{"id":"de854c38-6c31-4183-a977-8d8e21448034","arxiv_id":"2502.08385","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":8,"one_line_summary":"A field-level Bayesian model of non-linear peculiar velocities recovers the true Hubble constant from simulated type Ia supernovae, and ignoring velocities biases H0 by only 0.4 ± 0.5 km/s/Mpc, arguing the Hubble tension is not a local velocity artifact.","lead":"This paper builds a Bayesian statistical model that uses realistic simulated supernovae to test whether the local motions of galaxies distort measurements of the Hubble constant. It finds the distortion is small, about 0.4 km/s/Mpc, suggesting the Hubble tension is not caused by local velocity effects.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Validation is self-referential: mock 'true' velocities come from the same 2M++ posterior used in the analysis, so the 0.4 km/s/Mpc bias result is not yet tested against an independent non-linear velocity field.","rationale":"The central claim has two parts: (1) the Bayesian hierarchical model recovers H0 from simulated SNe with peculiar velocities, and (2) non-linear velocity dynamics are unlikely to explain the H0 tension because ignoring them changes H0 by only ~0.4 km/s/Mpc. Part (1) is validated in a self-consistent way: mock data are drawn from the same 2M++ velocity posterior that supplies the model's velocity distribution, so the recovery test checks the statistical machinery but not the fidelity of the velocity reconstruction. Part (2) is more exposed: the 0.023<z<0.046 bias is computed using a single 2M++ realisation as the true velocity field, with no independent cross-check in that redshift range. The paper does test the z<0.023 recovery with SIBELIUS N-body velocities and finds consistency, which is genuine evidence that the pipeline is robust to a more non-linear velocity model at low z; however, that test is not applied to the main bias result. The admitted need to model sub-2.65 Mpc/h dispersion externally (Section 2.3) further weakens the claim that all relevant non-linear velocity effects have been quantified. These issues do not invalidate the method or the small-bias conclusion, but they make the central astrophysical conclusion conditional on the fidelity of the 2M++ reconstruction at the scales and redshifts used. Hence CONDITIONAL remains the appropriate verdict, and no change to the reader's verdict is needed.","tokens_in":17312,"tokens_out":8404,"duration_ms":88710,"concrete_test":"Repeat the Section 3.2 'wrongly ignore peculiar velocities' analysis at 0.023<z<0.046 with mock data generated from the SIBELIUS-DARK full N-body peculiar velocities at the simulated host positions, which include velocity dispersion below 2.65 Mpc/h and are produced by a full gravity solver, instead of the 2M++ velocities. Keep the same N_SN ~ 200, sigma_mu = 0.13 mag, and sigma_z = 0.001 settings. If the inferred <Delta H/H0> shifts by more than ~1 km/s/Mpc, the conclusion that non-linear velocity dynamics cannot explain the H0 tension is not robust; if it remains 0.4 ± 0.5 km/s/Mpc, the concern is settled. As a secondary check, compare the 2M++ posterior-mean velocity field to observed peculiar velocities from independent data at the same locations to look for systematic bias.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 2.5 generates mock redshifts and distance moduli using the 2M++ BORG peculiar velocity realisation that matches the SIBELIUS initial conditions, with covariance estimated from ~240 realisations of the same reconstruction. Section 2.3 then uses the mean of those same realisations and the same covariance as the model. The z<0.023 recovery test is therefore a prior-predictive self-consistency check: it verifies the Bayesian machinery but cannot detect a systematic error in the reconstructed velocity field. The central quantitative claim, that ignoring peculiar velocities biases H0 by only 0.4±0.5 km/s/Mpc at 0.023<z<0.046 (Section 3.2), relies entirely on this single 2M++ realisation as the truth. The only independent cross-check with full N-body SIBELIUS velocities is reported for the z<0.023 recovery (Section 3.2), not for the z>0.023 bias measurement. The paper itself concedes (Section 2.3) that small-scale velocity dispersion below 2.65 Mpc/h must be modelled externally for real data, so the 0.4 km/s/Mpc result does not yet rule out a larger bias from unmodelled non-linear velocity dynamics at smaller scales or from external tidal fields beyond the 200 Mpc simulation volume.