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REVIEW 2 major objections 7 minor 67 references

Searches for stochastic gravitational-wave backgrounds

T0 review · 2 major / 7 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read A Bayesian search could cut detection of the black-hole background from roughly 40 months to about a day.

desk verdict Useful lecture notes with a clean pedagogical arc, but the flashy '~1 day' BBH detection projection in §9.3 is built on a mismatched baseline and should be corrected before the notes are used as a reference. read the letter →

arxiv 1909.00269 v2 pith:ISA6W3P2 submitted 2019-08-31 gr-qc astro-ph.IM

Joseph D. Romano This is my paper · ORCID
classification gr-qcastro-ph.IM
keywords stochasticgravitational-wavebackgroundcross-correlationsearchoverlapfunctionBayesianinferencebinaryblackholemergerspopcorndataanalysispulsartimingarrays
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

These lecture notes explain how stochastic gravitational-wave backgrounds are searched for, and argue that the standard cross-correlation method is not the best tool for one important target: the popcorn-like background of stellar-mass black-hole mergers. The notes present a Bayesian mixture search, proposed in [47], which divides data into short segments and asks of each segment whether it contains a chirp or just noise. Simulations cited in the notes show this method reduces the time to detect the black-hole-merger background by roughly a factor of 1000, from about 40 months to about one day at design sensitivity. If that holds, the first detection of a stochastic gravitational-wave background could come almost immediately once advanced ground-based detectors reach design performance, rather than after years of integration.

What carries the argument

The load-bearing object is the mixture signal prior $p(h|\xi,\lambda)=\xi\,\delta\big(h-\mathrm{chirp}(\lambda)\big)+(1-\xi)\delta(h)$, combined with a segmentation of the data into short (e.g., 4-second) intervals that contain at most one merger. Marginalizing the per-segment likelihood over the chirp parameters leaves a likelihood that is linear in the merger-fraction parameter $\xi$; multiplying these per-segment likelihoods and applying Bayes' theorem yields a posterior for $\xi$. This structure lets the search use noise-only segments as evidence and restricts the search volume to chirp-like tracks. By contrast, the standard method's optimal filter is $\tilde{Q}(f)\propto \Gamma_{12}(f)H(f)/(P_1(f)P_2(f))$, tuned to a stationary Gaussian background.

What would settle it

Inject simulated design-sensitivity data where the merger rate is high enough that a 4-second segment sometimes contains two mergers, run the mixture search, and check whether the time to 3-sigma detection still falls by roughly a factor of 1000; the assumption of at most one chirp per segment is what fails first.

Watch

Extended reading notes

Core claim

The notes' central claim is that a background consisting of discrete, non-overlapping merger events is better searched for by a likelihood that models each short data segment as either a known chirp waveform or pure noise, rather than by the usual cross-correlation statistic that assumes a stationary Gaussian background. After segmenting the data and marginalizing over chirp parameters, the only remaining parameter is the fraction of segments containing a merger, and the full likelihood is the product of per-segment mixture likelihoods. In toy simulations, this Bayesian search achieves a signal-to-noise ratio of 15.3 versus 8.9 for standard cross-correlation on the same data, and the cited simulations [47] indicate a factor-of-approximately-1000 reduction in time to detection. The notes therefore conclude that at design sensitivity the black-hole-merger background, previously expected to require 40 months of observation, could be detected in roughly one day.

Load-bearing premise

The method assumes that each short segment contains at most one black-hole-merger signal and that the chirp waveform shape and duration are known exactly for every segment.

Editorial extensions

If this is right

  • A 3-sigma detection of the stellar-mass black-hole-merger background could come after roughly a day of design-sensitivity observation, instead of the 40 months predicted for cross-correlation.
  • Because the background is persistent, a claimed detection could be confirmed over time by the same search as the signal-to-noise ratio grows with observation time.
  • The search measures the merger-fraction parameter directly, so data from segments with no merger still tighten the posterior rather than simply diluting the average correlation.
  • The method can use two detectors to reject glitches, so the advantage of the mixture likelihood does not come at the cost of giving up instrumental-artifact rejection.

