arxiv: 2509.24904 · v2 · submitted 2025-09-29 · 🌌 astro-ph.CO · astro-ph.HE· astro-ph.IM· physics.data-an· stat.CO

Graph-based Summary Statistics for Revealing the Stochastic Gravitational Wave Background in Pulsar Timing Arrays

M. Alakhras , S. M. S. Movahed This is my paper

Pith reviewed 2026-05-18 12:44 UTC · model grok-4.3

classification 🌌 astro-ph.CO astro-ph.HEastro-ph.IMphysics.data-anstat.CO

keywords stochastic gravitational wave backgroundpulsar timing arrayscorrelation graphHellings-Downs correlationNANOGravgraph summary statisticsgravitational wave detection

0 comments

The pith

Graph-based statistics on pulsar timing residuals detect the stochastic gravitational wave background down to strain amplitudes of 1.2 times 10 to the minus 15.

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

The paper develops a method that represents pulsar timing residuals as a network with pulsars as nodes and their pairwise correlations as edge weights. Summary statistics drawn from this network, particularly the average clustering coefficient and fluctuations in edge weights, are shown to pick out the specific angular pattern expected from a stochastic gravitational wave background. The work evaluates how the number of pulsars, observation length, and signal strength affect these measures, then applies the technique first to synthetic data to establish sensitivity and finally to the NANOGrav 15-year observations. A sympathetic reader would care because an independent, network-based confirmation of the background would strengthen the case for a new cosmological probe at nanohertz frequencies.

Core claim

The authors construct a correlation graph from pulsar timing residuals and demonstrate that the average clustering coefficient together with edge weight fluctuation act as the most discriminative summary statistics for identifying a common signal. After an initial common-signal detection, the second cumulant of edge weights at angular separations above 40 degrees excludes non-Hellings-Downs templates. This procedure yields a lowest detectable SGWB strain amplitude of approximately 1.2 times 10 to the minus 15 at current PTA sensitivities. Fisher forecasts indicate that the logarithmic amplitude and spectral index can be recovered to 1.5 percent and 19.5 percent precision respectively at the

What carries the argument

A correlation graph whose nodes are pulsars and whose edges are weighted by the measured timing-residual correlations; the graph's topological measures isolate the quadrupolar angular dependence of the Hellings-Downs curve.

Load-bearing premise

The method assumes that an initial common-signal detection followed by template exclusion does not introduce selection biases that would mask or mimic the Hellings-Downs pattern in the graph statistics.

What would settle it

Failure to recover an injected SGWB signal of amplitude 1.2 times 10 to the minus 15 in end-to-end simulations that include realistic red noise and other common-mode processes, or a reanalysis of the NANOGrav 15-year data set that yields no evidence above 2 sigma, would falsify the claimed sensitivity and detection.

Figures

Figures reproduced from arXiv: 2509.24904 by M. Alakhras, S. M. S. Movahed.

**Figure 2.** Figure 2: FIG. 2: (a) Sky distribution of mock PTA pulsars (green stars) and NANOGrav pulsars (red circles) in celestial coordinates [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3: (a) Simulated residuals for three representative pulsars showing noise-only (blue triangles) and SGWB+noise (green [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4: Recovered angular correlation patterns for (a) Hellings & Downs (HD), (b) Monopole, (c) Dipole, and (d) CURN [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5: The pipeline for constructing a weighted correlation network from PTA data. Nodes represent pulsars, pulsar pairs that [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗

**Figure 6.** Figure 6: FIG. 6: Correlation graphs constructed from mock PTA data for different angular thresholds: (a) 10 [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗

**Figure 7.** Figure 7: FIG. 7: The density plots for distinct components employed in the construction of graphs are shown for a range of angular [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗

**Figure 8.** Figure 8: FIG. 8: The constructed graph from PTA data for a range of angular separation values ( [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗

**Figure 9.** Figure 9: FIG. 9: The empirical distributions of graph measures across angular thresholds for 10000 realizations. The graph measures [PITH_FULL_IMAGE:figures/full_fig_p014_9.png] view at source ↗

**Figure 10.** Figure 10: FIG. 10: The binary representation of 90-component summary statistics responses to conditions assumed by evaluation metrics, [PITH_FULL_IMAGE:figures/full_fig_p015_10.png] view at source ↗

**Figure 9.** Figure 9: This result confirms that average strength is [PITH_FULL_IMAGE:figures/full_fig_p015_9.png] view at source ↗

**Figure 9.** Figure 9: The only measure that performs well for SGWB [PITH_FULL_IMAGE:figures/full_fig_p016_9.png] view at source ↗

**Figure 11.** Figure 11: FIG. 11: Decision strategy for the SGWB detection pipeline. The sole pathway for a positive detection requires a positive [PITH_FULL_IMAGE:figures/full_fig_p017_11.png] view at source ↗

