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REVIEW 4 major objections 5 minor 41 references

A search for extra polarisations using a Gaussian process in Gravitational-Wave Transient Catalogue 3

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read A Gaussian-process search of null streams from 42 three-detector gravitational-wave events finds no evidence for scalar or vector polarisations, and sets a 90% upper limit of 0.39 on the fractional strain of any extra-polarisation signal…

desk verdict Solid GP null-stream search with a credible null result; the headline 0.39 upper limit needs a leakage check on the event that sets it. read the letter →

arxiv 2507.02335 v1 pith:AJV6MPUX submitted 2025-07-03 gr-qc astro-ph.HE

Shun Yin Cheung , Lachlan Passenger , Paul D. Lasky , Eric Thrane This is my paper
classification gr-qcastro-ph.HE
keywords gravitationalwavespolarisationsnullstreamGaussianprocessgeneralrelativitytestsGWTC-3Bayesfactorupperlimits
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

This paper tests whether gravitational waves carry polarisation states beyond the two (plus and cross) predicted by general relativity. It builds a null stream, a weighted combination of three detectors' data in which the ordinary tensor signal cancels, for 42 three-detector events from the third gravitational-wave transient catalogue, and models any residual signal with a Gaussian process whose kernel encodes that deviations should be localised near merger with a characteristic frequency. No event shows evidence of non-standard polarisations: all natural-log Bayes factors are below about 1.8. The tightest constraint is placed on GW190602_175927, where any extra-polarisation strain is below 39 percent of the general-relativity strain at 90 percent credibility.

What carries the argument

The central object is the gravitational-wave null stream: a linear combination $d_{\rm null}(t) = d_1(t) - \eta(\theta)d_2(t+\tau_{12}) - \zeta(\theta)d_3(t+\tau_{13})$ chosen so the plus and cross polarisations cancel, leaving noise plus any non-standard polarisation signal. The search models that residual with a Gaussian process whose covariance kernel $K_{ij} = k_0 e^{-f_0^2(t_i^2+t_j^2)/2w^2}\cos(2\pi f_0|t_i-t_j|) e^{-f_0^2 (t_i-t_j)^2/2l^2}$ encodes prior beliefs: the deviation is localised near merger, oscillates at a characteristic frequency, and need not be time-symmetric. A Bayes factor compares $k_0>0$ (deviation present) with $k_0=0$ (general relativity).

What would settle it

Construct the null stream for GW190602_175927 using extrinsic parameters drawn from the full posterior rather than the maximum-likelihood point, and recompute the Bayes factor; if the natural-log Bayes factor moves from -0.41 to above 8, the central no-deviation claim would collapse. Alternatively, inject a breathing-mode signal with signal-to-noise ratio around 6 into off-source data from the same catalogue and require the pipeline to recover a natural-log Bayes factor above 8 as it does in simulated O4-like noise; failure would show the search is not sensitive to the signals it claims to bound.

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Extended reading notes

Core claim

The paper claims that, if one accepts the maximum-likelihood extrinsic parameters used to build each null stream, the Gaussian-process search finds no signal attributable to scalar or vector polarisations in any of the 42 analysed events. The Bayes factors are consistent with the off-source background (Kolmogorov-Smirnov p = 0.93), and the upper limits on fractional strain deviation range from 0.39 to 7.90, with the most constraining event being GW190602_175927.

Load-bearing premise

The null stream built from the maximum-likelihood estimates of sky position, polarisation angle, and coalescence time is a faithful null stream for all 42 events; if those estimates are biased for any event, residual tensor signal could masquerade as a non-standard polarisation.

Editorial extensions

If this is right

  • If correct, the two-polarisation prediction of general relativity stands for all 42 three-detector events in the catalogue with ringdown frequency below 512 Hz.
  • Any non-standard polarisation in GW190602_175927 carries less than 39 percent of the general-relativity strain at 90 percent credibility, the tightest such limit from this search.
  • The Bayes-factor distribution of the 42 events is statistically consistent with off-source noise (p = 0.93), so the null-stream search is not picking up excess non-stationary noise.
  • The search's sensitivity is limited by the least sensitive observatory in the three-detector network, so future more sensitive networks would improve the constraints.

