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CosmoPyro: Gradients for Gravitational-Wave Cosmology

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Konstantin Leyde, Elena Colangeli

Cosmology and Nongalactic Astrophysics · Submitted 18 Aug 2026 · 105 references

Pith's verdict: Solid, useful spectral-siren tool with new GP-2D mass model and new GWTC-5 h values, but the GP-2D headline number carries an admitted, unquantified systematic and the validation is weaker than it first looks.

T0 · AI review

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arXiv ID2608.18281 (version 1)
Pith ID4XCQR55D, Pith's permanent record of this paper and its review
CitationElena Colangeli, Konstantin Leyde. "CosmoPyro: Gradients for Gravitational-Wave Cosmology." arXiv:2608.18281 (2026). https://pith.science/paper/4XCQR55D
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The paper

The paper claims

Flexible mass models recover the Hubble constant from gravitational waves.

The reading

This paper introduces CosmoPyro, a fully differentiable hierarchical Bayesian pipeline that infers the Hubble constant from gravitational-wave events while modeling the source-frame mass distribution as a Gaussian process rather than a fixed parametric shape. Applied to the 231 confident black-hole mergers in the fifth gravitational-wave transient catalog, the one-dimensional model returns $h = 0.66^{+0.17}_{-0.20}$ and the two-dimensional model returns $h = 0.57^{+0.20}_{-0.15}$. Both are consistent with the latest measurements from the same catalog within $1\sigma$, even though the two models reconstruct noticeably different mass distributions. On a simulated catalog of 1000 events at anticipated next-run sensitivity, both models recover the injected $h = 0.67$ at the $1\sigma$ level. A sympathetic reader would take this as evidence that spectral-siren cosmology can proceed without knowing the true mass distribution in advance.

What carries the argument

The load-bearing object is a Gaussian random field $\mathrm{GF}$ defined on the logarithm of the mass distribution, $\log p(\mathrm{mass}) \sim \mathrm{GF}$, with smoothness controlled by a power spectrum through an amplitude $A_{\mathrm{PS}}$ and a cutoff wavenumber $k_{\mathrm{cut}}$. GP-1D applies the field to the primary mass $m_{1,s}$ and gives the mass ratio a running power-law distribution; GP-2D applies it jointly to $S = \log(m_{1,s}+m_{2,s})$ and $\delta = -\log q$, so that correlations between total mass and mass ratio are learned rather than assumed. The field is generated on a grid in Fourier space and interpolated to event parameters, and automatic differentiation makes gradient-based sampling of the roughly 25,000 field parameters feasible. Selection effects enter through Monte Carlo estimates of the detection probability, with a variance penalty guarding against noisy likelihood estimates.

Extended reading notes

Core claim

The paper's claim is that a Gaussian random field placed on the logarithm of the source-frame mass distribution is a workable replacement for parametric mass models in spectral-siren cosmology, and that the Hubble constant can be recovered without committing to a particular functional form. With the one-dimensional Gaussian process (GP-1D), the inferred value is $h = 0.66^{+0.17}_{-0.20}$; with the two-dimensional process (GP-2D) that jointly models total mass and mass ratio, it is $h = 0.57^{+0.20}_{-0.15}$. The two mass distributions differ markedly, yet both $h$ posteriors remain consistent with the latest measurements within $1\sigma$. In a simulated 1000-event O5-like catalog with a known injected value $h = 0.67$, both models return $h = 0.58^{+0.09}_{-0.09}$ and $h = 0.58^{+0.11}_{-0.10}$, recovering the truth at the $1\sigma$ level. The paper reads this as evidence that the method does not need the true mass-distribution family to be known in advance.

Load-bearing premise

The load-bearing assumption is that one shared correlation lengthscale can describe how smooth the true mass distribution is in both the total-mass and mass-ratio directions of the two-dimensional model, so if the true smoothness differs between those directions, the inferred Hubble constant can be biased.

Editorial extensions

If this is right

  • Spectral-siren $H_0$ measurements no longer have to commit to a parametric mass model, giving a direct check on a known source of systematic bias.
  • If the richer correlation structure favored by the two-dimensional model is real, mass-ratio modeling choices become a leading systematic in current $h$ measurements rather than a negligible detail.
  • At next-run catalog sizes of about 1000 events, either flexible model constrains $h$ to roughly $\pm 0.1$ and recovers the injected value, so the method is ready for O5-scale data.
  • Marginalizing over the Gaussian-process power-spectrum hyperparameters is the recommended default, because fixing them changes the reconstructed mass distribution more than it changes $h$.
  • The same differentiable pipeline extends to non-parametric tests of modified gravitational-wave propagation without re-parameterizing the mass model.