**Figure 12.** Figure 12: FIG. 12: Detection rate and false alarm probability (FAP) of the SGWB graph-based pipeline as a function of number of [PITH_FULL_IMAGE:figures/full_fig_p018_12.png] view at source ↗

**Figure 13.** Figure 13: FIG. 13: The merit feature vectors for NG15 dataset (red diamond) compared to the null distributions. Upper panels shows [PITH_FULL_IMAGE:figures/full_fig_p019_13.png] view at source ↗

**Figure 14.** Figure 14: FIG. 14: left panel: The relative statistical error, [PITH_FULL_IMAGE:figures/full_fig_p020_14.png] view at source ↗

**Figure 15.** Figure 15: FIG. 15: The constraints on log [PITH_FULL_IMAGE:figures/full_fig_p021_15.png] view at source ↗

read the original abstract

In this work, we propose a graph-based method implemented on the pulsar timing residuals (PTRs) for stochastic gravitational wave background (SGWB) detection within the nano-Hertz frequency regime and examining uncertainties of its parameters. We construct a correlation graph with pulsars as its nodes, and analyze the graph-based summary statistics, including structural characteristics of complex network, for identifying SGWB in the real and synthetic datasets. The effect of the number of pulsars, the observation time span, and the strength of the SGWB on the graph-based feature vector is evaluated. Our results demonstrate that the Discriminative Summary Statistics for common signal detection consists of the average clustering coefficient and the edge weight fluctuation. The SGWB detection conducted after the observation of a common signal and then exclusion of non-Hellings \& Downs templates is performed by the second cumulant of edge weight for angular separation thresholds $\bar{\zeta}\gtrsim 40^{\circ}$. The lowest detectable value of SGWB strain amplitude utilizing our graph-based measures at the current PTAs sensitivity is $A_{\rm SGWB}\gtrsim 1.2\times 10^{-15}$. Fisher forecasts confirmed that the uncertainty levels of $\log_{10} A_{\rm SGWB}$ and spectral index reach $1.5\%$ and $19.5\%$, respectively, at $2\sigma$ confidence interval. A weak evidence for an SGWB at $\sim 2.3\sigma$ level is obtained by applying our graph-based method to the NANOGrav 15-year dataset.

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.

Desk Editor's Note private letter to a colleague

Graph stats on pulsar timing residuals give a new handle on SGWB searches, but the two-step common-signal then HD-filter pipeline needs bias checks before the sensitivity and 2.3-sigma claims can be taken at face value.

read the letter

The main point is that this paper builds correlation graphs from pulsar timing residuals and pulls out complex-network summary statistics—average clustering coefficient and edge-weight fluctuation—to flag the Hellings-Downs pattern expected from a stochastic gravitational wave background. That specific framing does not show up in the standard PTA correlation papers they cite, so the method itself is new in this subfield. They test how the features respond to changes in pulsar count, observation span, and signal strength on synthetic data, run Fisher forecasts that give roughly 1.5% uncertainty on log amplitude and 19.5% on spectral index at 2 sigma, and apply the whole thing to the NANOGrav 15-year set to report a 2.3-sigma hint plus a claimed lowest detectable amplitude around 1.2 times 10 to the minus 15. Those pieces are concrete and worth seeing in detail. The soft spot is the detection sequence itself. They first require a common-signal detection, then use the second cumulant of edge weights only for angular separations above 40 degrees to drop non-HD templates. That ordering can introduce selection effects, and the abstract does not show a full accounting of how it changes false-positive rates or whether realistic red-noise processes could pass the cut and mimic the graph signatures. If those steps correlate with the very features being measured, both the sensitivity number and the real-data significance become harder to interpret cleanly. This is for PTA analysts and nano-Hertz GW people who already know the usual correlation methods and want an alternative statistic to cross-check against. A reader comfortable with network measures applied to time-series data will get the most out of the method section. The work has enough structure and some real-data application that it deserves a serious referee rather than a desk reject, though any review will need to focus on whether the pipeline controls selection bias and whether the graph statistics stay independent of the initial common-signal test.

Referee Report

2 major / 2 minor

Summary. The paper proposes a graph-based method for detecting the stochastic gravitational wave background (SGWB) in pulsar timing array data by constructing correlation graphs with pulsars as nodes and extracting summary statistics such as the average clustering coefficient and edge-weight fluctuation. It evaluates these on synthetic datasets to assess dependence on number of pulsars, observation span, and SGWB amplitude, then applies a two-step pipeline (common-signal detection followed by exclusion of non-Hellings-Downs templates via the second cumulant of edge weight for angular separations ≳40°) to claim a lowest detectable strain amplitude A_SGWB ≳ 1.2×10^{-15} at current PTA sensitivities. Fisher forecasts for parameter uncertainties and a ~2.3σ weak evidence result on the NANOGrav 15-year dataset are also reported.

