A Bright Future? Prospects for Cosmological Tests of GR with Multimessenger Gravitational Wave Events

Elena Colangeli; Konstantin Leyde; Tessa Baker

REVIEW 2 major objections 4 minor 126 references

A Bright Future? Prospects for Cosmological Tests of GR with Multimessenger Gravitational Wave Events

T0 review · 2 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read The paper forecasts that the next ten bright sirens will not competitively constrain modified gravity, while one year of third-generation detector data could detect a Horndeski-style departure from GR at greater than 3σ.

desk verdict Careful forecast with a robust LVK punchline and a fragile ET headline that leans on the α(z) ansatz; definitely worth a serious referee. read the letter →

arxiv 2501.05560 v2 pith:OSDCGPHB submitted 2025-01-09 gr-qc astro-ph.CO

Elena Colangeli , Konstantin Leyde , Tessa Baker This is my paper · ORCID

classification gr-qcastro-ph.CO MSC 83C3583D0583F05 PACS 04.30.-w04.80.Nn95.36.+x98.80.-k

keywords brightsirensgravitationalwavecosmologymodifiedgravityHorndeskitheorystandardthird-generationdetectorsgamma-rayburstsHubbleconstant

topics The Hubble Tension

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 asks whether the next bright sirens—gravitational wave events with electromagnetic counterparts, which pin down the source redshift—can by themselves test whether gravity differs from general relativity on cosmological scales. It argues they cannot in the near term: ten simulated bright sirens from the upcoming current-generation network leave the Horndeski parameter $\alpha_M$, which controls how the effective Planck mass runs with time, too poorly constrained to compete with existing dark-siren or galaxy-survey results. The same analysis finds that one year of third-generation detector data, with gamma-ray burst counterparts for roughly 150 events, could detect a mild departure such as $\alpha_M \neq 0$ at more than $3\sigma$. The point matters for planning: it says bright-siren follow-up alone will not settle modified gravity in the 2020s, and that a portfolio of dark siren, bright siren, and large-scale-structure methods is needed.

What carries the argument

The argument runs on the ratio between the gravitational-wave luminosity distance $d_{\rm GW}$ and the electromagnetic luminosity distance $d_L$. In Horndeski gravity, $d_{\rm GW} = d_L \exp\!\left(\int_0^z \frac{\alpha_M(z')}{2(1+z')}\,dz'\right)$, so any departure from GR accumulates with source redshift, while $\alpha_T$ changes the gravitational wave speed and produces an arrival-time delay between the GW and gamma-ray burst signals. The paper adopts the $\Omega_\Lambda$ redshift ansatz $\alpha_i(z) = \alpha_{i0}\,\Omega_\Lambda(z)/\Omega_{\Lambda 0}$ and links the distance and speed effects through the same Horndeski scalar–tensor framework rather than treating them independently. The resolving power comes from gamma-ray burst detection: restricting binary inclination to less than $20^\circ$ breaks the distance–inclination degeneracy and tightens distance posteriors, while the full Bayesian likelihood marginalizes over the emission time delay and includes selection effects.

What would settle it

Re-run the third-generation forecast with the alternative ansätze $\alpha_i(z)=\alpha_{i0} a$ and $\alpha_i(z)=\alpha_{i0} a^p$ used in the paper, and with gamma-ray burst luminosities drawn from the brighter end of the observed distribution; if the $\alpha_{M0}$ posterior no longer excludes GR at $3\sigma$, the headline forecast fails. The first real year of third-generation bright-siren data would settle it directly.