Reading between the lines

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

  • The notes do not draw the race implication, but if the factor-of-1000 timing holds, ground-based interferometers might announce an astrophysical stochastic background before pulsar timing arrays announce the supermassive-black-hole background, despite the decades of pulsar-timing limits.
  • The success of the mixture prior suggests a general principle: for backgrounds made of rare, well-modeled transients, detection time is set by the event rate and waveform-model accuracy, not by total background power; this could be exported to searches for subthreshold bursts in other detectors.
  • A practical test the notes do not perform would be to replace the idealized known-chirp prior with a waveform bank or an explicit model of waveform mismatch, and quantify how the factor-of-1000 advantage degrades as template error grows.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 7 minor

Summary. These lecture notes provide a pedagogical introduction to searches for stochastic gravitational-wave backgrounds (GWBs). Part I covers the mathematical characterization of GWBs, including the plane-wave expansion, ensemble averages, and the energy-density spectrum, and develops the cross-correlation method with optimal filtering for simple examples. Part II addresses non-trivial detector response, overlap functions for interferometers, pulsar timing arrays, and electric dipole antennas, and presents a Bayesian mixture method for detecting the popcorn-like stellar-mass binary black-hole (BBH) background. The notes include a toy simulation of the Bayesian method, a comparison with the standard cross-correlation search, and a central quantitative claim that the Bayesian method reduces the time to detection by roughly a factor of 1000, from 40 months to about one day at design sensitivity. The paper is written as lecture notes with appended exercises.

Significance. The pedagogical value of these notes is high: they present standard material in a clear, self-contained way, with derivations sketched and consolidated in an appendix, and with code and simulated data publicly available. The exposition of the Bayesian mixture search for the BBH background is a useful entry point to [47]. However, the paper is a review rather than a new research contribution, and its significance depends on the accuracy of its attributions. The factor-of-1000 speedup claim, if correct, would be a strong motivation for early detection of the BBH background; as presented, the claim rests on an unsupported conversion of the 40-month total-background estimate into a one-day projection for the BBH-only background, which requires correction.

major comments (2)
  1. [Section 9.3, Figure 3] The sentence '40 months of observation to detect the BBH background at the 3-σ level using the standard cross-correlation method (see Figure 3)' misidentifies the baseline: Figure 3 and the 40-month estimate come from [4] and refer to the median total BNS+BBH background, not the BBH component alone. Since the BBH-only contribution is smaller, its cross-correlation detection time at design sensitivity is longer than 40 months, so the conversion 40 months / 1000 ≈ 1 day is not a valid arithmetic shortcut. The claim as stated is internally inconsistent with Section 1.2, which correctly describes the 40-month estimate for the combined background.
  2. [Sections 9.2 and 9.3, Eq. (9.1)] The factor-of-1000 reduction in time to detection is attributed to [47] and is not derived or verified in these notes. The toy simulation in Section 9.2 assumes a known chirp shape and duration and marginalizes only over amplitude and arrival time, so the quoted speedup is conditional on that idealized model. The notes do not provide the BBH-only cross-correlation baseline or an analysis of how the speedup depends on segment length, merger rate, or waveform systematics; therefore the projection of 'about one day' at design sensitivity is not supported without additional calculation, and Section 10's concluding statement should be correspondingly qualified.
minor comments (7)
  1. [Section 10] The word 'stochatic' should be 'stochastic'.
  2. [Section 5.1] The word 'ampltitude' should be 'amplitude'; also, 'agree to 3.5%' should be 'agree to within 3.5%' (or 'disagree by 3.5%').
  3. [Section 6.3.2] The words 'reponse' and 'senstive' should be 'response' and 'sensitive', respectively.
  4. [Section 8.3] The word 'probabilites' should be 'probabilities'.
  5. [Section 1.2 and Figure 2 caption] The text gives the BBH in-band duration as roughly 1 s, while the reprinted caption from [4] says 14 s on average; please reconcile these definitions or clarify that they refer to different frequency bands.
  6. [Figure 2 caption] The caption in the manuscript includes extraneous text from the source paper; please rewrite it to clearly credit [4] and remove unrelated content.
  7. [Section 9.3] The phrase 'converted the signal+noise to noise-only Bayes factor B10(d) to a signal-to-noise ratio using (8.19) and (8.9)' is confusing; please specify that B10(d) is the Bayes factor for model M1 (signal+noise) versus M0 (noise-only) and that Eq. (8.19) is applied in the informative-data limit.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the lecture notes are a review whose Section 9 speedup claim is cited to Smith and Thrane, and the foundational methods are derived or standard background material.

full rationale

The paper is a review/lecture-note introduction, not a self-contained derivation of a new result. The cross-correlation formalism in Sections 4-7 is derived from stated assumptions (e.g., the optimal filter in Eq. (4.20) is obtained by maximizing SNR, with the derivation assigned to Exercise A.4), and the standard references [9, 41] are background citations, not load-bearing self-citations that force the paper's conclusions. The Bayesian mixture search of Section 9 is explicitly attributed to Smith and Thrane [47], including the mixture prior (9.1), the segmented likelihood (9.3), and the quoted factor-of-1000 speedup; the notes do not claim to derive that factor. The toy simulation in Section 9.2 is an injection-recovery exercise that reports a posterior peaked at the injected value xi=0.25; it is not a fitted parameter being relabeled as a prediction. The only questionable step is the end of Section 9.3, where '40 months of observation to detect the BBH background' refers to a 40-month SNR=3 estimate that, per the caption of Figure 3 taken from [4], is for the median total (BNS+BBH) background, not the BBH-only component. This is an arithmetic/attribution concern about the extrapolation rather than a circular reduction, because the 40-month number and the factor-1000 come from different external sources and the paper does not construct one from the other by definition. Accordingly, no circularity step is exhibited, and the score is 0.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