Significance. If validated, the graph-theoretic framing could offer a complementary visualization and summary-statistic approach to standard Hellings-Downs correlation analyses in PTA searches for nano-Hz SGWB. The reported Fisher uncertainties (1.5% on log10 A and 19.5% on spectral index at 2σ) and application to real data provide concrete benchmarks, though the method's novelty lies primarily in the network-derived discriminants rather than in fundamentally new physics.

major comments (2)

[Abstract / detection pipeline] Abstract and detection pipeline description: the headline sensitivity A_SGWB ≳ 1.2×10^{-15} and the NANOGrav 2.3σ claim both rest on a sequential procedure that first requires detection of a common signal and then applies the second cumulant of edge weight only for angular separations ζ-bar ≳40° to reject non-HD templates. No quantification of the false-positive rate or selection bias induced by this ordering is provided, so it is unclear whether the quoted sensitivity and significance remain valid once the full pipeline is accounted for.
[Results on synthetic and real datasets] The claim that the average clustering coefficient and edge-weight fluctuation constitute the 'Discriminative Summary Statistics' for common-signal detection is presented without an explicit ablation or ROC analysis showing that these two features remain orthogonal to the initial common-signal test and are not dominated by realistic red-noise processes or timing-model residuals that can produce correlated but non-HD signatures.

minor comments (2)

[Methods] Notation for the angular-separation threshold is introduced as ζ-bar in the abstract but should be defined consistently in the methods section with an explicit equation or figure reference.
[Fisher forecasts] The Fisher-forecast section would benefit from a brief statement of the assumed noise model and covariance matrix used to derive the 1.5% and 19.5% uncertainties.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful and constructive review of our manuscript. We address each major comment below and have revised the manuscript to incorporate additional analyses where needed to strengthen the presentation of the detection pipeline and the role of the graph-based statistics.

read point-by-point responses

Referee: [Abstract / detection pipeline] Abstract and detection pipeline description: the headline sensitivity A_SGWB ≳ 1.2×10^{-15} and the NANOGrav 2.3σ claim both rest on a sequential procedure that first requires detection of a common signal and then applies the second cumulant of edge weight only for angular separations ζ-bar ≳40° to reject non-HD templates. No quantification of the false-positive rate or selection bias induced by this ordering is provided, so it is unclear whether the quoted sensitivity and significance remain valid once the full pipeline is accounted for.

Authors: We acknowledge that the sequential nature of the pipeline requires explicit validation of the combined false-positive rate. The two-step approach follows standard PTA search practice, with the graph statistics applied only after a common signal is identified to test for the Hellings-Downs pattern at large angular separations. In the revised manuscript we have added Monte Carlo results applying the full pipeline to large ensembles of noise-only realizations that include realistic red-noise spectra and timing-model residuals. These simulations quantify the false-positive rate at the quoted amplitude threshold and confirm that the reported sensitivity and the 2.3σ NANOGrav result remain stable once the ordering is taken into account. The abstract and methods section have been updated to include this quantification. revision: yes
Referee: [Results on synthetic and real datasets] The claim that the average clustering coefficient and edge-weight fluctuation constitute the 'Discriminative Summary Statistics' for common-signal detection is presented without an explicit ablation or ROC analysis showing that these two features remain orthogonal to the initial common-signal test and are not dominated by realistic red-noise processes or timing-model residuals that can produce correlated but non-HD signatures.

Authors: We agree that an explicit ablation study and ROC analysis would better demonstrate the added value of these two statistics. The original manuscript showed their dependence on SGWB amplitude and their superiority to other graph features, but did not include a full ROC comparison against red-noise-dominated cases. We have now performed and included such analyses: ROC curves are presented for the clustering coefficient and edge-weight fluctuation under a range of red-noise models and timing residuals, confirming that the two statistics retain discriminative power beyond the common-signal test and are not dominated by non-HD correlated noise. These results are added to the results section and supplementary material. revision: yes

Circularity Check

0 steps flagged

No significant circularity in graph-based SGWB detection method

full rationale

The paper constructs correlation graphs from pulsar timing residuals and extracts summary statistics (average clustering coefficient and edge weight fluctuation) as discriminative features for SGWB. The pipeline first identifies a common signal then applies the second cumulant of edge weight at angular separations ≳40° to exclude non-HD templates; the claimed sensitivity A_SGWB ≳ 1.2×10^{-15} and 2.3σ NANOGrav result follow from applying these statistics to synthetic and real data. No step reduces a claimed prediction or first-principles result to its own inputs by construction, no load-bearing self-citation or imported uniqueness theorem appears, and the Hellings-Downs reference is the external standard pattern rather than an internal fit. The derivation remains self-contained with independent methodological content.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the standard PTA assumption that an isotropic SGWB produces Hellings-Downs correlations in timing residuals, plus a data-driven choice of angular threshold and post-selection on common signals; no new physical entities are postulated.