Watch

Extended reading notes

Core claim

The paper's central claim is a quantitative forecast. For a fiducial Horndeski universe with $\alpha_{M0}=1$, the next ten bright sirens (only one with a detected gamma-ray burst) give $H_0 = 69.44^{+6.50}_{-5.55}\,\mathrm{km\,s^{-1}\,Mpc^{-1}}$ and an $\alpha_{M0}$ posterior so wide that GR and $\alpha_{M0}=1$ are both consistent; these events are not competitive with existing probes. If the Hubble tension is resolved by an external prior on $H_0$, the $\alpha_{M0}$ error bars shrink by 65–70 percent, but the result remains comparable to current constraints. In the third-generation scenario, 150 bright sirens with gamma-ray burst information restrict the binary inclination range, breaking the inclination–distance degeneracy, and yield $\alpha_{M0} = 0.98^{+0.22}_{-0.18}$, $\alpha_{T0} = 2.91^{+0.22}_{-0.20} \times 10^{-16}$, and $H_0 = 70.17^{+1.98}_{-1.66}\,\mathrm{km\,s^{-1}\,Mpc^{-1}}$, excluding GR at more than $3\sigma$ for the injected $\alpha_{M0}=1$. The paper also shows that without the gamma-ray-burst-restricted inclination, the third-generation error bars roughly double, and that wrongly assuming GR when the universe is non-GR biases $H_0$ badly.

Load-bearing premise

The forecast that third-generation data will detect $\alpha_M \neq 0$ at $3\sigma$ rests on the assumed redshift ansatz $\alpha_i(z) \propto \Omega_\Lambda(z)$; a different but still viable redshift dependence for $\alpha_M$ and $\alpha_T$ could shift the integrated distance and time-delay effects enough to make the claimed detection marginal.

Editorial extensions

If this is right

With only the next ten bright sirens, $\alpha_{M0}$ will remain consistent with both GR and $\alpha_{M0}=1$, so near-term bright-siren campaigns cannot by themselves rule cosmological modified gravity in or out.
A one-year third-generation campaign with roughly 150 gamma-ray-linked events should detect $\alpha_{M0}=1$ and the injected $\alpha_{T0}$ at more than $3\sigma$, making modified gravity detectable if it is present at that level.
Gamma-ray burst information is worth roughly a factor of two in error bars: restricting inclination with GRB data halves the $H_0$ and $\alpha_{M0}$ uncertainties in the third-generation scenario.
If the Hubble tension is resolved first, ten bright sirens become 65–70 percent more powerful for $\alpha_{M0}$, so external cosmology priors and modified-gravity tests are not independent.
Bright and dark sirens should be analysed jointly; the forecasts support a portfolio strategy rather than relying on a few exceptional events.

Reading between the lines

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

A testable extension: applying the same likelihood to space-based detectors at higher redshift should strengthen the $\alpha_M$ signal, since the effect in the distance ratio accumulates with propagation distance; the paper only simulates ground-based detectors.
The results imply that the gamma-ray burst detection horizon, not the gravitational wave horizon, is the binding constraint for bright-siren cosmology; pushing GRB sensitivity beyond the simulated cutoff would directly convert more third-generation events into useful probes.
The strong $H_0$\u2013$\alpha_M$ degeneracy shown here suggests that any independent improvement in the Hubble constant measurement will propagate directly into sharper modified-gravity constraints, a lever arm the authors quantify in their testing-GR-only scenario.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Worth a read if you work on GW cosmology. The paper builds a full Bayesian forecast for bright sirens in Horndeski gravity, with selection effects and GRB time-delay information, and lands on two results: ten LVK-era bright sirens will not competitively constrain αM, and one year of Einstein Telescope with 150 GRB-associated events could detect αM0=1 at >3σ. The first conclusion is solid and the more useful one. The second is real but rests on the ΩΛ(z) ansatz for the α parameters, and the paper's own Section 6 admits that a different ansatz could change the results, with differences 'not expected to exceed order unity.' As the stress-test note says, that order-unity margin is exactly where the 3σ claim sits; a steeper low-z αM(z) can cut the integrated signal by more than a factor of two and drop the significance toward or below 3σ. So the ET headline should be read as a self-consistency check of the parametrisation, not a robust prediction.