The notes inherit standard assumptions of general relativity and stochastic data analysis from the cited literature. These assumptions are stated in the relevant sections but are not the paper's own inventions.

assumptions (4)
  • domain assumption Gravitational waves are transverse-traceless perturbations of spacetime, described by the plane-wave expansion in Eq. (3.1).
    Standard general relativity background used throughout Section 3 and all subsequent calculations.
  • domain assumption The stochastic background is Gaussian, stationary, isotropic, and unpolarized in the basic formalism (Section 3.2, Eq. 3.5).
    The basic cross-correlation formalism is derived under these assumptions.
  • domain assumption Detector noise is uncorrelated between detectors (Section 4.1).
    The cross-correlation estimator uses the vanishing of the noise cross-correlation to isolate the shared signal.
  • domain assumption For the Bayesian BBH search, each 4-second data segment contains at most one BBH merger signal, and the chirp waveform shape and duration are known (Sections 9.1 and 9.2).
    The mixture signal prior in Eq. (9.1) encodes this assumption, and it underlies the factor-1000 time-to-detection gain reported from the Smith and Thrane simulation.

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Cite this review

Pith. "Pith review of Searches for stochastic gravitational-wave backgrounds." pith.science (2026). https://pith.science/paper/ISA6W3P2

@misc{pith2026190900269,
  author       = {Pith},
  title        = {Pith review of: Searches for stochastic gravitational-wave backgrounds},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ISA6W3P2}},
  note         = {Machine review of arXiv:1909.00269}
}
read the original abstract

These lecture notes provide a brief introduction to methods used to search for a stochastic background of gravitational radiation -- a superposition of gravitational-wave signals that are either too weak or too numerous to individually detect. The focus of these notes is on relevant data analysis techniques, not on the particular astrophysical or cosmological sources that are responsible for producing the background. The lecture notes are divided into two main parts: (i) an overview, consisting of a description of different types of gravitational-wave backgrounds and an introduction to the method of cross-correlating data from multiple detectors, which can be used to extract the signal from the noise; (ii) details, extending the previous discussion to non-trivial detector response, non-trivial overlap functions, and a recently proposed Bayesian method to search for the gravitational-wave background produced by stellar-mass binary black hole mergers throughout the universe. Suggested exercises for the reader are given throughout the text, and compiled in an appendix.

Figures

Figures reproduced from arXiv: 1909.00269 by the authors.