Reading between the lines

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

  • A re-analysis that marginalises over the extrinsic parameters rather than fixing them at maximum likelihood could tighten or weaken the upper limits; the paper validates the approximation only for GW170814.
  • The same Gaussian-process null-stream pipeline applied to next-generation ground-based detector networks, where the third-most-sensitive detector is much better, could push fractional limits below 0.1.
  • The kernel's flexibility makes the upper limits prior-dependent; a wider time-localisation prior could change the bounds for individual events.
  • If a future event shows a natural-log Bayes factor above 8 in this pipeline, the natural next step is to reconstruct the deviation signal and check whether its antenna-pattern combination matches a specific scalar or vector mode rather than a glitch.
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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

4 major / 5 minor

Summary. The paper searches for non-standard gravitational-wave polarisations (beyond GR's plus and cross) in 42 three-detector events from GWTC-3. The authors construct a null stream using maximum-likelihood estimates of the extrinsic parameters, model any residual non-standard-polarisation signal with a Gaussian-process covariance kernel taken from Passenger et al. (2025), and perform Bayesian parameter estimation to compute Bayes factors for a signal versus GR. They find no evidence of extra polarisations: all natural-log Bayes factors are below 2 (maximum 1.79), and a Kolmogorov-Smirnov test comparing the event Bayes factors with 112 off-source segments gives p = 0.93. They also report upper limits on the fractional strain deviation δsmax/hmax, with the lowest value 0.39 at 90% credibility for GW190602_175927. The pipeline is validated with a breathing-mode injection (ln B = 8.8) and with a GR-only injection, which produces no false positive.

Significance. If the central claims hold, this is a useful null-stream-based test of GR in GWTC-3, adding a flexible Gaussian-process search to the existing catalogue of extra-polarisation constraints. The no-evidence result is supported by consistently small Bayes factors and by a background comparison, and the upper limits, especially the 0.39 fractional-deviation limit for GW190602_175927, are new quantitative bounds. The paper also benefits from explicit injection tests demonstrating both detection efficiency for a breathing mode and safety for a GR-only signal. The significance is, however, conditional on the validity of the maximum-likelihood null-stream approximation, which is currently validated only for a single high-SNR event.

major comments (4)
  1. [§2.5 and Appendix A] The null stream in Eq. (1) is constructed from the maximum-likelihood estimate of θ = {α, δ, ψ, tc}, and the adequacy of this approximation is validated only for GW170814 in Appendix A. Figure 6 compares kernel-parameter posteriors for that single event, but does not compare Bayes factors or the upper limits δsmax/hmax, and no leakage check is shown for GW190602_175927, the event that produces the headline 0.39 limit. For lower-SNR events, the posterior widths of the extrinsic parameters are larger, and a residual tensor signal can remain in d_null. Since this residual is absent from both the signal covariance S in Eq. (9) and the noise covariance N in Eq. (15), the likelihood in Eq. (12) omits a real signal term, which can bias k0 and the quoted upper limits. The authors should either marginalise over the extrinsic parameters using Eq. (A4)–(A7) for the full catalogue, or demonstrate through injections across the catalogue's range of sky locations, SNRs, and PE uncertainties that the residual-tensor leakage is negligible.
  2. [§4, off-source test] The off-source KS test (p = 0.93) does not retire the leakage concern, because each off-source segment receives one fixed GW150914-like injection rather than injections drawn from the sky locations, SNRs, and PE uncertainties of the 42 catalogue events. As a result, the background distribution of ln B does not probe the degree to which a biased or broad PE posterior for, say, GW190602_175927 could leak tensor signal into the null stream. I recommend adding a leakage test that uses the actual PE posteriors (or realistic draws from them) for a subset of catalogue events, and reporting the residual tensor SNR in the constructed null stream as a function of event SNR and sky location.
  3. [§4, upper-limit method] The procedure for computing δsmax/hmax is not fully defined. Steps 1 and 2 appear to compute separate 90% upper limits on δsmax and hmax, and step 3 divides them, but a ratio of two upper limits is not itself a 90% upper limit on the ratio. To support the statement 'δsmax/hmax < 0.39 at 90% credibility' for GW190602_175927, the authors should construct the posterior (or posterior predictive) distribution of the ratio directly, using joint draws over the kernel parameters and the GW extrinsic parameters, and report the Monte Carlo uncertainty from the 100 draws.
  4. [§5] The conclusion states that the null stream can search for extra polarisations 'without risk of false positive detections from waveform misspecification.' This is overstated: the null stream is built using extrinsic parameters obtained from a specific waveform model (IMRPhenomPv2), and waveform errors can bias those parameters, which in turn can leave a residual tensor signal in the null stream. The current analysis does not quantify that risk. I suggest softening the claim or adding a test that uses different waveform models in the PE stage and checks whether the null-stream Bayes factors and upper limits change materially.
minor comments (5)
  1. [Abstract and title] There are typographical issues: 'Gravitational-Wave T ransient Catalogue' and 'W ave' in the title, and 'GW190602 175927' appears without an underscore in the abstract while Table 1 uses 'GW190602_175927'.
  2. [Figure 5 caption] The caption says the off-source distribution is blue and the GWTC-3 distribution is orange, but the text in §4 says 'in blue' for the GWTC-3 events; please make the color convention consistent.
  3. [Eq. (19)] The Bayes factor expression integrates only over k0, but the numerator should be the evidence marginalised over all kernel hyperparameters (k0, w, f0, l) with k0 > 0; please clarify the notation so that L(d|k0) is understood to be the likelihood marginalised over the remaining kernel parameters.
  4. [Appendix B / Table 1] The table header contains 'T able 1' and the table is split across pages without repeated column headers; adding repeated headers would improve readability.
  5. [References] The reference to Gürsel and Tinto should include the diacritics ('Gürsel'), and the Einstein-aether reference is listed as 'Jacobson & Mattingly 2004' without a journal or DOI; please complete the bibliographic information.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the null result is an observed Bayes-factor analysis on public GWTC-3 data, benchmarked against off-source segments; self-citations to Passenger et al. (2025) supply the GP kernel and likelihood but are not circular.