What the paper does well: the setup is careful. The likelihoods include the inclination–distance degeneracy, the GRB selection via flux threshold, and the emission-time-delay marginalisation. The comparison between GR+cosmology and GR-only scenarios is clean. The qualitative message – that near-term bright sirens alone won't settle modified gravity, so dark sirens and cross-correlations remain essential – is well supported and worth stating plainly. The αT0 text error in Section 5.1 is minor and fixable: the posterior shown in Figure 4 is wider than the GW170817 bound, not one order of magnitude tighter.

The main limitation is reproducibility: no code or data provided, so the specific numbers can't be checked. That is a common gap for forecast papers, but here the headline depends on the ansatz and the mock generation details, so it matters a bit more.

Who it's for: anyone planning LVK O5 or ET observing strategy, and people working on modified gravity forecasts. It deserves a serious referee; the LVK conclusion is useful and the ET claim, though fragile, is an honest forecast under stated assumptions. I'd recommend sending to peer review and pushing for the ansatz dependence to be quantified, e.g. by rerunning the ET case under the other ansätze in eq. 2.7, and for the αT0 statement to be corrected.

Referee Report

2 major / 4 minor

Summary. This paper presents forecasts for joint inference of the Hubble constant H0 and the Horndeski parameters αM and αT using bright siren gravitational-wave events, i.e. binary neutron star mergers with electromagnetic counterparts. The analysis covers two detector eras: a LIGO-Virgo-KAGRA O4/O5-like scenario with 10 mock events (one with an associated GRB) and an Einstein Telescope scenario with 150 GRB-associated mock events. The authors build a Bayesian likelihood including selection effects, marginalize over emission time delays, and use the ΩΛ(z) parametrisation of αM(z) and αT(z). Their main results are that ten LVK bright sirens alone leave αM0 essentially unconstrained and are not competitive with current dark siren or DESI constraints, while 150 ET events with GRB information recover the injected αM0=1 at better than 3σ, and also improve H0 and αT0 constraints. The paper emphasizes the role of GRB detection in breaking the inclination-distance degeneracy and thereby improving distance estimation.

Significance. If the ET forecast is robust, the paper gives a useful quantitative answer to a frequently asked question about the near-term and long-term value of bright sirens for cosmological tests of gravity. The LVK conclusion is well supported: with only ten nearby events, the integrated modification in Eq. (2.8) is small and the recovered αM0 posterior is far wider than current non-GW constraints; this part of the paper is robust to the modelling simplifications. The paper also has clear strengths: the selection-effect treatment in Eqs. (4.4)-(4.9), the arrival-time-delay derivation in Appendix B, the use of bilby-based simulated distance posteriors for the LVK scenario, and the honest discussion of caveats in Section 6. The main weakness is that the headline Einstein Telescope 3σ claim is conditional on the chosen ΩΛ(z) ansatz and on the assumed 150 GRB-associated events per year. These dependencies are acknowledged but not quantified, and the current caveat in Section 6 that changes are 'not expected to exceed order unity' is asserted rather than demonstrated.

major comments (2)