Figure 1
Figure 1. Skymap of ∆T /T0 for the cosmic microwave background radiation (https://www. cosmos.esa.int/documents/387566/425793/2015_SMICA_CMB/). of the temperature fluctuations in the cosmic microwave background (CMB) blackbody radiation, ∆T /T0, relative to the T0 = 2.73 K isotropic component [36, 16]. (The dipole contribution due to our motion with respect to the cosmic rest frame has also been subtracted out.) The CMB is a … view at source ↗
Figure 2
Figure 2. FIG. 2. We present a simulated time series of duration 10 gpg ) [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 4
Figure 4. Detectors and potential sources of GWBs across the GW spectrum. Note that the GWB [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figures from the paper (17 more)
Figure 6
Figure 6. Figure 6: Simulated time-domain output of a particular combination of the LISA data over a 2-year [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
Figure 7
Figure 7. Figure 7: Simulated time-domain data (including the signals for an individual BNS merger and [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]
Figure 63
Figure 63. Figure 63: Graphical representation of the six di Graphical representation of the six di↵erent pola [PITH_FULL_IMAGE:figures/full_fig_p011_63.png]
Figure 9
Figure 9. Figure 9: Coordinate system and unit vectors used in the plane-wave expansion of a GWB. [PITH_FULL_IMAGE:figures/full_fig_p012_9.png]
Figure 10
Figure 10. Figure 10: Two masses m1, m2 in orbit around their common of mass. of the relative separation, total mass, and reduced mass of the system. In terms of these quantities, Kepler’s third law and the total orbital energy of the system can be written as ω 2 r 3 = GM , Eorb = − GMµ 2r…
Figure 11
Figure 11. Figure 11: Simulated time-domain data for the three different cases discussed in the main text: [PITH_FULL_IMAGE:figures/full_fig_p021_11.png]
Figure 16
Figure 16. Figure 16: Same as Figure 15 but including the pulsar term and taking [PITH_FULL_IMAGE:figures/full_fig_p027_16.png]
Figure 3
Figure 3. Figure 3: FIG. 3. The surface of the earth (15 [PITH_FULL_IMAGE:figures/full_fig_p031_3.png]
Figure 21
Figure 21. Figure 21: Graphical representation of the integrand of the (Earth-only) overlap function for pulsar [PITH_FULL_IMAGE:figures/full_fig_p033_21.png]
Figure 22
Figure 22. Figure 22: Geometry for calculating the overlap function for a pair of short, colocated electric [PITH_FULL_IMAGE:figures/full_fig_p033_22.png]
Figure 23
Figure 23. Figure 23: Schematic representation of Bayes’ theorem. [PITH_FULL_IMAGE:figures/full_fig_p037_23.png]
Figure 24
Figure 24. Figure 24: Schematic representation of the likelihood function [PITH_FULL_IMAGE:figures/full_fig_p038_24.png]
Figure 25
Figure 25. Figure 25: Different signal priors for h(t). Panel (a): Determinsitic (sinusoid) signal prior. Panel (b): Stochastic signal prior. For the stochastic signal prior, h(t) values are drawn from a Gaussian distribution with variance Sh. 39 [PITH_FULL_IMAGE:figures/full_fig_p039_25.png]
Figure 27
Figure 27. Figure 27: Simulated BBH and BNS data in two coincident and coaligned detectors. The confusion [PITH_FULL_IMAGE:figures/full_fig_p042_27.png]
Figure 28
Figure 28. Figure 28: The cumulative posterior distribution for [PITH_FULL_IMAGE:figures/full_fig_p043_28.png]
Figure 29
Figure 29. Figure 29: Posterior distributions for ξ for the first 16 segments (first 4 sec) of data. Since the injected signals were relatively large, the posteriors having positive (negative) slope correspond to the segments having (not having) an injected BBH chirp signal. 43 [PITH_FULL…
Figure 30
Figure 30. Figure 30: Cumulative posterior distributions for ξ, obtained by combining the likelihood functions for the first n segments of data. The bottom-rightmost plot is also shown in [PITH_FULL_IMAGE:figures/full_fig_p044_30.png]

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Reference graph

Works this paper leans on

67 extracted references · 35 canonical work pages

  1. [4]

    GW170817: Implications for the Stochastic Gravitational-Wave Back- ground from Compact Binary Coalescences

    Abbott, B. P. et al., “GW170817: Implications for the Stochastic Gravitational-Wave Back- ground from Compact Binary Coalescences”, Phys. Rev. Lett., 120(9), 091101 (Mar 2018). [DOI], [ADS], [arXiv:1710.05837 [gr-qc]]

    arXiv 2018

  2. [47]

    Optimal Search for an Astrophysical Gravitational-Wave Background

    Smith, Rory and Thrane, Eric, “Optimal Search for an Astrophysical Gravitational-Wave Background”, Phys. Rev. X , 8, 021019 (Apr 2018). [DOI]URL: https://link.aps.org/doi/10.1103/PhysRevX.8.021019

    doi:10.1103/physrevx.8.021019 2018

  3. [1]

    GW150914: Implications for the stochastic gravitational wave background from binary black holes

    Abbott, B. P. et al. (Virgo, LIGO Scientific), “GW150914: Implications for the stochastic gravitational wave background from binary black holes”, Phys. Rev. Lett. , 116(13), 131102 (2016). [DOI], [arXiv:1602.03847 [gr-qc]]

    arXiv 2016

  4. [2]

    Observation of Gravitational Waves from a Binary Black Hole Merger

    Abbott, B. P. et al., “Observation of Gravitational Waves from a Binary Black Hole Merger”, Physical Review Letters , 116(6), 061102 (February 2016). [DOI], [ADS], [arXiv:1602.03837 [gr- qc]]

    arXiv 2016

  5. [3]

    GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral

    Abbott, B. P. et al., “GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral”, Phys. Rev. Lett., 119(16), 161101 (Oct 2017). [DOI], [ADS], [arXiv:1710.05832 [gr-qc]]

    arXiv 2017

  6. [5]

    Discriminating between a Stochastic Gravita- tional Wave Background and Instrument Noise

    Adams, Matthew R. and Cornish, Neil J., “Discriminating between a Stochastic Gravita- tional Wave Background and Instrument Noise”, Phys. Rev. , D82, 022002 (2010). [DOI], [arXiv:1002.1291 [gr-qc]]

    arXiv 2010

  7. [6]

