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arxiv: 2507.01294 · v2 · submitted 2025-07-02 · 🌀 gr-qc · astro-ph.HE

A Gaussian process framework for testing general relativity with gravitational waves

Lachlan Passenger , Shun Yin Cheung , Nir Guttman , Nikhil Kannachel , Paul D. Lasky , Eric Thrane This is my paper

Pith reviewed 2026-05-19 07:06 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.HE
keywords gravitational wavesgeneral relativityGaussian processesbinary black hole mergersGWTC-3tests of gravitystrong-field regime
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The pith

A Gaussian process framework tests general relativity in gravitational waves from black hole mergers and finds no deviations.

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

The paper introduces a Gaussian process method to search for deviations from general relativity in gravitational wave signals without assuming any particular alternative theory. It uses a kernel that builds in the expectation that any such deviation would be concentrated near the merger with a typical frequency scale. Demonstrations on simulated signals and real events from the Gravitational-Wave Transient Catalog 3 show the data remain consistent with general relativity. Limits on the size of possible deviations reach as low as 7 percent of the strain amplitude for one loud event at 90 percent credibility. A reader would care because the approach opens a route to broad, assumption-light tests of gravity in the strongest fields accessible to observation.

Core claim

We introduce a Gaussian process framework to search for deviations from general relativity in gravitational-wave signals from binary black hole mergers with minimal assumptions. We employ a kernel that enforces our prior beliefs that if gravitational waveforms deviate from the predictions of general relativity the deviation is likely to be localised in time near the merger with some characteristic frequency. We demonstrate this formalism with simulated data and apply it to events from Gravitational-Wave Transient Catalog 3. We find no evidence for a deviation from general relativity. We limit the fractional deviation in gravitational-wave strain to as low as 7% (90% credibility) of thestrain

What carries the argument

Gaussian process regression equipped with a kernel that restricts potential deviations to a localized window in time near merger and a characteristic frequency band.

If this is right

  • The framework supplies quantitative upper limits on fractional waveform deviations for each event analyzed.
  • Current data from binary black hole mergers remain compatible with general relativity at the level of a few percent in strain amplitude.
  • The same kernel and inference procedure can be applied to additional events as detector sensitivity improves.
  • The method complements existing parametrized tests by remaining agnostic to the functional form of any new physics.

Where Pith is reading between the lines

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

  • Extending the kernel to allow separate localization in the inspiral versus ringdown phases could isolate where any new effects appear.
  • Application to neutron-star merger signals would test gravity in the presence of matter, a regime not covered by the current black-hole sample.
  • If future detections exceed the reported limits, the framework itself would indicate the need for kernels with broader temporal support.

Load-bearing premise

Any deviation from general relativity must appear as a time-localized feature near the merger with some characteristic frequency.

What would settle it

A gravitational-wave signal whose residuals from the general-relativity template require a kernel with support spread far from the merger time or lacking a single characteristic frequency scale.

Figures

Figures reproduced from arXiv: 2507.01294 by Eric Thrane, Lachlan Passenger, Nikhil Kannachel, Nir Guttman, Paul D. Lasky, Shun Yin Cheung.