Reading between the lines

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

  • Inference: the roughly $0.09$ gap between the GP-1D and GP-2D $h$ medians on the same data is a plausible measure of the current systematic budget from mass-ratio modeling; a Bayes-factor comparison, which the paper leaves for future work, would indicate which model the data favor.
  • Inference: the paper's shared-lengthscale caveat points to an immediate extension, a two-dimensional Gaussian process with independent correlation lengths in $S$ and $\delta$; if that model shifts $h$, the shift quantifies the misspecification.
  • Inference: because the machinery scales to tens of thousands of inferred field parameters, it could absorb redshift-dependent mass evolution or mass-spin correlations, systematics the paper flags as increasingly important for larger catalogs.
  • Inference: the GP-2D reconstruction's flat mass-ratio distribution around $20\,M_\odot$ is a testable prediction for fixed-$h$ population analyses with existing catalogs.
Original abstract

Gravitational-wave (GW) observations of stellar-mass compact binary coalescences directly measure the source luminosity distance. Combined with the source redshift, these measurements constrain the current expansion rate of the Universe, the Hubble constant, $H_0$, or $h=H_0 / [100 \,{\rm km \,s^{-1} \, Mpc^{-1}}]$. For most GW signals no electromagnetic redshift measurement is expected, but the GW signal itself depends on the redshifted (detector-frame) masses. Assuming a source-frame mass distribution therefore enables a redshift estimate for each source. Combining the redshift estimates with the distance measurements provides a weak constraint on $H_0$ for each individual source that tightens with the number of sources in the catalog. However, the shape of the source-frame mass distribution is not known a priori, and previous work has relied on parametric models (piecewise power-laws with Gaussian components), and one-dimensional Gaussian processes. Here, we introduce CosmoPyro, a fully differentiable hierarchical Bayesian inference code that models the mass distribution using either one- or two-dimensional Gaussian processes. With the latest GW transient catalog (GWTC-5) we find $h = 0.66^{+0.17}_{-0.20}$ and $h = 0.57^{+0.20}_{-0.15}$ (median with $1\sigma$ uncertainty), for the one- and two-dimensional case, respectively. Despite the noticeably different inferred mass distributions, both models yield $H_0$ values consistent with the latest LVK measurements within $1 \sigma$. While our main results marginalize over the Gaussian-process power-spectrum hyperparameters, the measurement is also robust against fixing these hyperparameters over a range comparable to their measured uncertainty.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 7,873 input tokens.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.80 · human participants 0.02 · controlled comparison 0.14 · randomized assignment 0.01 · states quantitative result 0.99 · compares with prior results 0.92 · mentions code or data availability 0.05.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