free parameters (1)

angular separation threshold = 40 degrees
Threshold ζ-bar ≳ 40° selected for the second-cumulant analysis to discriminate SGWB.

axioms (1)

domain assumption Pulsar timing residuals exhibit correlations following the Hellings-Downs pattern in the presence of an isotropic SGWB
Invoked when constructing the correlation graph and when excluding non-HD templates.

pith-pipeline@v0.9.0 · 5837 in / 1658 out tokens · 50072 ms · 2026-05-18T12:44:11.082224+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

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

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

The merit feature vector for common signal detection consists of the average clustering coefficient and the edge weight fluctuation. ... The SGWB detection conducted after the observation of a common signal and then exclusion of non-Hellings & Downs templates is performed by the second cumulant of edge weight for angular separation thresholds ζ-bar ≳40°.
IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Fisher forecasts confirmed that the uncertainty levels of log10 A_SGWB and spectral index reach 2.2% and 28.3%, respectively, at 2σ confidence interval.

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.

Reference graph

Works this paper leans on

213 extracted references · 213 canonical work pages · 4 internal anchors

[1]

A. A. Penzias and R. W. Wilson. A Measurement of Ex- cess Antenna Temperature at 4080 Mc/s.Astrophysical Journal, 142:419–421, July 1965

work page 1965
[2]

Planck 2018 results

Planck Collaboration. Planck 2018 results. I. Overview and the cosmological legacy of Planck.Astronomy and Astrophysics, 641:A1, September 2020

work page 2018
[3]

Peebles.The Large-Scale Structure of the Uni- verse

P.J.E. Peebles.The Large-Scale Structure of the Uni- verse. Princeton Series in Physics. Princeton University Press, 2020

work page 2020
[4]

Bernardeau, S

F. Bernardeau, S. Colombi, E. Gazta˜ naga, and R. Scoc- cimarro. Large-scale structure of the universe and cosmological perturbation theory.Physics Reports, 367(1):1–248, 2002

work page 2002
[5]

Klebesadel, Ian B

Ray W. Klebesadel, Ian B. Strong, and Roy A. Olson. Observations of Gamma-Ray Bursts of Cosmic Origin. In E. Fenimore and M. Galassi, editors,Gamma-Ray Bursts: 30 Years of Discovery, volume 727 ofAmerican Institute of Physics Conference Series, pages 3–6. AIP, September 2004

work page 2004
[6]

A Roadmap to Gamma-Ray Bursts: New Developments and Applica- tions to Cosmology.Galaxies, 9(4):77, October 2021

Orlando Luongo and Marco Muccino. A Roadmap to Gamma-Ray Bursts: New Developments and Applica- tions to Cosmology.Galaxies, 9(4):77, October 2021

work page 2021
[7]

Schreier, R

E. Schreier, R. Levinson, H. Gursky, E. Kellogg, H. Tananbaum, and R. Giacconi. Evidence for the Bi- nary Nature of Centaurus X-3 from UHURU X-Ray Observations.Astrophysical Journal Letters, 172:L79, March 1972

work page 1972
[8]

Schatz and K

H. Schatz and K. E. Rehm. X-ray binaries.Nuclear Physics A, 777:601–622, October 2006

work page 2006
[9]

Hewish, S

A. Hewish, S. J. Bell, J. D. H. Pilkington, P. F. Scott, and R. A. Collins. Observation of a Rapidly Pulsat- ing Radio Source.Nature, 217(5130):709–713, February 1968

work page 1968
[10]

Philippov and M

A. Philippov and M. Kramer. Pulsar Magnetospheres and Their Radiation.Annual Review of Astron and As- trophys, 60:495–558, August 2022

work page 2022
[11]

Spectrum of a Stellar Object Identi- fied with the Radio Source 3c 286.Astrophysical Jour- nal, 136:684, September 1962

Maarten Schmidt. Spectrum of a Stellar Object Identi- fied with the Radio Source 3c 286.Astrophysical Jour- nal, 136:684, September 1962

work page 1962
[12]

N¨ aherungsweise Integration der Feldgleichungen der Gravitation.Sitzungsberichte der Königlich Preussischen Akademie der Wis- senschaften, pages 688–696, January 1916

Albert Einstein. N¨ aherungsweise Integration der Feldgleichungen der Gravitation.Sitzungsberichte der Königlich Preussischen Akademie der Wis- senschaften, pages 688–696, January 1916

work page 1916
[13]

¨Uber Gravitationswellen.Sitzungs- berichte der Königlich Preussischen Akademie der Wissenschaften, pages 154–167, January 1918

Albert Einstein. ¨Uber Gravitationswellen.Sitzungs- berichte der Königlich Preussischen Akademie der Wissenschaften, pages 154–167, January 1918

work page 1918
[14]

S. W. Hawking, W. Israel, and B. Dolan. Book-Review - Three Hundred Years of Gravitation.Irish Astronomical Journal, 21:161, September 1993

work page 1993
[15]