    Detecting a Stochastic Gravitational Wave Back- ground in the presence of a Galactic Foreground and Instrument Noise

    Adams, Matthew R. and Cornish, Neil J., “Detecting a Stochastic Gravitational Wave Back- ground in the presence of a Galactic Foreground and Instrument Noise”, Phys. Rev., D89(2), 022001 (2014). [DOI], [arXiv:1307.4116 [gr-qc]]

    arXiv 2014

  8. [7]

    The Stochastic Gravity-Wave Background: Sources and Detection

    Allen, B., “The Stochastic Gravity-Wave Background: Sources and Detection”, in Marck, J.- A. and Lasota, J.-P., eds., Relativistic Gravitation and Gravitational Radiation, p. 373, (1997). [ADS], [gr-qc/9604033]

    arXiv 1997

Show all 67 references
  1. [8]

    Detection of anisotropies in the gravitational-wave stochastic background

    Allen, B. and Ottewill, A. C., “Detection of anisotropies in the gravitational-wave stochastic background”, Phys. Rev. D, 56, 545–563 (July 1997). [DOI], [ADS], [gr-qc/9607068]

    1997 arXiv

  2. [9]

    Detecting a stochastic background of gravitational radiation: Signal processing strategies and sensitivities

    Allen, Bruce and Romano, Joseph D., “Detecting a stochastic background of gravitational radiation: Signal processing strategies and sensitivities”, Phys. Rev. D, 59(10), 102001 (May 1999). [DOI], [ADS], [arXiv:gr-qc/9710117 [gr-qc]]

    1999 arXiv

  3. [10]

    Confusion noise level due to galactic and extragalactic binaries

    Bender, P. L. and Hils, D., “Confusion noise level due to galactic and extragalactic binaries”, Classical and Quantum Gravity , 14, 1439–1444 (June 1997). [DOI], [ADS]

    1997

  4. [11]

    Stochastic backgrounds in alternative theories of gravity: Overlap reduction functions for pulsar timing arrays

    Chamberlin, S. J. and Siemens, X., “Stochastic backgrounds in alternative theories of gravity: Overlap reduction functions for pulsar timing arrays”, Phys. Rev. D, 85(8), 082001 (April 2012). [DOI], [ADS], [arXiv:1111.5661 [astro-ph.HE]]

    2012 arXiv

  5. [12]

    Optimal detection strategies for measuring the stochastic gravitational ra- diation background with laser interferometric antennas

    Christensen, N., “Optimal detection strategies for measuring the stochastic gravitational ra- diation background with laser interferometric antennas”, Phys. Rev. D, 55, 448–454 (January 1997). [DOI], [ADS]

    1997

  6. [13]

    Subtraction of correlated noise in global networks of gravitational-wave interferometers

    Coughlin, Michael W. et al., “Subtraction of correlated noise in global networks of gravitational-wave interferometers” (2016). [arXiv:1606.01011 [gr-qc]]. 51

    2016 arXiv

  7. [14]

    Anisotropy of the astrophysical grav- itational wave background: Analytic expression of the angular power spectrum and correla- tion with cosmological observations

    Cusin, Giulia, Pitrou, Cyril and Uzan, Jean-Philippe, “Anisotropy of the astrophysical grav- itational wave background: Analytic expression of the angular power spectrum and correla- tion with cosmological observations”, Phys. Rev. D, 96(10), 103019 (Nov 2017). [DOI], [ADS], [...

    2017 arXiv

  8. [15]

    Pulsar timing measurements and the search for gravitational waves

    Detweiler, S., “Pulsar timing measurements and the search for gravitational waves”, ApJ, 234, 1100–1104 (December 1979). [DOI], [ADS]

    1979

  9. [16]

    Cosmic Black-Body Radia- tion

    Dicke, R. H., Peebles, P. J. E., Roll, P. G. and Wilkinson, D. T., “Cosmic Black-Body Radia- tion.”, ApJ, 142, 414–419 (July 1965). [DOI], [ADS]

    1965

  10. [17]

    Time delay analysis of LISA gravi- tational wave data: Elimination of spacecraft motion effects

    Estabrook, F. B., Tinto, Massimo and Armstrong, J. W., “Time delay analysis of LISA gravi- tational wave data: Elimination of spacecraft motion effects”, Phys. Rev., D62, 042002 (2000). [DOI]

    2000

  11. [18]

    Sensitivity of the Laser Interferometer Gravitational Wave Observatory to a stochastic background, and its dependence on the detector orientations

    Flanagan, ´Eanna ´E., “Sensitivity of the Laser Interferometer Gravitational Wave Observatory to a stochastic background, and its dependence on the detector orientations”, Phys. Rev. D, 48, 2389 (1993)

