 4) together with an appendix that varies the amplitude and shape parameters of these three functions within current observational uncertainties (10–30 % shifts). We will also marginalize over the overall normalization of b_GW(z) as a single nuisance parameter in the main Fisher analysis. The resulting constraints on H0 and Ω_m remain at the few-percent level under these variations, and the abstract will be updated to clarify that the headline numbers refer to the fiducial setup with demonstrated stability. revision: yes

Circularity Check

0 steps flagged

Standard Fisher forecast with explicit fiducial inputs; no circular reduction

full rationale

The paper sets up the angular cross-power spectrum C_ℓ^{GW-g} using stated fiducial forms for the GW redshift distribution n_GW(z), clustering bias b_GW(z), and CSST photo-z scatter, then applies the Fisher matrix to forecast parameter errors. The quoted 1.04% and 2.04% precisions are the direct output of this procedure under those inputs. No step reduces by construction to a self-definition, a fitted quantity renamed as prediction, or a load-bearing self-citation chain. The derivation remains self-contained as a transparent forecast and does not equate the result to its modeling assumptions beyond the explicit, conventional choices typical of such studies.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The work rests on standard domain assumptions about GW sources tracing galaxies and on external specifications of detector sensitivity and survey depth; no new entities are introduced.

free parameters (1)
  • GW clustering bias parameter
    Treated as a free parameter that is simultaneously constrained with cosmology.
axioms (1)
  • domain assumption GW events originate in galaxies and trace the large-scale structure
    Explicitly stated in the first sentence of the abstract.

pith-pipeline@v0.9.0 · 5769 in / 1169 out tokens · 37269 ms · 2026-05-18T04:44:36.734193+00:00 · methodology

discussion (0)

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

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Forward citations

Cited by 1 Pith paper

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

  1. Robust parameter inference for Taiji via time-frequency contrastive learning and normalizing flows

    gr-qc 2026-04 unverdicted novelty 6.0

    A glitch-robust amortized inference framework combining normalizing flows, time-frequency multimodal fusion, and contrastive learning outperforms MCMC for Taiji massive black hole binary parameter estimation under noi...

Reference graph

Works this paper leans on

132 extracted references · 132 canonical work pages · cited by 1 Pith paper · 32 internal anchors

  1. [1]

    The DESI Experiment Part I: Science,Targeting, and Survey Design

    A. Aghamousaet al.(DESI), (2016), arXiv:1611.00036 [astro-ph.IM]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  2. [2]

    Euclid Definition Study Report

    R. Laureijset al.(EUCLID), (2011), arXiv:1110.3193 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  3. [3]

    Mellier, Abdurro’uf, J

    Y. Mellieret al.(Euclid), Astron. Astrophys.697, A1 (2025), arXiv:2405.13491 [astro-ph.CO]

    work page arXiv 2025

  4. [4]

    P. A. Abellet al.(LSST Science, LSST Project), (2009), arXiv:0912.0201 [astro-ph.IM]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  5. [5]

    Gonget al.(CSST), (2025), arXiv:2507.04618 [astro- ph.IM]

    Y. Gonget al.(CSST), (2025), arXiv:2507.04618 [astro- ph.IM]

    work page arXiv 2025

  6. [6]

    Dodelsonet al.(SDSS), Astrophys

    S. Dodelsonet al.(SDSS), Astrophys. J.572, 140 (2001), arXiv:astro-ph/0107421

    work page arXiv 2001

  7. [7]

    The 2dF Galaxy Redshift Survey: Power-spectrum analysis of the final dataset and cosmological implications

    S. Coleet al.(2dFGRS), Mon. Not. Roy. Astron. Soc. 362, 505 (2005), arXiv:astro-ph/0501174

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  8. [8]

    D. J. Eisensteinet al.(SDSS), Astrophys. J.633, 560 (2005), arXiv:astro-ph/0501171

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  9. [9]

    E. A. Kazinet al.(SDSS), Astrophys. J.710, 1444 (2010), arXiv:0908.2598 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  10. [10]

    What galaxy surveys really measure

    C. Bonvin and R. Durrer, Phys. Rev. D84, 063505 (2011), arXiv:1105.5280 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  11. [11]

    Cosmological Parameter Estimation with Large Scale Structure Observations

    E. Di Dio, F. Montanari, R. Durrer, and J. Lesgourgues, JCAP01, 042 (2014), arXiv:1308.6186 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  12. [12]