B. Allen. The Stochastic Gravity-Wave Background: Sources and Detection. In Jean-Alain Marck and Jean-Pierre Lasota, editors,Relativistic Gravitation and Gravitational Radiation, pages 373–417, January 1997

work page 1997
[16]

B. S. Sathyaprakash and Bernard F. Schutz. Physics, Astrophysics and Cosmology with Gravitational Waves. Living Reviews in Relativity, 12(1):2, December 2009

work page 2009
[17]

Figueroa

Chiara Caprini and Daniel G. Figueroa. Cosmologi- cal backgrounds of gravitational waves.Classical and Quantum Gravity, 35(16):163001, August 2018

work page 2018
[18]

Stochastic gravitational wave back- grounds.Reports on Progress in Physics, 82(1):016903, January 2019

Nelson Christensen. Stochastic gravitational wave back- grounds.Reports on Progress in Physics, 82(1):016903, January 2019

work page 2019
[19]

B. P. Abbott et al. Observation of Gravitational Waves from a Binary Black Hole Merger.Physical Review Let- ters, 116(6):061102, February 2016

work page 2016
[20]

Mandic, E

V. Mandic, E. Thrane, S. Giampanis, and T. Regim- bau. Parameter Estimation in Searches for the Stochas- tic Gravitational-Wave Background.Physical Review Letters, 109(17):171102, October 2012

work page 2012
[21]

B. P. Abbott et al. An upper limit on the stochastic gravitational-wave background of cosmological origin. Nature, 460(7258):990–994, August 2009

work page 2009
[22]

Stochastic gravitational wave background: Meth- ods and implications.Progress in Particle and Nuclear Physics, 128:104003, January 2023

Nick van Remortel, Kamiel Janssens, and Kevin Tur- bang. Stochastic gravitational wave background: Meth- ods and implications.Progress in Particle and Nuclear Physics, 128:104003, January 2023

work page 2023
[23]

B. Allen. Stochastic gravity-wave background in inflationary-universe models.Physical Review D, 37(8):2078–2085, April 1988

work page 2078
[24]

M. C. Guzzetti, N. Bartolo, M. Liguori, and S. Matar- rese. Gravitational waves from inflation.Nuovo Ci- mento Rivista Serie, 39(9):399–495, August 2016

work page 2016
[25]

Scalar Induced Gravitational Waves Review.Universe, 7(11):398, October 2021

Guillem Dom` enech. Scalar Induced Gravitational Waves Review.Universe, 7(11):398, October 2021

work page 2021
[26]

A topic review on probing primordial black hole dark matter with scalar induced gravitational waves.iScience, 24(8):102860, August 2021

Chen Yuan and Qing-Guo Huang. A topic review on probing primordial black hole dark matter with scalar induced gravitational waves.iScience, 24(8):102860, August 2021

work page 2021
[27]

Stochastic approach to grav- itational waves from inflation.Physical Review D, 105(2):023521, January 2022

Gianmassimo Tasinato. Stochastic approach to grav- itational waves from inflation.Physical Review D, 105(2):023521, January 2022

work page 2022
[28]

Primordial black holes and gravitational waves from inflation.General Relativity and Gravita- tion, 57(5):82, May 2025

Misao Sasaki. Primordial black holes and gravitational waves from inflation.General Relativity and Gravita- tion, 57(5):82, May 2025

work page 2025
[29]

Gravita- tional radiation from cosmic strings.Physical Review 24 D, 31(12):3052–3058, June 1985

Tanmay Vachaspati and Alexander Vilenkin. Gravita- tional radiation from cosmic strings.Physical Review 24 D, 31(12):3052–3058, June 1985

work page 1985
[30]

Vilenkin

A. Vilenkin. Cosmic strings and domain walls.Physics Reports, 121(5):263–315, January 1985

work page 1985
[31]

M. B. Hindmarsh and T. W. B. Kibble. Cosmic strings. Reports on Progress in Physics, 58(5):477–562, May 1995

work page 1995
[32]

Gravita- tional wave bursts from cusps and kinks on cosmic strings.Physical Review D, 64(6):064008, September 2001

Thibault Damour and Alexander Vilenkin. Gravita- tional wave bursts from cusps and kinks on cosmic strings.Physical Review D, 64(6):064008, September 2001

work page 2001
[33]

Blanco-Pillado, Ken D

Jose J. Blanco-Pillado, Ken D. Olum, and Benjamin Shlaer. Large parallel cosmic string simulations: New results on loop production.Physical Review D, 83(8):083514, April 2011

work page 2011
[34]

Stochastic gravitational waves from cosmic string loops in scal- ing.Journal of Cosmology and Astroparticle Physics, 2017(12):027, December 2017

Christophe Ringeval and Teruaki Suyama. Stochastic gravitational waves from cosmic string loops in scal- ing.Journal of Cosmology and Astroparticle Physics, 2017(12):027, December 2017

work page 2017
[35]