    1993

  12. [19]

    Mapping gravitational- wave backgrounds using methods from CMB analysis: Application to pulsar timing arrays

    Gair, J., Romano, J. D., Taylor, S. and Mingarelli, C. M. F., “Mapping gravitational- wave backgrounds using methods from CMB analysis: Application to pulsar timing arrays”, Phys. Rev. D, 90(8), 082001 (October 2014). [DOI], [ADS], [arXiv:1406.4664 [gr-qc]]

    2014 arXiv

  13. [20]

    Mapping gravitational-wave backgrounds of arbitrary polarisation using pulsar timing arrays

    Gair, J. R., Romano, J. D. and Taylor, S. R., “Mapping gravitational-wave backgrounds of arbitrary polarisation using pulsar timing arrays”, Phys. Rev. D, 92(10), 102003 (November 2015). [DOI], [ADS], [arXiv:1506.08668 [gr-qc]]

    2015 arXiv

  14. [21]

    Gregory, Phil C., Bayesian Logical Data Analysis for the Physical Sciences: A Comparative Approach with Mathematica Support, (Cambridge University Press, Cambridge, UK, New York, NY, 2005)

    2005

  15. [22]

    Primordial gravitons and possibility of their observation

    Grishchuk, L. P., “Primordial gravitons and possibility of their observation”, Journal of Ex- perimental and Theoretical Physics Letters , 23, 293 (1976)

    1976

  16. [23]

    Hartle, James B., Gravity: An Introduction to Einstein’s General Relativity , (Addison Wesley, 2002)

    2002

  17. [24]

    Upper limits on the istotropic gravitational radiation background from pulsar timing analysis

    Hellings, R. W. and Downs, G. S., “Upper limits on the istotropic gravitational radiation background from pulsar timing analysis”, ApJ, 265, L39–L42 (1983)

    1983

  18. [25]

    Helstrom, Carl W., Statistical Theory of Signal Detection, 2nd edition , (Pergamon Press, Oxford, London, Edinburgh, New York, Toronto, Sydney, Paris, Braunschweig, 1968)

    1968

  19. [26]

    Understanding the gravitational-wave Hellings and Downs curve for pulsar timing arrays in terms of sound and electromagnetic waves

    Jenet, F. A. and Romano, J. D., “Understanding the gravitational-wave Hellings and Downs curve for pulsar timing arrays in terms of sound and electromagnetic waves”,American Journal of Physics, 83, 635–645 (July 2015). [DOI], [ADS], [arXiv:1412.1142 [gr-qc]]

    2015 arXiv

  20. [27]

    Anisotropies in the stochastic gravitational- wave background: Formalism and the cosmic string case

    Jenkins, Alexander C. and Sakellariadou, Mairi, “Anisotropies in the stochastic gravitational- wave background: Formalism and the cosmic string case”, Phys. Rev. D, 98(6), 063509 (Sep 2018). [DOI], [ADS], [arXiv:1802.06046 [astro-ph.CO]]

    2018 arXiv

  21. [28]

    The Primordial Inflation Explorer (PIXIE): a nulling polarimeter for cos- mic microwave background observations

    Kogut, A. et al., “The Primordial Inflation Explorer (PIXIE): a nulling polarimeter for cos- mic microwave background observations”, Journal of Cosmology and Astro-Particle Physics , 2011(7), 025 (Jul 2011). [DOI], [ADS], [arXiv:1105.2044 [astro-ph.CO]]. 52

    2011 arXiv

  22. [29]

    Kolb, E. W. and Turner, M., The Early Universe , (Addison Wesley, 1990)

    1990

  23. [30]

    Detecting Gravitational Waves of Alternative Theories Using Pulsar Timing

    Lee, K., Jenet, F. and Price, R., “Detecting Gravitational Waves of Alternative Theories Using Pulsar Timing”, in American Astronomical Society Meeting Abstracts , Bulletin of the American Astronomical Society, 39, 102.07, (December 2007). [ADS]

    2007

  24. [31]

    Gravitational wave experiments and early universe cosmology

    Maggiore, M., “Gravitational wave experiments and early universe cosmology”, Phys. Rep., 331, 283–367 (July 2000). [DOI], [ADS], [gr-qc/9909001]

    2000 arXiv

  25. [32]

    The BOOMERanG experiment and the curvature of the universe

    Masi, S., “The BOOMERanG experiment and the curvature of the universe”, Progress in Particle and Nuclear Physics , 48(1), 243–261 (Jan 2002). [DOI], [ADS], [arXiv:astro-ph/0201137 [astro-ph]]

    2002 arXiv

  26. [33]

    Characterizing gravitational wave stochastic background anisotropy with pulsar timing arrays