Gravitational-wave (GW) observations of stellar-mass compact binary coalescences directly measure the source luminosity distance. Combined with the source redshift, these measurements constrain the current expansion rate of the Universe, the Hubble constant, $H_0$, or $h=H_0 / [100 \,{\rm km \,s^{-1} \, Mpc^{-1}}]$. For most GW signals no electromagnetic redshift measurement is expected, but the GW signal itself depends on the redshifted (detector-frame) masses. Assuming a source-frame mass distribution therefore enables a redshift estimate for each source. Combining the redshift estimates with the distance measurements provides a weak constraint on $H_0$ for each individual source that tightens with the number of sources in the catalog. However, the shape of the source-frame mass distribution is not known a priori, and previous work has relied on parametric models (piecewise power-laws with Gaussian components), and one-dimensional Gaussian processes. Here, we introduce CosmoPyro, a fully differentiable hierarchical Bayesian inference code that models the mass distribution using either one- or two-dimensional Gaussian processes. With the latest GW transient catalog (GWTC-5) we find $h = 0.66^{+0.17}_{-0.20}$ and $h = 0.57^{+0.20}_{-0.15}$ (median with $1\sigma$ uncertainty), for the one- and two-dimensional case, respectively. Despite the noticeably different inferred mass distributions, both models yield $H_0$ values consistent with the latest LVK measurements within $1 \sigma$. While our main results marginalize over the Gaussian-process power-spectrum hyperparameters, the measurement is also robust against fixing these hyperparameters over a range comparable to their measured uncertainty.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Gravitational-wave (GW) observations of stellar-mass compact binary coalescences directly measure the source luminosity distance. background 1.00 0.07 0.02 asserted 1.00
s1 Combined with the source redshift, these measurements constrain the current expansion rate of the Universe, the Hubble constant, $H_0$, or $h=H_0 / [100 \,{\rm km \,s^{-1} \, Mpc^{-1}}]$. background 1.00 0.07 0.04 asserted 0.98
s2 For most GW signals no electromagnetic redshift measurement is expected, but the GW signal itself depends on the redshifted (detector-frame) masses. background 0.98 0.06 0.02 asserted 0.80
s3 Assuming a source-frame mass distribution therefore enables a redshift estimate for each source. method 0.60 0.11 0.03 asserted 0.83
s4 Combining the redshift estimates with the distance measurements provides a weak constraint on $H_0$ for each individual source that tightens with the number of sources in the catalog. background 0.86 0.12 0.08 asserted 0.93
s5 However, the shape of the source-frame mass distribution is not known a priori, and previous work has relied on parametric models (piecewise power-laws with Gaussian components), and one-dimensional Gaussian processes. gap 0.96 0.03 0.02 asserted 1.00
s6 Here, we introduce CosmoPyro, a fully differentiable hierarchical Bayesian inference code that models the mass distribution using either one- or two-dimensional Gaussian processes. contribution 0.92 0.93 0.06 asserted 1.00
s7 With the latest GW transient catalog (GWTC-5) we find $h = 0.66^{+0.17}_{-0.20}$ and $h = 0.57^{+0.20}_{-0.15}$ (median with $1\sigma$ uncertainty), for the one- and two-dimensional case, respectively. result 1.00 0.97 0.63 asserted 1.00
s8 Despite the noticeably different inferred mass distributions, both models yield $H_0$ values consistent with the latest LVK measurements within $1 \sigma$. result 0.60 0.94 0.33 asserted 0.60
s9 While our main results marginalize over the Gaussian-process power-spectrum hyperparameters, the measurement is also robust against fixing these hyperparameters over a range comparable to their measured uncertainty. result 0.68 0.94 0.08 asserted 0.99

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from analysis of existing data 0.99.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

References
How the literature uses it

1 arXiv paper cite this in 4 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 1 sentence without a confident label

Uses its method or tool 1 paper

What it cites · 109 sentences without a confident label

Uses the method or tool of 12 papers
Uses data or values from 5 papers
Compares with 8 papers
Cites as background 26 papers
  • The authors in [ref] explore a Gaussian process on the (logarithm of the) heavier mass component, modeling the lighter component mass with a power law, while [ref] uses a one-dimensional binned Gaussian process for GWTC-3 [ref] (the third data release from the LIGO-Virgo-KAGRA collaboration, following the third observing run, O3), but also models the two-dimensional mass distribution in $$ and $$, the ratio of the two component masses, $/$.

    GWTC-3: Compact Binary Coalescences Observed by LIGO and Virgo During the Second Part of the Third Observing Run · Introduction · 0.80

  • The authors in [ref] explore a Gaussian process on the (logarithm of the) heavier mass component, modeling the lighter component mass with a power law, while [ref] uses a one-dimensional binned Gaussian process for GWTC-3 [ref] (the third data release from the LIGO-Virgo-KAGRA collaboration, following the third observing run, O3), but also models the two-dimensional mass distribution in $$ and $$, the ratio of the two component masses, $/$.

    No need to know: astrophysics-free gravitational-wave cosmology · Introduction · 0.80

  • The authors in [ref] explore a Gaussian process on the (logarithm of the) heavier mass component, modeling the lighter component mass with a power law, while [ref] uses a one-dimensional binned Gaussian process for GWTC-3 [ref] (the third data release from the LIGO-Virgo-KAGRA collaboration, following the third observing run, O3), but also models the two-dimensional mass distribution in $$ and $$, the ratio of the two component masses, $/$.

    Beyond Gaps and Bumps: Spectral Siren Cosmology with Non-Parametric Population Models · Introduction · 0.80

Discussion

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