Blanco-Pillado and Ken D

Jose J. Blanco-Pillado and Ken D. Olum. Stochastic gravitational wave background from smoothed cosmic string loops.Physical Review D, 96(10):104046, Novem- ber 2017

work page 2017
[36]

Multi-messenger constraints on Abelian-Higgs cosmic string networks

Mark Hindmarsh and Jun’ya Kume. Multi-messenger constraints on Abelian-Higgs cosmic string networks. Journal of Cosmology and Astroparticle Physics, 2023(4):045, April 2023

work page 2023
[37]

Constrain- ing Modified Theories of Gravity with Gravitational- Wave Stochastic Backgrounds.Physical Review Letters, 117(9):091102, August 2016

Andrea Maselli, Stefania Marassi, Valeria Ferrari, Kostas Kokkotas, and Raffaella Schneider. Constrain- ing Modified Theories of Gravity with Gravitational- Wave Stochastic Backgrounds.Physical Review Letters, 117(9):091102, August 2016

work page 2016
[38]

Maggiore

M. Maggiore. Gravitational wave experiments and early universe cosmology.Physics Reports, 331(6):283–367, July 2000

work page 2000
[39]

Laser Interferometer Space Antenna

Pau Amaro-Seoane et al. Laser Interferometer Space Antenna.arXiv e-prints, page arXiv:1702.00786, Febru- ary 2017

work page internal anchor Pith review Pith/arXiv arXiv 2017
[40]

Abbott et al

R. Abbott et al. All-sky search for long-duration gravitational-wave bursts in the third Advanced LIGO and Advanced Virgo run.Physical Review D, 104(10):102001, November 2021

work page 2021
[41]

Punturo et al

M. Punturo et al. The Einstein Telescope: a third- generation gravitational wave observatory.Classical and Quantum Gravity, 27(19):194002, October 2010

work page 2010
[42]

Current status of space grav- itational wave antenna DECIGO and B-DECIGO

Seiji Kawamura et al. Current status of space grav- itational wave antenna DECIGO and B-DECIGO. Progress of Theoretical and Experimental Physics, 2021(5):05A105, May 2021

work page 2021
[43]

Ballmer, Lisa Bar- sotti, Nergis Mavalvala, and Matthew Evans

Sheila Dwyer, Daniel Sigg, Stefan W. Ballmer, Lisa Bar- sotti, Nergis Mavalvala, and Matthew Evans. Gravita- tional wave detector with cosmological reach.Physical Review D, 91(8):082001, April 2015

work page 2015
[44]

The US Program in Ground- Based Gravitational Wave Science: Contribution from the LIGO Laboratory.Bulletin of the AAS, 51(3):141, May 2019

David Reitze, LIGO Laboratory: California Institute of Technology, LIGO Laboratory: Massachusetts Institute of Technology, LIGO Hanford Observatory, and LIGO Livingston Observatory. The US Program in Ground- Based Gravitational Wave Science: Contribution from the LIGO Laboratory.Bulletin of the AAS, 51(3):141, May 2019

work page 2019
[45]

M. A. McLaughlin. The North American Nanohertz Ob- servatory for Gravitational Waves.Classical and Quan- tum Gravity, 30(22):224008, November 2013

work page 2013
[46]

Demorest et al

P. Demorest et al. The North American Nanohertz Ob- servatory for Gravitational Waves. InAmerican As- tronomical Society Meeting Abstracts, volume 237 of American Astronomical Society Meeting Abstracts, page 101.01, January 2021

work page 2021
[47]

The Student Teams of As- trophysics ResearcherS (STARS) Undergraduate Pro- gram in the North American Nanohertz Observatory for Gravitational Waves

Timothy Dolch et al. The Student Teams of As- trophysics ResearcherS (STARS) Undergraduate Pro- gram in the North American Nanohertz Observatory for Gravitational Waves. InAmerican Astronomical Society Meeting #240, volume 240 ofAmerican Astronomical Society Meeting Abstracts, page 315.01, June 2022

work page 2022
[48]

The NANOGrav 15 yr Data Set: Search for Signals from New Physics.Astrophysical Journal Letters, 951(1):L11, July 2023

Adeela Afzal et al. The NANOGrav 15 yr Data Set: Search for Signals from New Physics.Astrophysical Journal Letters, 951(1):L11, July 2023

work page 2023
[49]

The Parkes Pulsar Timing Array Project.Publication of Korean Astronomical Society, 30(2):577–581, September 2015

George Hobbs. The Parkes Pulsar Timing Array Project.Publication of Korean Astronomical Society, 30(2):577–581, September 2015

work page 2015
[50]

The Parkes Pulsar Timing Array project: second data release.Publications of the Astron

Matthew Kerr et al. The Parkes Pulsar Timing Array project: second data release.Publications of the Astron. Soc. of Australia, 37:e020, June 2020

work page 2020
[51]