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper develops a Bayesian hierarchical model for inferring the Hubble constant H0 from type Ia supernova (SNIa) redshift and distance-modulus data, incorporating the non-linear peculiar velocity field of the local Universe as reconstructed from the 2M++ catalogue with the BORG algorithm. The velocity information enters through a per-SN mean and covariance, and the model marginalises analytically over unknown cosmological and peculiar redshifts, using a series of approximations to make the high-dimensional integral tractable. The method is tested on mock SNIa catalogues generated from the SIBELIUS-DARK simulation with GALFORM-based SNIa rates: at 0.023<z<0.046, ignoring peculiar velocities is reported to bias H0 by only 0.4±0.5 km/s/Mpc, while at z<0.023 the model is claimed to recover the ground-truth H0 (67.77 km/s/Mpc) even when a wrong fiducial H0 is assumed. The authors conclude that the Hubble tension is unlikely to originate in unaccounted-for non-linear velocity dynamics.","tokens_in":17650,"tokens_out":5183,"duration_ms":58585,"significance":"The paper is a well-structured methods contribution with several genuine strengths: it uses a constrained simulation of the local Universe rather than random N-body simulations; it builds SNIa host populations from individual galaxy star-formation histories; and it propagates the full non-linear velocity covariance at the locations of SNe, going beyond the common 250 km/s dispersion approximation. The analytic marginalisation in Equations (23)-(42) is a useful step toward field-level H0 inference and could enable inclusion of z<0.023 SNe, which are currently discarded. If the method survives external validation, the paper will be an important addition to the literature on local velocity systematics and H0. However, the current validation is largely a self-consistency test: mock data are generated from one realisation of the same 2M++ posterior whose mean and covariance are then used in the analysis. The main quantitative claim (0.4±0.5 km/s/Mpc bias) and the stronger conclusion about the H0 tension therefore do not yet have the independent support they would need to be fully load-bearing.","major_comments":[{"comment":"The mock-data validation is self-referential. Section 2.5 step (iv) draws observed peculiar redshifts from a Gaussian with mean equal to one 2M++ realisation and covariance C, while the analysis in Section 2.3 uses the mean peculiar redshift across the same set of ~240 realisations and the same covariance. The 0.4±0.5 km/s/Mpc bias measurement at 0.023<z<0.046 is therefore a test that the Bayesian machinery is internally consistent under the assumption that the 2M++ posterior is the correct description of the velocity field. It cannot detect a systematic error in the reconstructed velocity field, such as a bias from external tidal fields or from inaccurate small-scale velocity modelling. The one independent cross-check mentioned, using SIBELIUS gravity-solver velocities, is reported only for the z<0.023 recovery (Section 3.2, final paragraph) and no quantitative result is given there. The authors should repeat the 0.023<z<0.046 bias measurement with SIBELIUS velocities as the true velocity field, or with an external velocity field, and report the resulting bias; without this, the central quantitative claim is not yet validated against an independent non-linear velocity prediction.","section":"Section 2.5 and Section 2.3 (mock generation and covariance)"},{"comment":"The analytic posterior rests on three unquantified approximations: the Doppler term replaces the true peculiar redshift by its mean in Equation (11); the z_c^2 prior is approximated by ztilde^2 and the lower integration limits are extended to -infinity in Equation (31); and the distance modulus is linearised around ztilde in Equation (27). The text states that these have 'very little impact' or 'insignificant impact', but no error estimate or comparison with an exact integration is provided. These approximations are most stressed precisely in the z<0.023 regime that the paper aims to open up. The authors attempted nested sampling but found it non-robust, so the analytic result has not been validated against a high-dimensional integration. A quantitative check, for example a comparison on a few reduced-dimension mocks or a controlled integration on a subset of SNe, is needed to demonstrate that the approximations do not bias the recovered H0.","section":"Section 2.4, Equations (11), (23), (30)-(31)"},{"comment":"The conclusion that 'it is unlikely that the H0 tension originates in unaccounted-for non-linear velocity dynamics' is stronger than the evidence presented. Section 2.3 states that the 2M++ reconstruction is trusted only above 2.65 Mpc/h and that small-scale velocity dispersion must be modelled externally for real data; Section 4 also mentions possible peculiar velocities sourced outside the 200 Mpc volume. The paper does not estimate the size of these missing contributions. Even if the internal self-consistency test were clean, the result would only bound the bias from the modelled scales and internal dynamics, not from all unaccounted-for velocity dynamics. The conclusion should be rephrased to state that, within the modelled scales and the 2M++ reconstruction, no significant velocity-induced bias is found, rather than making a global statement about the origin of the H0 tension.","section":"Section 4 and Section 2.3 (conclusions versus stated