Figure 1
Figure 1. Figure 1: Example deviations from GR drawn from our kernel (Eq. 5), with scale factor k0 = 10−45, characteristic frequency f0 = 100 Hz, width w = 2.0, and length l = 2.5. These kernel functions depend on several parameters: • The scale factor k0 determines the overall ampli￾tude of δs(t). The typical strain amplitude for a deviation scales like k 1/2 0 . • The width w determines the typical duration of the signal δs… view at source ↗
Figure 2
Figure 2. Figure 2: Posterior distribution of the Gaussian process hyper-parameters for a simulated signal with a deviation from GR drawn from our kernel. The contours are the 1,2 and 3σ intervals. The true values are plotted as orange cross hairs, and are included within at least the 3σ interval for all hyper-parameters. 80 40 0 40 80 0.00015 0.00000 0.00015 whitened residual strain H1 80 40 0 40 80 L1 Time (ms) [PITH_FULL_… view at source ↗
Figure 3
Figure 3. Figure 3: Reconstruction of the whitened deviation strain δs for a simulated signal that includes a deviation from GR drawn from our kernel. The blue curve is the whitened strain in each detector. The orange curve is the true injected δs. The black curve is the median estimate of δs using Gaussian process regression, and the grey shaded region is the 90% credible interval on δs [PITH_FULL_IMAGE:figures/full_fig_p00… view at source ↗
Figure 4
Figure 4. Figure 4: Cumulative distribution function (CDF) of the log-signal-to-noise Bayes factor ln B for 174 segments of real￾istic noise, π(B) (blue curve). Also indicated is the value of ln B for GW150914 residual data (black dotted line) and for GW190916 200658 residual data (red dotted line), the event with the highest ln B, though still typical of the distribution of ln B for noise segments. signal is described by IMR… view at source ↗
Figure 5
Figure 5. Figure 5: Posterior distribution of the Gaussian process hyper-parameters for a simulated gravitational-wave signal with a parameterised deviation from GR in the form of a δβ2 ̸= 0 phase coefficient. The contours are the 1,2 and 3σ intervals. 80 40 0 40 80 0.00015 0.00000 0.00015 whitened residual strain H1 80 40 0 40 80 L1 Time (ms) [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Reconstruction of the whitened deviation strain δs for deviation from GR parameterised by the δβ2 phase coefficient. The blue curve is the whitened strain in each detector. The orange curve is the true injected δs. The black curve is the median estimate of δs using Gaussian process regression, and the grey shaded region is the 90% credible interval on δs [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Posterior distribution of the Gaussian process hyper-parameters for GW150914 residual data. The contours are the 1,2 and 3σ intervals. The posterior on k0 does not exclude the lower bound of 10−46, indicating no signal is present in the data. 80 40 0 40 80 0.00015 0.00000 0.00015 whitened residual strain H1 80 40 0 40 80 L1 Time (ms) [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Reconstruction of the whitened deviation strain δs for GW150914 residual data. The blue curve is the whitened residual strain in each detector. The black curve is the median estimate of δs using Gaussian process regression, and the grey shaded region is the 90% credible interval on δs, which shows no signal is present in the data [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Comparison between the log-signal-to-noise Bayes factor ln B distributions for 174 noise segments (blue) and the 60 GWTC-3 GW events (orange) analysed. Since the data are consistent with GR, we calculate upper limits on the fractional strain of the non-GR de￾viation δs for each GW event: 1. We take random draws of hyper-posterior samples Λk. 2. For each sample, we take a random draw of δs(t), the time-doma… view at source ↗
read the original abstract

Gravitational-wave astronomy provides a promising avenue for the discovery of new physics beyond general relativity as it probes extreme curvature and ultra-relativistic dynamics. However, in the absence of a compelling alternative to general relativity, it is difficult to carry out an analysis that allows for a wide range of deviations. To that end, we introduce a Gaussian process framework to search for deviations from general relativity in gravitational-wave signals from binary black hole mergers with minimal assumptions. We employ a kernel that enforces our prior beliefs that - if gravitational waveforms deviate from the predictions of general relativity - the deviation is likely to be localised in time near the merger with some characteristic frequency. We demonstrate this formalism with simulated data and apply it to events from Gravitational-Wave Transient Catalog 3. We find no evidence for a deviation from general relativity. We limit the fractional deviation in gravitational-wave strain to as low as 7% (90% credibility) of the strain of GW190701_203306.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 2 minor

Summary. The paper introduces a Gaussian process framework to search for deviations from general relativity in gravitational-wave signals from binary black hole mergers. A kernel is employed that encodes the prior belief that any deviations are localised in time near the merger with some characteristic frequency. The method is demonstrated on simulated data and applied to selected events from the GWTC-3 catalog, yielding no evidence for deviations from GR and an upper limit on the fractional deviation in gravitational-wave strain of 7% (90% credibility) for the event GW190701_203306.