The Parkes Pulsar Timing Array third data release.Publications of the Astron

Andrew Zic et al. The Parkes Pulsar Timing Array third data release.Publications of the Astron. Soc. of Australia, 40:e049, December 2023

work page 2023
[52]

R. N. Manchester et al. The Parkes Pulsar Timing Array Project.Publications of the Astron. Soc. of Australia, 30:e017, January 2013

work page 2013
[53]

Champion

Michael Kramer and David J. Champion. The European Pulsar Timing Array and the Large European Array for Pulsars.Classical and Quantum Gravity, 30(22):224009, November 2013

work page 2013
[54]

Desvignes et al

G. Desvignes et al. High-precision timing of 42 millisec- ond pulsars with the European Pulsar Timing Array. Monthly Notices of the RAS, 458(3):3341–3380, May 2016

work page 2016
[55]

Precision pulsar timing with the ORT and the GMRT and its applications in pulsar astrophysics.Journal of Astrophysics and Astronomy, 39(4):51, August 2018

Bhal Chandra Joshi et al. Precision pulsar timing with the ORT and the GMRT and its applications in pulsar astrophysics.Journal of Astrophysics and Astronomy, 39(4):51, August 2018

work page 2018
[56]

Hobbs et al

G. Hobbs et al. The International Pulsar Timing Ar- ray project: using pulsars as a gravitational wave de- tector.Classical and Quantum Gravity, 27(8):084013, April 2010

work page 2010
[57]

J. P. W. Verbiest et al. The International Pulsar Timing Array: First data release.Monthly Notices of the RAS, 458(2):1267–1288, May 2016

work page 2016
[58]

J. M. Cordes, M. Kramer, T. J. W. Lazio, B. W. Stap- pers, D. C. Backer, and S. Johnston. Pulsars as tools for fundamental physics & astrophysics.New Astron- omy Review, 48(11-12):1413–1438, December 2004

work page 2004
[59]

T. J. W. Lazio. The Square Kilometre Array pul- sar timing array.Classical and Quantum Gravity, 30(22):224011, November 2013

work page 2013
[60]

P. E. Dewdney, P. J. Hall, R. T. Schilizzi, and T. J. L. W. Lazio. The Square Kilometre Array.IEEE Proceedings, 97(8):1482–1496, August 2009

work page 2009
[61]

The five-hundred-meter aper- ture spherical radio telescope (FAST) project

Rendong Nan and Di Li. The five-hundred-meter aper- ture spherical radio telescope (FAST) project. InMa- terials Science and Engineering Conference Series, vol- ume 44 ofMaterials Science and Engineering Confer- ence Series, page 012022. IOP, April 2013

work page 2013
[62]

Renzini, Boris Goncharov, Alexander C

Arianna I. Renzini, Boris Goncharov, Alexander C. Jenkins, and Patrick M. Meyers. Stochastic Gravitational-Wave Backgrounds: Current Detection Efforts and Future Prospects.Galaxies, 10(1):34, Febru- ary 2022

work page 2022
[63]

Tania Regimbau, Thomas Dent, Walter Del Pozzo, Ste- 25 fanos Giampanis, Tjonnie G. F. Li, Craig Robinson, Chris Van Den Broeck, Duncan Meacher, Carl Ro- driguez, B. S. Sathyaprakash, and Katarzyna W´ ojcik. Mock data challenge for the Einstein Gravitational- Wave Telescope.Physical Review D, 86(12):122001, De- cember 2012

work page 2012
[64]

Tania Regimbau, Duncan Meacher, and Michael Cough- lin. Second Einstein Telescope mock science challenge: Detection of the gravitational-wave stochastic back- ground from compact binary coalescences.Physical Re- view D, 89(8):084046, April 2014

work page 2014
[65]

SWIGLAL: Python and Octave interfaces to the LALSuite gravitational-wave data analysis li- braries.SoftwareX, 12:100634, July 2020

Karl Wette. SWIGLAL: Python and Octave interfaces to the LALSuite gravitational-wave data analysis li- braries.SoftwareX, 12:100634, July 2020

work page 2020
[66]

Lasky, Colm Talbot, Kendall Ackley, Sylvia Biscoveanu, Qi Chu, Atul Divarkala, Paul J

Gregory Ashton, Moritz Huebner, Paul D. Lasky, Colm Talbot, Kendall Ackley, Sylvia Biscoveanu, Qi Chu, Atul Divarkala, Paul J. Easter, Boris Goncharov, Fran- cisco Hernandez Vivanco, Jan Harms, Marcus E. Lower, Grant D. Meadors, Denyz Melchor, Ethan Payne, Matthew D. Pitkin, Jade Powell, Nikhil Sarin, and Rory J. E. Smith. Bilby: A user-friendly bayesian ...

work page 2019
[67]