limitations)"},{"comment":"Figure 5 shows nine individual H0 posteriors, several of which have MAP values around 1-2 sigma from the ground truth (e.g., panels e and f). The paper states that 100 mock datasets were checked and found consistent with the ground truth, but no summary statistics are given. The authors should report the distribution of MAP values across the 100 datasets (mean offset, scatter, and fraction within 1 sigma) to demonstrate that the quoted per-dataset uncertainties are well calibrated and that the consistency claim is not based on a selected subset.","section":"Section 3.2, Figure 5"}],"minor_comments":[{"comment":"The caption contains a typo: 'Flowchart of the the Bayesian hierarchical model' should read 'Flowchart of the Bayesian hierarchical model'.","section":"Figure 2 caption"},{"comment":"The definition and sign convention for alpha_B should be clarified. As written, Equation (6) equates alpha_B to log(1+Delta H/H0), but alpha_B is defined in Equation (5) as a Hubble-diagram intercept; the relationship between the two should be stated explicitly to avoid confusion.","section":"Equations (5)-(6)"},{"comment":"The statement that the covariance matrices are 'robust to this number' of 240 realisations is not supported by a convergence test. A short figure or a quantitative stability check would strengthen the claim that Nsim is sufficient.","section":"Section 2.3"},{"comment":"In Figure 3(c), the highest-mass bin of strongly star-forming galaxies is stated to contain very few members, but the actual number is not given. Reporting the bin count would help readers judge the significance of the discrepancy.","section":"Section 3.1, Figure 3"},{"comment":"The patch contributions shown in Figure 4(b) appear to have no uncertainty estimates. Given the small number of SNe per patch (0.7-4.2 sources), error bars or a statement that the values are noise-dominated should be added.","section":"Section 3.2, Figure 4(b)"},{"comment":"The caveat that 'It remains to be checked against real data whether the more accurate velocity modelling ... will yield results on H0 at z<0.023 consistent with existing studies' is an important qualification and should be reflected in the abstract or conclusion, since the current abstract makes a stronger statement about recovering ground-truth H0 and ruling out velocity explanations of the tension.","section":"Section 4"}],"recommendation":"major_revision","confidential_remarks":"The paper is a promising methods contribution, but the editors should be aware that the central quantitative claim is currently a prior-predictive self-consistency check rather than an independent validation. The requested additions (external-velocity cross-check, quantified approximation errors, and a calibration summary for the 100 mocks) are feasible within the scope of the paper and would substantially raise its impact. The manuscript is appropriate for MNRAS subject to those revisions."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nWhat is actually new: Tsaprazi and Heavens take the Bayesian field-level treatment of peculiar velocities for H0 from SNe Ia, previously done with linear velocity correlations (Carreres et al. 2024, Peterson et al. 2022), and extend it to the full non-linear velocity covariance from the 2M++ BORG reconstruction. They build on the SIBELIUS-DARK constrained simulation with GALFORM galaxy formation, so the SN hosts sit in realistic large-scale structure. The paper is a solid methodological extension, and the main quantitative result — ignoring peculiar velocities biases H0 by 0.4 ± 0.5 km/s/Mpc at 0.023 < z < 0.046 — is plausible and consistent with earlier work (Odderskov et al. 2016, Wu & Huterer 2017). They also show the method recovers the true H0 for z < 0.023 SNe, which are normally discarded.\n\nThe SNIa rate modelling is careful: they compare host properties to SDSS-II data, show the rate model matches observed trends, and check that uniform rates give the same velocity-bias result. That is a useful robustness test. The analytic derivation is transparent about the approximations it makes, and the authors note where they have tested insensitivity.\n\nThe main soft spot is the validation design. Mock data are generated using the 2M++ peculiar velocity realisation that matches the SIBELIUS initial conditions, and the analysis uses the mean and covariance of ~240 realisations from the same reconstruction. So the H0 recovery is a prior-predictive self-consistency check: it verifies the machinery but cannot detect a systematic error in the reconstructed velocity field. The z > 0.023 bias measurement relies on this single 2M++ realisation as truth; the independent SIBELIUS full N-body velocities are only used for the z < 0.023 test. The paper itself concedes that small-scale velocity dispersion below 2.65 Mpc/h must be modelled externally for real data, which limits the force of the conclusion that non-linear velocities do not explain the Hubble tension. That conclusion is probably right — it matches independent evidence — but this particular test does not nail it.