    Mingarelli, C. M. F., Sidery, T., Mandel, I. and Vecchio, A., “Characterizing gravitational wave stochastic background anisotropy with pulsar timing arrays”, Phys. Rev. D, 88(6), 062005 (September 2013). [DOI], [ADS], [arXiv:1306.5394 [astro-ph.HE]]

    2013 arXiv

  27. [34]

    W., Thorne, K

    Misner, C. W., Thorne, K. S. and Wheeler, J. A., Gravitation, (W.H. Freeman and Company, San Francisco, 1973)

    1973

  28. [35]

    Component Separation of a Isotropic Gravitational Wave Background

    Parida, Abhishek, Mitra, Sanjit and Jhingan, Sanjay, “Component Separation of a Isotropic Gravitational Wave Background”, Journal of Cosmology and Astroparticle Physics , 2016 (10 2015). [DOI]

    2016

  29. [36]

    A Measurement of Excess Antenna Temperature at 4080 Mc/s

    Penzias, A. A. and Wilson, R. W., “A Measurement of Excess Antenna Temperature at 4080 Mc/s.”, ApJ, 142, 419–421 (July 1965). [DOI], [ADS]

    1965

  30. [37]

    Gravitational Radiation from Point Masses in a Keplerian Orbit

    Peters, P. C. and Mathews, J., “Gravitational Radiation from Point Masses in a Keplerian Orbit”, Phys. Rev., 131, 435–440 (Jul 1963). [DOI]URL: https://link.aps.org/doi/10.1103/PhysRev.131.435

    1963 doi

  31. [38]

    A Practical Theorem on Gravitational Wave Backgrounds

    Phinney, E. S., “A Practical Theorem on Gravitational Wave Backgrounds”, arXiv e-prints , astro-ph/0108028 (Aug 2001). [ADS], [arXiv:astro-ph/0108028 [astro-ph]]

    2001 arXiv

  32. [39]

    Planck 2018 results. VII. Isotropy and Statistics of the CMB

    Planck Collaboration et al., “Planck 2018 results. VII. Isotropy and Statistics of the CMB”, arXiv e-prints, arXiv:1906.02552 (Jun 2019). [ADS], [arXiv:1906.02552 [astro-ph.CO]]

    2018 arXiv

  33. [40]

    The LISA optimal sensitivity

    Prince, Thomas A., Tinto, Massimo, Larson, Shane L. and Armstrong, J. W., “The LISA optimal sensitivity”, Phys. Rev., D66, 122002 (2002). [DOI], [arXiv:gr-qc/0209039 [gr-qc]]

    2002 arXiv

  34. [41]

    Detection methods for stochastic gravitational- wave backgrounds: a unified treatment

    Romano, Joseph D. and Cornish, Neil. J., “Detection methods for stochastic gravitational- wave backgrounds: a unified treatment”, Living Reviews in Relativity, 20(1), 2 (Apr 04, 2017). [DOI]URL: https://doi.org/10.1007/s41114-017-0004-1

    2017 doi

  35. [42]

    Expected properties of the first gravitational wave signal detected with pulsar timing arrays

    Rosado, Pablo A., Sesana, Alberto and Gair, Jonathan, “Expected properties of the first gravitational wave signal detected with pulsar timing arrays”, Mon. Not. Roy. Astron. Soc. , 451(3), 2417–2433 (2015). [DOI], [arXiv:1503.04803 [astro-ph.HE]]

    2015 arXiv

  36. [43]

    Ryden, B., Introduction to cosmology, (Cambridge University Press, 2016)URL: http://www.cambridge.org/de/academic/subjects/astronomy/ cosmology-and-relativity/introduction-cosmology-2nd-edition-1?format=HB . 53

    2016

  37. [44]

    Opportunities for detecting ultralong gravitational waves

    Sazhin, M. V., “Opportunities for detecting ultralong gravitational waves”, Soviet Ast., 22, 36–38 (February 1978). [ADS]

    1978

  38. [45]

    Signature of gravity waves in polarization of the mi- crowave background

    Seljak, Uros and Zaldarriaga, Matias, “Signature of gravity waves in polarization of the mi- crowave background”, Phys. Rev. Lett. , 78, 2054–2057 (1997). [DOI], [arXiv:astro-ph/9609169 [astro-ph]]

    1997 arXiv

  39. [46]

    The stochastic background: scaling laws and time to detection for pulsar timing arrays

    Siemens, X., Ellis, J., Jenet, F. and Romano, J. D., “The stochastic background: scaling laws and time to detection for pulsar timing arrays”, Classical and Quantum Gravity , 30(22), 224015 (November 2013). [DOI], [ADS], [arXiv:1305.3196 [astro-ph.IM]]