Significance. If the result holds, the work provides a flexible, data-driven approach to testing GR in the strong-field regime without specifying a particular alternative theory. Credit is given for the direct application to real GWTC-3 events and the derivation of quantitative credibility limits on strain deviations. The Gaussian-process construction is a strength for allowing a broad but still tractable search space.

major comments (2)
  1. [Abstract] Abstract: the phrasing 'with minimal assumptions' is not supported by the kernel choice, which explicitly enforces that deviations (if present) are localised near merger and possess a characteristic frequency. This prior restricts the class of detectable deviations, so the reported 7% (90% credibility) limit on fractional strain deviation for GW190701_203306 applies only within that morphology and is not a model-independent bound.
  2. [Method] Method (kernel and hyperparameter treatment): the central claim that the posterior on the fractional deviation is robust rests on the kernel hyperparameters, yet no quantitative validation metrics, error budgets, or explicit marginalisation procedure over length-scale and amplitude are supplied. This leaves the credibility of the 'no evidence' conclusion and the 7% limit only weakly supported.
minor comments (2)
  1. [Simulations section] Clarify in the text how the simulated injections were constructed and whether they include deviations outside the kernel support to test the method's sensitivity.
  2. Figure captions should explicitly state the kernel form and the prior ranges used for the hyperparameters.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful review and constructive feedback. We address the major comments point by point below, indicating where revisions will be made to improve clarity and support for our claims.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the phrasing 'with minimal assumptions' is not supported by the kernel choice, which explicitly enforces that deviations (if present) are localised near merger and possess a characteristic frequency. This prior restricts the class of detectable deviations, so the reported 7% (90% credibility) limit on fractional strain deviation for GW190701_203306 applies only within that morphology and is not a model-independent bound.

    Authors: We agree that the kernel choice incorporates specific prior beliefs regarding the localization and frequency content of deviations, which restricts the class of signals to which the method is sensitive. The phrase 'minimal assumptions' was intended to contrast the approach with tests that assume a particular alternative theory, but we recognize that it may overstate the generality. We will revise the abstract to remove this phrasing and instead describe the framework as incorporating physically motivated priors on the time localization and characteristic frequency of deviations. The reported credibility limits will be explicitly qualified as applying within this class of deviations. revision: yes

  2. Referee: [Method] Method (kernel and hyperparameter treatment): the central claim that the posterior on the fractional deviation is robust rests on the kernel hyperparameters, yet no quantitative validation metrics, error budgets, or explicit marginalisation procedure over length-scale and amplitude are supplied. This leaves the credibility of the 'no evidence' conclusion and the 7% limit only weakly supported.

    Authors: The manuscript does describe the choice of kernel hyperparameters based on the expected duration and frequency scale of the merger, with the posterior obtained after integrating over the Gaussian process coefficients. However, we acknowledge that more explicit documentation of the marginalization and robustness checks would strengthen the presentation. We will add a dedicated subsection that details the priors on the length-scale and amplitude hyperparameters, the numerical marginalization procedure, and quantitative validation results from a suite of injection-recovery tests. These will include sensitivity analyses showing how the recovered fractional deviation posteriors respond to variations in the hyperparameters, along with associated error budgets. revision: yes

Circularity Check

0 steps flagged

No significant circularity; framework applied to external data with explicit kernel choice

full rationale

The paper presents a Gaussian process model whose kernel is introduced as an explicit modeling choice that encodes prior beliefs about the time-frequency support of any GR deviation. This choice is stated directly rather than derived from the target events or fitted to them. The analysis is then applied to simulated injections and to external events drawn from the GWTC-3 catalog; the reported upper limits and 'no evidence' conclusion are posterior results conditioned on the observed data under that kernel. No equation or step reduces the final claim to a tautological restatement of the kernel or to a self-citation chain. The derivation therefore remains self-contained against external benchmarks and does not meet the criteria for any of the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on a domain assumption about the form of possible deviations that is encoded directly into the kernel; the framework also depends on standard Gaussian-process mathematics and on the external GWTC-3 catalog.

free parameters (1)
  • kernel length-scale and amplitude hyperparameters
    Parameters controlling the characteristic frequency and strength of allowed deviations; their values are not reported in the abstract.
axioms (1)
  • domain assumption If gravitational waveforms deviate from the predictions of general relativity, the deviation is likely to be localised in time near the merger with some characteristic frequency.
    This prior belief is explicitly built into the choice of kernel as stated in the abstract.

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Reference graph

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