    Kaiser, Mon

    N. Kaiser, Mon. Not. Roy. Astron. Soc.227, 1 (1987)

    work page 1987

  13. [13]

    A. S. Szalay, T. Matsubara, and S. D. Landy, Astro- phys. J. Lett.498, L1 (1998), arXiv:astro-ph/9712007

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  14. [14]

    The linear power spectrum of observed source number counts

    A. Challinor and A. Lewis, Phys. Rev. D84, 043516 (2011), arXiv:1105.5292 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  15. [15]

    J. Yoo, A. L. Fitzpatrick, and M. Zaldarriaga, Phys. Rev. D80, 083514 (2009), arXiv:0907.0707 [astro- ph.CO]. 13

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  16. [16]

    DESI DR2 Results II: Measurements of Baryon Acoustic Oscillations and Cosmological Constraints

    M. Abdul Karimet al.(DESI), (2025), arXiv:2503.14738 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  17. [17]

    Wu and X

    P.-J. Wu and X. Zhang, Phys. Rev. D112, 063514 (2025), arXiv:2411.06356 [astro-ph.CO]

    work page arXiv 2025

  18. [18]

    Li, P.-J

    T.-N. Li, P.-J. Wu, G.-H. Du, S.-J. Jin, H.-L. Li, J.- F. Zhang, and X. Zhang, Astrophys. J.976, 1 (2024), arXiv:2407.14934 [astro-ph.CO]

    work page arXiv 2024

  19. [19]

    Du, P.-J

    G.-H. Du, P.-J. Wu, T.-N. Li, and X. Zhang, Eur. Phys. J. C85, 392 (2025), arXiv:2407.15640 [astro-ph.CO]

    work page arXiv 2025

  20. [20]

    Li, Y.-H

    T.-N. Li, Y.-H. Li, G.-H. Du, P.-J. Wu, L. Feng, J.-F. Zhang, and X. Zhang, Eur. Phys. J. C85, 608 (2025), arXiv:2411.08639 [astro-ph.CO]

    work page arXiv 2025

  21. [21]

    Ye, S.-J

    G. Ye and S.-J. Lin, (2025), arXiv:2505.02207 [astro- ph.CO]

    work page arXiv 2025

  22. [22]

    Y.-H. Pang, X. Zhang, and Q.-G. Huang, Sci. China Phys. Mech. Astron.68, 280410 (2025), arXiv:2503.21600 [astro-ph.CO]

    work page arXiv 2025

  23. [23]

    Wu, Comparison of dark energy models using late- universe observations 10.48550/arXiv.2504.09054 (2025), arXiv:2504.09054 [astro-ph.CO]

    P.-J. Wu, Phys. Rev. D112, 043527 (2025), arXiv:2504.09054 [astro-ph.CO]

    work page arXiv 2025

  24. [24]

    Li, G.-H

    T.-N. Li, G.-H. Du, Y.-H. Li, P.-J. Wu, S.-J. Jin, J.-F. Zhang, and X. Zhang, (2025), arXiv:2501.07361 [astro- ph.CO]

    work page arXiv 2025

  25. [25]

    Du, T.-N

    G.-H. Du, T.-N. Li, P.-J. Wu, L. Feng, S.-H. Zhou, J.-F. Zhang, and X. Zhang, (2025), arXiv:2501.10785 [astro- ph.CO]

    work page arXiv 2025

  26. [26]

    Feng, T.-N

    L. Feng, T.-N. Li, G.-H. Du, J.-F. Zhang, and X. Zhang, Phys. Dark Univ.48, 101935 (2025), arXiv:2503.10423 [astro-ph.CO]

    work page arXiv 2025

  27. [27]

    Ling, G.-H

    J.-L. Ling, G.-H. Du, T.-N. Li, J.-F. Zhang, S.-J. Wang, and X. Zhang, (2025), arXiv:2505.22369 [astro-ph.CO]

    work page arXiv 2025

  28. [28]

    Li, Y.-M

    T.-N. Li, Y.-M. Zhang, Y.-H. Yao, P.-J. Wu, J.-F. Zhang, and X. Zhang, (2025), arXiv:2506.09819 [astro- ph.CO]

    work page arXiv 2025

  29. [29]