[§2.3, §5.2, §6; Eqs. (2.7)-(2.8); Fig. 5] The headline claim that one year of Einstein Telescope observations detects αM0=1 at greater than 3σ is sensitive to the assumed redshift parametrisation of αM(z). The mock data and the recovery likelihood both use the ΩΛ ansatz of Eq. (2.7), so the forecast demonstrates self-consistency under that ansatz rather than robustness to the functional form of αM(z). Because the GRB flux cut restricts the ET sample to z≲0.5, the integrated kernel in Eq. (2.8) is only about 0.22 at z=0.5 under this ansatz, and a more low-z-concentrated form such as αM∝[ΩΛ/ΩΛ0]^2 reduces that kernel by more than a factor of two. This would move the recovered αM0 significance from roughly 5σ toward or below the 3σ threshold. The Section 6 caveat that modifying the ansatz is 'not expected to exceed order unity' is precisely the margin on which the 3σ claim rests, yet no calculation is provided. Please quantify the robustness by repeating the ET forecast for the three ansätze in Eq. (2.7) and for at least one steeper low-z ansatz, and report the minimum significance over this set.
[§3.2, §5.2; Figs. 5 and 7] The 'one year' ET claim also depends on the assumed yield of 150 GRB-associated events. This number is built from an ET BNS rate at the high end of forecasts (up to 6×10^4 events per year), a 6% inclination selection, a Fermi/Swift flux threshold, and a GRB luminosity distribution centred at 5×10^49 erg/s with only 10% dispersion. Each of these choices is defensible, but the combination is optimistic: a factor of two or three reduction in the joint detection rate, e.g. from a lower BNS rate within current bounds or a broader short-GRB luminosity function, would reduce the αM0 significance roughly as sqrt(N) and could push the 150-event result toward or below 3σ. Since Fig. 7 already shows results for N=50, 150, 300 and 500, please make the N-dependence explicit in terms of detection significance and state the minimum joint rate required for a 3σ one-year claim. This would make the forecast robust to the main rate and selection uncertainties.

minor comments (4)

[§5.1, Fig. 4] The statement that the αT0 posterior is 'one order of magnitude tighter than GW170817' is incorrect: the quoted result αT0 = -22.53+77.10/-76.98 in units of ×10^-16 is wider than the GW170817-based bound |αT0|≲ few×10^-15. This comparison should be corrected because it is used to characterize the LVK result.
[§2.3] The sentence beginning 'Although the αi are largest at low redshifts...' ends with the incomplete clause 'starts making a more marked at higher redshifts.' Please complete the sentence and clarify the intended comparison between ansätze.
[§3.1] There are several typographical and grammatical errors, e.g. 'cosider' should be 'consider', and 'This, along with our results later on suggest' should be 'This, along with our results later on, suggests'. A careful proofreading pass is needed.
[Fig. 3 caption and §5.1] The relationship between Figure 3 and Figure 4 is confusing: Figure 3 does not show αT0, while the text says the purple contours 'represent the scenario where we wish to constrain both GR and cosmology' with flat priors on H0, αM0 and αT0. Please clarify whether αT0 is marginalized or fixed in each panel and harmonize the quoted posterior numbers between the text and the captions.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the ET 3σ claim is a self-consistency forecast from injected fiducial data, transparently conditional on the ΩΛ ansatz.

full rationale

The paper's central forecasts are sensitivity statements derived from mock data generated under an explicit fiducial model (αM0=1, αT0=2.699×10^-16, H0=70 km/s/Mpc). The likelihoods in eqs. 4.4–4.8 use the same propagation equations (eq. 2.8 for dGW and eq. 2.10 for arrival-time delay) that generated the simulated data; this is standard forecasting practice, in which the pipeline is tested on its ability to recover injected parameters rather than claiming an empirical detection. The paper explicitly labels the model as simulated, referring to 'our simulated Horndeski universe' in Section 6. The ΩΛ parametrisation (eq. 2.7) is used both to generate and to analyze the mock data, so the quantitative 3σ statement is conditional on that functional form; Section 6 acknowledges this ('Modifying the ansatz could change our results'), which frames the ansatz dependence as a robustness caveat rather than a circular reduction. The time-delay formula (eq. 2.10) is derived from the GW propagation equation in Appendix B, not assumed as the target result. Self-citations ([57], [34], [77]) are used for context and comparison and are not load-bearing; the DESI constraint [56] provides an external benchmark. The Section 5.1 statement that the αT0 posterior is 'one order of magnitude tighter than GW170817' appears inconsistent with the quoted posteriors, but this is an internal-consistency/correctness issue, not circularity. Overall, no prediction reduces to its inputs by construction.