full rationale

The claimed derivation chain is: construct a null stream from maximum-likelihood extrinsic parameters (Eq. 1), model extra-polarisation signals with a Gaussian-process covariance (Eqs. 7-10), compute Bayes factors versus k0=0 (Eq. 19), and compare with off-source background. The central quantities are not equal to the inputs by construction: the null stream removes GR tensor signals by antenna-pattern algebra (Gürsel & Tinto 1989), not by fitting the GP; k0 is a free amplitude with a stated log-uniform prior and is marginalized with dynesty; and the 'no evidence' conclusion is an observed outcome on 42 public GWTC-3 events, explicitly benchmarked against 112 off-source segments giving a Kolmogorov-Smirnov p-value of 0.93. The GP kernel and likelihood are adopted from the authors' prior work (Passenger et al. 2025), but this is a methodological self-citation rather than a circular reduction: the kernel's functional form is an openly stated ansatz with physically motivated properties (localized near merger, characteristic frequency, asymmetry), and the pipeline is tested with injections and off-source noise. Appendix A checks the one approximation that could couple the method to its inputs (using maximum-likelihood extrinsic parameters instead of marginalizing over them) on GW170814; that is a validation choice, and any concern about residual tensor leakage is a correctness or robustness risk, not definitional circularity. No equation in the paper reduces to a fitted parameter renamed as a prediction, and no uniqueness claim is imported from the authors' prior work.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The analysis adds no new physical entities. The Gaussian process kernel, its hyperparameter priors, the null-stream construction, and the noise model are all modeling inputs; the central result is an upper limit. The most consequential assumptions are the kernel's signal-morphology prior and the use of maximum-likelihood extrinsic parameters.