    Li, P.-J

    T.-N. Li, P.-J. Wu, G.-H. Du, Y.-H. Yao, J.-F. Zhang, and X. Zhang, Phys. Dark Univ.50, 102068 (2025), arXiv:2507.07798 [astro-ph.CO]

    work page arXiv 2025

  30. [30]

    Li, G.-H

    T.-N. Li, G.-H. Du, P.-J. Wu, J.-Z. Qi, J.-F. Zhang, and X. Zhang, (2025), arXiv:2507.13811 [astro-ph.CO]

    work page arXiv 2025

  31. [31]

    Du, T.-N

    G.-H. Du, T.-N. Li, P.-J. Wu, J.-F. Zhang, and X. Zhang, (2025), arXiv:2507.16589 [astro-ph.CO]

    work page arXiv 2025

  32. [32]

    Obser- vational challenges to holographic and Ricci dark energy paradigms: Insights from ACT DR6 and DESI DR2,

    P.-J. Wu, T.-N. Li, G.-H. Du, and X. Zhang, (2025), arXiv:2509.02945 [astro-ph.CO]

    work page arXiv 2025

  33. [33]

    Zhou, T.-N

    S.-H. Zhou, T.-N. Li, G.-H. Du, J.-Q. Jiang, J.-F. Zhang, and X. Zhang, (2025), arXiv:2509.10836 [astro- ph.CO]

    work page arXiv 2025

  34. [34]

    Zhang, T.-N

    Y.-M. Zhang, T.-N. Li, G.-H. Du, S.-H. Zhou, L.- Y. Gao, J.-F. Zhang, and X. Zhang, (2025), arXiv:2510.12627 [astro-ph.CO]

    work page arXiv 2025

  35. [35]

    Updated constraints on interact- ing dark energy: A comprehensive analysis using multiple CMB probes, DESI DR2, and supernovae observations,

    T.-N. Li, G.-H. Du, Y.-H. Li, Y. Li, J.-L. Ling, J.-F. Zhang, and X. Zhang, (2025), arXiv:2510.11363 [astro- ph.CO]

    work page arXiv 2025

  36. [36]

    S. Zhou, Z. Chen, and Y. Yu, (2025), 10.1007/s11433- 025-2755-x, arXiv:2506.04671 [astro-ph.CO]

    work page doi:10.1007/s11433- 2025

  37. [37]

    Songet al., Astrophys

    Y. Songet al., Astrophys. J.976, 244 (2024), arXiv:2408.08589 [astro-ph.CO]

    work page arXiv 2024

  38. [38]

    Xionget al., Astrophys

    Q. Xionget al., Astrophys. J.985, 131 (2025), arXiv:2410.19388 [astro-ph.CO]

    work page arXiv 2025

  39. [39]

    H. Lin, F. Deng, Y. Gong, and X. Chen, Mon. Not. Roy. Astron. Soc.529, 1542 (2024), arXiv:2310.10140 [astro-ph.CO]

    work page arXiv 2024

  40. [40]

    Q. Liu, X. Er, Z. Fan, D. Z. Liu, G. Li, C. Wei, Z. Ban, X. Li, and D. Yue, Res. Astron. Astrophys.23, 075021 (2023), arXiv:2305.03976 [astro-ph.CO]

    work page arXiv 2023

  41. [41]

    Shiet al., Sci

    F. Shiet al., Sci. China Phys. Mech. Astron.68, 249511 (2025), arXiv:2501.08503 [astro-ph.CO]

    work page arXiv 2025

  42. [42]

    J.-H. Yan, Y. Gong, M. Wang, H. Miao, and X. Chen, Res. Astron. Astrophys.24, 115013 (2024), arXiv:2407.17154 [astro-ph.CO]

    work page arXiv 2024

  43. [43]

    Y. Gong, X. Liu, Y. Cao, X. Chen, Z. Fan, R. Li, X.-D. Li, Z. Li, X. Zhang, and H. Zhan, Astrophys. J.883, 203 (2019), arXiv:1901.04634 [astro-ph.CO]

    work page arXiv 2019

  44. [44]

    Y. Cao, B. Hu, J. Yao, and H. Zhan, Astrophys. J.970, 49 (2024), arXiv:2311.13185 [astro-ph.CO]

    work page arXiv 2024

  45. [45]