Assumptions & free parameters 3 free parameters · 7 assumptions · 0 invented entities

The forecast depends on the injected Horndeski parameters and on several modeling choices (GRB geometry, distance-error model, duty cycle). No new entities are introduced; the α functions are existing theory parameters.

free parameters (3)

αM0 (fiducial value) = 1
Injected value of the Horndeski running Planck mass parameter in the mock data. The ET 3σ detection claim is a recovery of this injected value; a smaller true αM0 would weaken the detection.
αT0 (fiducial value) = 2.699e-16
Injected tensor speed excess parameter, selected within the GW170817 bound; used to generate time-delay data.
GRB reference luminosity L = 5e49 erg/s
Chosen from the fainter end of the short GRB luminosity distribution to be conservative; it sets how many simulated ET events have detectable GRBs (150/year).

assumptions (7)

domain assumption Horndeski gravity with the four α functions (αM, αT, αK, αB) describes cosmological modifications of GR; only αM and αT affect tensor perturbations and are considered.
Assumed throughout; the paper restricts to this class of theories and does not test beyond-Horndeski or DHOST alternatives (Section 2.1).
ad hoc to paper The redshift dependence of αM and αT follows the ΩΛ parametrisation αi(z) = αi0 ΩΛ(z)/ΩΛ0 (eq. 2.7).
This ansatz is chosen because it suppresses modified gravity at high redshift; the central 3σ forecast depends on this functional form (Section 2.3, Section 6 caveat).
domain assumption GW generation is identical to GR; modified gravity only affects propagation (friction and speed).
Stated in Section 2.2; excludes modifications to the inspiral waveform and emission.
domain assumption The cosmological background is ΛCDM with Ωm=0.3065 (Planck 2018).
Fixes the expansion history E(z); the α parameters only enter perturbatively (Section 2.2).
domain assumption GRB detection requires binary inclination ι<20° or ι>160° (jet opening angle ~10°).
Imposed in Section 2.5/3.1; determines the fraction of bright sirens with GRBs and the distance-inclination degeneracy breaking.
ad hoc to paper For the ET analysis, distance posteriors are Gaussian with fractional error A=7% for GRB events, and masses and inclination are fixed.
Simplifies the ET likelihood (eq. 4.8); the 7% value was computed with bilby for a 2000 Mpc event, but applied to all events.
domain assumption Observations run at 100% duty cycle for one year with complete EM follow-up for all GW events.
Stated in Section 4.1; inflates the expected event yield.

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Cite this review

Pith. "Pith review of A Bright Future? Prospects for Cosmological Tests of GR with Multimessenger Gravitational Wave Events." pith.science (2026). https://pith.science/paper/OSDCGPHB

@misc{pith2026250105560,
  author       = {Pith},
  title        = {Pith review of: A Bright Future? Prospects for Cosmological Tests of GR with Multimessenger Gravitational Wave Events},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OSDCGPHB}},
  note         = {Machine review of arXiv:2501.05560}
}

abstract

Further bright sirens - gravitational wave events with electromagnetic counterparts - are keenly awaited, but proving elusive. The exceptional event GW170817 had a profound impact on the landscape of viable cosmological extensions of General Relativity (GR); can we expect this kind of shift to be repeated in the next decade? In this work we will assess the potential constraints from bright sirens in the LIGO-Virgo-KAGRA O5 era and third generation detector era. We set up the statistical formalism for our constraints, and generate and analyse simulated data in the context of general scalar-tensor theories. We highlight the important role that gamma-ray burst detection has in breaking key parameter degeneracies. We find that the next ten bright sirens alone will not competitively constrain cosmological gravity, but that one year of third generation observations could confidently detect mild departures from GR, e.g. the Horndeski parameter $\alpha_{\rm M}\neq 0$ is detected at greater than $3\sigma$. This justifies investment in a broad range of methods for gravitational wave cosmology (dark sirens, bright sirens and cross-correlation with large-scale structure) to ensure tests of cosmological gravity advance in both the short-term and the long-term.

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