LISACode: A scientific simulator of LISA.Physical Review D, 77(2):023002, January 2008

Antoine Petiteau, G´ erard Auger, Hubert Halloin, Olivier Jeannin, Eric Plagnol, Sophie Pireaux, Tania Regimbau, and Jean-Yves Vinet. LISACode: A scientific simulator of LISA.Physical Review D, 77(2):023002, January 2008

work page 2008
[68]

Ellis, Michele Vallisneri, Stephen R

Justin A. Ellis, Michele Vallisneri, Stephen R. Tay- lor, and Paul T. Baker. Enterprise: Enhanced numer- ical toolbox enabling a robust pulsar inference suite, September 2020

work page 2020
[69]

G. B. Hobbs, R. T. Edwards, and R. N. Manch- ester. TEMPO2, a new pulsar-timing package - I. An overview.Monthly Notices of the RAS, 369(2):655–672, June 2006

work page 2006
[70]

Ray, Anne Archibald, Matthew Kerr, Ross J

Jing Luo, Scott Ransom, Paul Demorest, Paul S. Ray, Anne Archibald, Matthew Kerr, Ross J. Jennings, Mat- teo Bachetti, Rutger van Haasteren, Chloe A. Cham- pagne, Jonathan Colen, Camryn Phillips, Josef Zimmer- man, Kevin Stovall, Michael T. Lam, and Fredrick A. Jenet. PINT: A Modern Software Package for Pulsar Timing.Astrophysical Journal, 911(1):45, April 2021

work page 2021
[71]

Figueroa, and Bryan Zald´ ıvar

Androniki Dimitriou, Daniel G. Figueroa, and Bryan Zald´ ıvar. Fast likelihood-free reconstruction of gravi- tational wave backgrounds.Journal of Cosmology and Astroparticle Physics, 2024(9):032, September 2024

work page 2024
[72]

Jenk- ins, Sabino Matarrese, Alvise Raccanelli, Tania Regim- bau, Angelo Ricciardone, and Mairi Sakellariadou

Nicola Bellomo, Daniele Bertacca, Alexander C. Jenk- ins, Sabino Matarrese, Alvise Raccanelli, Tania Regim- bau, Angelo Ricciardone, and Mairi Sakellariadou. CLASS GWB: robust modeling of the astrophysical gravitational wave background anisotropies.Journal of Cosmology and Astroparticle Physics, 2022(6):030, June 2022

work page 2022
[73]

The Gravitational Wave Universe Tool- box

Shu-Xu Yi et al. The Gravitational Wave Universe Tool- box. A software package to simulate observations of the gravitational wave universe with different detectors.As- tronomy and Astrophysics, 663:A155, July 2022

work page 2022
[74]

Mundim, Christian D

Frank L¨ offler, Joshua Faber, Eloisa Bentivegna, Tanja Bode, Peter Diener, Roland Haas, Ian Hinder, Bruno C. Mundim, Christian D. Ott, Erik Schnetter, Gabrielle Allen, Manuela Campanelli, and Pablo Laguna. The Einstein Toolkit: a community computational infras- tructure for relativistic astrophysics.Classical and Quantum Gravity, 29(11):115001, June 2012

work page 2012
[75]

B. F. Schutz. Determining the Hubble constant from gravitational wave observations.Nature, 323(6086):310– 311, September 1986

work page 1986
[76]

Holz and Scott A

Daniel E. Holz and Scott A. Hughes. Using Gravitational-Wave Standard Sirens.Astrophysical Journal, 629(1):15–22, August 2005

work page 2005
[77]

B. P. Abbott et al. A gravitational-wave standard siren measurement of the Hubble constant.Nature, 551(7678):85–88, November 2017

work page 2017
[78]

Gravitational wave standard sirens and cosmological parameter measurement.Science China Physics, Mechanics, and Astronomy, 62(11):110431, November 2019

Xin Zhang. Gravitational wave standard sirens and cosmological parameter measurement.Science China Physics, Mechanics, and Astronomy, 62(11):110431, November 2019

work page 2019
[79]

Xuan-Neng Zhang, Ling-Feng Wang, Jing-Fei Zhang, and Xin Zhang. Improving cosmological parameter es- timation with the future gravitational-wave standard siren observation from the Einstein Telescope.Physi- cal Review D, 99(6):063510, March 2019

work page 2019
[80]

Brady, Hsin-Yu Chen, Will M

Rachel Gray, Ignacio Maga˜ na Hernandez, Hong Qi, Ankan Sur, Patrick R. Brady, Hsin-Yu Chen, Will M. Farr, Maya Fishbach, Jonathan R. Gair, Archis- man Ghosh, Daniel E. Holz, Simone Mastrogiovanni, Christopher Messenger, Dani` ele A. Steer, and John Veitch. Cosmological inference using gravitational wave standard sirens: A mock data analysis.Physical Revi...

work page 2020

Showing first 80 references.