    H. Lin, Y. Gong, X. Chen, K. C. Chan, Z. Fan, and H. Zhan, Mon. Not. Roy. Astron. Soc.515, 5743 (2022), arXiv:2203.11429 [astro-ph.CO]

    work page arXiv 2022

  46. [46]

    A. G. Abacet al.(KAGRA, Virgo, LIGO Scientific), Phys. Rev. Lett.135, 111403 (2025), arXiv:2509.08054 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  47. [47]

    P-V criticality of charged AdS black holes

    D. Kubiznak and R. B. Mann, JHEP07, 033 (2012), arXiv:1205.0559 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  48. [48]

    Wei, Y.-X

    S.-W. Wei, Y.-X. Liu, and R. B. Mann, Phys. Rev. D 100, 124033 (2019), arXiv:1909.03887 [gr-qc]

    work page arXiv 2019

  49. [49]

    R.-G. Cai, L. Li, and J.-K. Zhao, (2024), arXiv:2410.00717 [gr-qc]

    work page arXiv 2024

  50. [50]

    Xu and R

    Z.-M. Xu and R. B. Mann, (2025), arXiv:2504.05708 [gr-qc]

    work page arXiv 2025

  51. [51]

    Zhao, Z.-Y

    Z.-Q. Zhao, Z.-Y. Nie, J.-F. Zhang, and X. Zhang, (2025), arXiv:2504.04995 [gr-qc]

    work page arXiv 2025

  52. [52]

    Zhang, Z.-Q

    S.-H. Zhang, Z.-Q. Zhao, Z.-Y. Li, J.-F. Zhang, and X. Zhang, (2025), arXiv:2509.05103 [gr-qc]

    work page arXiv 2025

  53. [53]

    B. F. Schutz, Nature323, 310 (1986)

    work page 1986

  54. [54]

    W. Zhao, C. Van Den Broeck, D. Baskaran, and T. G. F. Li, Phys. Rev. D83, 023005 (2011), arXiv:1009.0206 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  55. [55]

    Estimating cosmological parameters by the simulated data of gravitational waves from the Einstein Telescope

    R.-G. Cai and T. Yang, Phys. Rev. D95, 044024 (2017), arXiv:1608.08008 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  56. [56]

    Impacts of gravitational-wave standard siren observation of the Einstein Telescope on weighing neutrinos in cosmology

    L.-F. Wang, X.-N. Zhang, J.-F. Zhang, and X. Zhang, Phys. Lett. B782, 87 (2018), arXiv:1802.04720 [astro- ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  57. [57]

    Improving cosmological parameter estimation with the future gravitational-wave standard siren observation from the Einstein Telescope

    X.-N. Zhang, L.-F. Wang, J.-F. Zhang, and X. Zhang, Phys. Rev. D99, 063510 (2019), arXiv:1804.08379 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  58. [58]

    Zhang, Sci

    X. Zhang, Sci. China Phys. Mech. Astron.62, 110431 (2019), arXiv:1905.11122 [astro-ph.CO]

    work page arXiv 2019

  59. [59]

    Zhang, M

    J.-F. Zhang, M. Zhang, S.-J. Jin, J.-Z. Qi, and X. Zhang, JCAP09, 068 (2019), arXiv:1907.03238 [astro-ph.CO]

    work page arXiv 2019

  60. [60]

    Wang, Z.-W

    L.-F. Wang, Z.-W. Zhao, J.-F. Zhang, and X. Zhang, JCAP11, 012 (2020), arXiv:1907.01838 [astro-ph.CO]

    work page arXiv 2020

  61. [61]

    Jin, D.-Z

    S.-J. Jin, D.-Z. He, Y. Xu, J.-F. Zhang, and X. Zhang, JCAP03, 051 (2020), arXiv:2001.05393 [astro-ph.CO]

    work page arXiv 2020

  62. [62]

    Qi, S.-J

    J.-Z. Qi, S.-J. Jin, X.-L. Fan, J.-F. Zhang, and X. Zhang, JCAP12, 042 (2021), arXiv:2102.01292 [astro-ph.CO]

    work page arXiv 2021

  63. [63]

    Jin, L.-F

    S.-J. Jin, L.-F. Wang, P.-J. Wu, J.-F. Zhang, and X. Zhang, Phys. Rev. D104, 103507 (2021), arXiv:2106.01859 [astro-ph.CO]

    work page arXiv 2021

  64. [64]