    2013 arXiv

  40. [48]

    Structure in the COBE Differential Microwave Radiometer First-Year Maps

    Smoot, G. F. et al., “Structure in the COBE Differential Microwave Radiometer First-Year Maps”, ApJ, 396, L1 (Sep 1992). [DOI], [ADS]

    1992

  41. [49]

    Are We There Yet? Time to Detection of Nanohertz Gravitational Waves Based on Pulsar-timing Array Limits

    Taylor, S. R., Vallisneri, M., Ellis, J. A., Mingarelli, C. M. F., Lazio, T. J. W. and van Haasteren, R., “Are We There Yet? Time to Detection of Nanohertz Gravitational Waves Based on Pulsar-timing Array Limits”, ApJ, 819, L6 (March 2016). [DOI], [ADS], [arXiv:1511.05564 [ast...

    2016 arXiv

  42. [50]

    Binary Black Hole Mergers in the first Advanced LIGO Observing Run

    The LIGO Scientific Collaboration et al., “Binary Black Hole Mergers in the first Advanced LIGO Observing Run”, ArXiv e-prints (June 2016). [ADS], [arXiv:1606.04856 [gr-qc]]

    2016 arXiv

  43. [51]

    GWTC-1: A Gravitational-Wave Transient Cata- log of Compact Binary Mergers Observed by LIGO and Virgo during the First and Second Observing Runs

    The LIGO Scientific Collaboration et al., “GWTC-1: A Gravitational-Wave Transient Cata- log of Compact Binary Mergers Observed by LIGO and Virgo during the First and Second Observing Runs”, arXiv e-prints, arXiv:1811.12907 (Nov 2018). [ADS], [arXiv:1811.12907 [astro- ph.HE]]

    2018 arXiv

  44. [52]

    Probing the anisotropies of a stochastic gravitational-wave background using a network of ground-based laser interferometers

    Thrane, E., Ballmer, S., Romano, J. D., Mitra, S., Talukder, D., Bose, S. and Mandic, V., “Probing the anisotropies of a stochastic gravitational-wave background using a network of ground-based laser interferometers”, Phys. Rev. D, 80(12), 122002 (December 2009). [DOI], [ADS],...

    2009 arXiv

  45. [53]

    Correlated magnetic noise in global networks of gravitational-wave detectors: Observations and implications

    Thrane, E., Christensen, N. and Schofield, R. M. S., “Correlated magnetic noise in global networks of gravitational-wave detectors: Observations and implications”, Phys. Rev. D, 87, 123009 (Jun 2013). [DOI]URL: http://link.aps.org/doi/10.1103/PhysRevD.87.123009

    2013 doi

  46. [54]

    Correlated noise in networks of gravitational-wave detectors: Subtraction and mitigation

    Thrane, E., Christensen, N., Schofield, R. M. S. and Effler, A., “Correlated noise in networks of gravitational-wave detectors: Subtraction and mitigation”, Phys. Rev. D, 90, 023013 (Jul 2014). [DOI]URL: http://link.aps.org/doi/10.1103/PhysRevD.90.023013

    2014 doi

  47. [55]

    http://bicepkeck.org/

    “ http://bicepkeck.org/”

  48. [56]

    http://litebird.jp/eng/?page_id=2

    “ http://litebird.jp/eng/?page_id=2”

  49. [57]

    https://github.com/josephromano/leshouches/tree/master/code

    “ https://github.com/josephromano/leshouches/tree/master/code”

  50. [58]

    https://gwcenter.icrr.u-tokyo.ac.jp/en/

    “ https://gwcenter.icrr.u-tokyo.ac.jp/en/”. 54

  51. [59]

    https://lambda.gsfc.nasa.gov/product/cobe/

    “ https://lambda.gsfc.nasa.gov/product/cobe/”

  52. [60]

    https://map.gsfc.nasa.gov

    “ https://map.gsfc.nasa.gov”

  53. [61]

    https://www.cosmos.esa.int/web/planck

    “ https://www.cosmos.esa.int/web/planck”

  54. [62]

    https://www.elisascience.org

    “ https://www.elisascience.org”

  55. [63]

    https://www.gw-openscience.org

    “ https://www.gw-openscience.org”

  56. [64]

    http://www.gw-indigo.org

    “ http://www.gw-indigo.org”

  57. [65]

    http://www.ligo.caltech.edu/

    “ http://www.ligo.caltech.edu/”

  58. [66]

    http://www.virgo-gw.eu

    “ http://www.virgo-gw.eu”

  59. [67]

    Wainstein, L. A. and Zubakov, V. D., Extractions of Signals from Noise , (Dover Publications Inc., 1971). 55

    1971

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.