free parameters (4)
  • k0 (GP amplitude scale) = posterior distribution, not a single value
    Log-uniform prior between 1e-47 and 1e-41; controls the overall strain amplitude of the modeled extra-polarization signal; the Bayes factor and upper limits depend on its posterior.
  • w (GP width) = posterior distribution, not a single value
    Uniform prior between 0.001 and 5; sets the time duration of the modeled deviation; the posterior is used to reconstruct the signal for limits.
  • f0 (GP characteristic frequency) = posterior distribution, not a single value
    Uniform prior between 50 and 1024 Hz; sets the oscillation timescale; also drives the event selection ringdown frequency below 512 Hz.
  • l (GP coherence length) = posterior distribution, not a single value
    Uniform prior between 0.05 and 5; controls how many cycles remain coherent; the posterior is used for signal reconstruction and limits.
assumptions (6)
  • standard math The null stream removes the GR tensor polarizations using antenna response functions given by Eqs. 2-3.
    This is the definition of the null stream from Gürsel & Tinto (1989); assumed to hold for the three-detector network.
  • ad hoc to paper Non-standard polarizations are mutually uncorrelated and share a common kernel K (Eq. 8-9).
    This is a modeling choice; no physical argument forces independence or a common covariance.
  • ad hoc to paper The kernel form in Eq. 10 (localized near merger, characteristic frequency, possible asymmetry) describes extra-polarization signals.
    This is the prior belief from Passenger et al. (2025); if the true signal has different morphology, the search loses sensitivity.
  • domain assumption Null-stream noise is Gaussian, stationary, and uncorrelated across frequencies, with PSD given by Eq. 5 and Eq. 15.
    Standard for GW data analysis; off-source segments are used to test robustness.
  • domain assumption Events with ringdown frequency below 512 Hz are selected for analysis.
    Chosen to match the f0 prior upper bound of 1024 Hz; excludes higher-frequency events.
  • domain assumption The maximum-likelihood estimate of extrinsic parameters is adequate for constructing null streams; uncertainty is not marginalized for the catalogue.
    Appendix A tests this on GW170814 only and concludes the effect is negligible.

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Cite this review

Pith. "Pith review of A search for extra polarisations using a Gaussian process in Gravitational-Wave Transient Catalogue 3." pith.science (2026). https://pith.science/paper/AJV6MPUX

@misc{pith2026250702335,
  author       = {Pith},
  title        = {Pith review of: A search for extra polarisations using a Gaussian process in Gravitational-Wave Transient Catalogue 3},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/AJV6MPUX}},
  note         = {Machine review of arXiv:2507.02335}
}
abstract

General relativity predicts that gravitational waves are described by two polarisation states: the plus $+$ state and cross $\times$ state. However, alternate theories of gravity allow up to six polarisations. We employ the gravitational-wave null stream, a linear combination of three or more detectors where the $+$ and $\times$ signals add to zero, leaving behind noise and potentially gravitational waves in non-standard polarisation states. We develop a Gaussian process model to search for extra polarisations beyond general relativity. Using data from 42 three-detector events from LIGO-Virgo-KAGRA's Third Gravitational-Wave Transient Catalogue, we find no evidence of non-standard polarisations. We set upper limits on the fractional deviation in gravitational-wave strain to be as low as 0.39 at 90% credibility for the event GW190602_175927.

Figures

Figures reproduced from arXiv: 2507.02335 by the authors.

Figure 1
Figure 1. shows multiple draws from the combined kernel. Each draw (coloured curve) in [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Posteriors of the kernel parameters for the breathing mode injection. We inject a draw from the kernel as a breathing mode signal into the individual detectors and analyse the resulting signal in the null stream. The k0 posterior rules out the lower bound of the prior, indicating the Gaussian process is detecting a signal. 0.15 0.10 0.05 0.00 0.05 0.10 0.15 time (s) 40 20 0 20 40 w h i t e n e d s t r a i n ( × 1 0 … view at source ↗
Figure 4
Figure 4. Posterior of log10 k0 for an injection of only +/× polarisations into the detectors. It is consistent with the lower bound of the k0 prior, indicating there is no signal in the null stream. form prior between [0.05, 1] for our mass ratio, a uniform prior between [4.6, 250 ]M⊙ for our chirp mass, a uni￾form prior between [0, 0.99] for our spin magnitudes and a power law prior with α = 2 between [10, 30000 ]Mpc [PITH… view at source ↗
Figures from the paper (2 more)
Figure 5
Figure 5. Figure 5: Natural log Bayes factors of 112 off-source seg￾ments (blue) and 42 three-detector events in GWTC-3 (or￾ange). All GWTC-3 events have a small Bayes factor with the highest of ln B = 1.79, indicating no signal. The back￾ground study show multiple off-source data segment…
Figure 6
Figure 6. Figure 6: Posterior distributions for the kernel parameters describing the event GW170814. In blue we show the result obtained by calculating the null stream with the maximum-likelihood parameters for right ascension, declination, polarisation angle and time of coalescence. In o…

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    Zevin, M., Coughlin, S., Bahaadini, S., et al. 2017, Classical and Quantum Gravity, 34, 064003, doi: 10.1088/1361-6382/aa5cea 9 APPENDIX A. MARGINALISING OVER UNCERTAINTY IN EXTRINSIC PARAMETERS The construction of a null stream with a three-detector network depends on four ex...

    2017 doi

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