    Wang, S.-J

    L.-F. Wang, S.-J. Jin, J.-F. Zhang, and X. Zhang, Sci. China Phys. Mech. Astron.65, 210411 (2022), arXiv:2101.11882 [gr-qc]

    work page arXiv 2022

  65. [65]

    P.-J. Wu, Y. Shao, S.-J. Jin, and X. Zhang, JCAP06, 052 (2023), arXiv:2202.09726 [astro-ph.CO]

    work page arXiv 2023

  66. [66]

    Jin, R.-Q

    S.-J. Jin, R.-Q. Zhu, L.-F. Wang, H.-L. Li, J.-F. Zhang, and X. Zhang, Commun. Theor. Phys.74, 105404 (2022), arXiv:2204.04689 [astro-ph.CO]

    work page arXiv 2022

  67. [67]

    L.-F. Wang, Y. Shao, S.-R. Xiao, J.-F. Zhang, and X. Zhang, JCAP05, 095 (2025), arXiv:2201.00607 14 [astro-ph.CO]

    work page arXiv 2025

  68. [68]

    Jin, R.-Q

    S.-J. Jin, R.-Q. Zhu, J.-Y. Song, T. Han, J.-F. Zhang, and X. Zhang, JCAP08, 050 (2024), arXiv:2309.11900 [astro-ph.CO]

    work page arXiv 2024

  69. [69]

    J. Yu, Z. Liu, X. Yang, Y. Wang, P. Zhang, X. Zhang, and W. Zhao, Astrophys. J. Suppl.270, 24 (2024), arXiv:2311.11588 [astro-ph.HE]

    work page arXiv 2024

  70. [70]

    Jin, Y.-Z

    S.-J. Jin, Y.-Z. Zhang, J.-Y. Song, J.-F. Zhang, and X. Zhang, Sci. China Phys. Mech. Astron.67, 220412 (2024), arXiv:2305.19714 [astro-ph.CO]

    work page arXiv 2024

  71. [71]

    Han, S.-J

    T. Han, S.-J. Jin, J.-F. Zhang, and X. Zhang, Eur. Phys. J. C84, 663 (2024), arXiv:2309.14965 [astro- ph.CO]

    work page arXiv 2024

  72. [72]

    Jin, S.-S

    S.-J. Jin, S.-S. Xing, Y. Shao, J.-F. Zhang, and X. Zhang, Chin. Phys. C47, 065104 (2023), arXiv:2301.06722 [astro-ph.CO]

    work page arXiv 2023

  73. [73]

    L. Feng, T. Han, J.-F. Zhang, and X. Zhang, Com- mun. Theor. Phys.77, 065403 (2025), arXiv:2409.04453 [astro-ph.HE]

    work page arXiv 2025

  74. [74]

    L. Feng, T. Han, J.-F. Zhang, and X. Zhang, Chin. Phys. C48, 095104 (2024), arXiv:2404.19530 [astro- ph.CO]

    work page arXiv 2024

  75. [75]

    T. Han, Z. Li, J.-F. Zhang, and X. Zhang, Universe11, 85 (2025), arXiv:2412.06873 [astro-ph.CO]

    work page arXiv 2025

  76. [76]

    Han, J.-F

    T. Han, J.-F. Zhang, and X. Zhang, (2025), arXiv:2504.17741 [astro-ph.CO]

    work page arXiv 2025

  77. [77]

    L. Feng, T. Han, J.-F. Zhang, and X. Zhang, (2025), arXiv:2507.17315 [astro-ph.CO]

    work page arXiv 2025

  78. [78]

    Jin, J.-Y

    S.-J. Jin, J.-Y. Song, T.-Y. Sun, S.-R. Xiao, H. Wang, L.-F. Wang, J.-F. Zhang, and X. Zhang, (2025), arXiv:2507.12965 [astro-ph.CO]

    work page arXiv 2025

  79. [79]

    B. P. Abbottet al.(LIGO Scientific, Virgo, 1M2H, Dark Energy Camera GW-E, DES, DLT40, Las Cumbres Observatory, VINROUGE, MASTER), Nature551, 85 (2017), arXiv:1710.05835 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  80. [80]

    B. P. Abbottet al.(LIGO Scientific, Virgo), Phys. Rev. Lett.119, 161101 (2017), arXiv:1710.05832 [gr-qc]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

Showing first 80 references.