\n\nThe analytic approximations are stated but their errors are not quantified. The authors say the final posterior is insensitive, and the z^2 prior check is mentioned, but a referee should ask for a concrete quantification. Also, no code or data are released, only available on request, which hampers reproducibility.\n\nOverall, this is a well-executed extension worth publishing. It deserves a serious referee. The main revisions should address the self-referential validation explicitly and add a quantitative assessment of the approximation errors. It would strengthen the paper to run the z > 0.023 bias test with SIBELIUS velocities as truth, even if the analysis covariance remains 2M++; that would be a genuinely independent cross-check.","headline":"A clean extension of field-level peculiar-velocity inference to the non-linear 2M++ covariance, with a self-consistent mock validation that stops short of an independent test of the velocity reconstruction.","tokens_in":18171,"tokens_out":2847,"would_cite":true,"duration_ms":29707,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A field-level velocity model recovers H0 from low-redshift supernovae and removes cosmic flows as the cause of the Hubble tension.","keywords":["type Ia supernovae","Hubble constant tension","peculiar velocities","Bayesian hierarchical model","local Universe reconstruction","2M++ survey","cosmic large-scale structure","supernova rate modelling"],"falsifier":"Apply the same pipeline to real low-redshift SNeIa with independent peculiar-velocity measurements, such as host-galaxy distances from other distance indicators; if including $z<0.023$ supernovae moves the inferred $H_0$ by substantially more than the $\\sim 0.5$ km s$^{-1}$ Mpc$^{-1}$ implied by the mocks, the reconstruction is not capturing the relevant velocity field.","tokens_in":17082,"feed_emoji":"🌌","tokens_out":5770,"duration_ms":55888,"temperature":0.7,"pith_summary":"The paper sets out to test whether the local pattern of non-linear peculiar velocities, rather than new physics, could be responsible for the Hubble constant tension. It generates mock type Ia supernova samples inside a constrained simulation of the local Universe and infers $H_0$ with a Bayesian hierarchical model that marginalises over each supernova's unknown cosmological redshift and peculiar velocity, using the mean and covariance of reconstructed velocity fields from the 2M++ catalogue. With simulated data, the model recovers the input $H_0$ even for supernovae below $z=0.023$, the regime that is normally discarded. When peculiar velocities are ignored, the inferred $H_0$ increases by only $\\sim 0.4 \\pm 0.5$ km s$^{-1}$ Mpc$^{-1}$ in the range $0.023 < z < 0.046$. The authors conclude that unaccounted-for non-linear velocity dynamics are unlikely to explain the $H_0$ tension.","feed_headline":"Peculiar velocities barely shift local H0, mocks show","feed_subtitle":"Field-level velocity model recovers true H0 and lets low-redshift supernovae join the analysis.","key_machinery":"The central object is a Bayesian hierarchical model in which each observed redshift and distance modulus is treated as a noisy measurement of an unknown cosmological redshift $z_c$ and an unknown peculiar redshift $z_p$, with $z_p$ tied to the 2M++ reconstruction through a multivariate Gaussian whose covariance is the Hartlap-corrected sample covariance across $\\sim 240$ forward-modelled velocity realisations. The key analytical step is integrating out $z_c$ and $z_p$ to leave a one-dimensional Gaussian posterior for $5\\alpha_B$ (the Hubble-diagram intercept), so the final $H_0$ estimate is a weighted combination of per-supernova estimates whose weights account for the non-linear velocity correlations.","core_discovery":"On the paper's own terms, the central discovery is that a field-level treatment of non-linear peculiar velocities, drawn from the Bayesian 2M++ reconstruction, removes low-redshift velocity systematics as a viable explanation of the Hubble tension. The authors build realistic SNIa mocks by placing supernovae in the SIBELIUS-DARK constrained simulation according to GALFORM star-formation histories, then fit them with a hierarchical model that propagates the full non-linear velocity covariance into the $H_0$ posterior. The model reproduces the ground-truth $H_0$ when applied to mocks that include $z<0.023$ supernovae, and it yields only a minimal $H_0$ shift when peculiar velocities are ignored at $0.023<z<0.046$. This opens the door to using low-redshift supernovae, currently excluded, in $H_0$ measurements.","pith_inferences":["If the result carries over to real data, extending $H_0$ samples to $z\\sim0$ could change the local value's error budget and shift the comparison with early-Universe estimates.","The analytic marginalisation over $z_p$ and $z_c$ could be applied to other low-redshift distance indicators, such as gravitational-wave standard sirens, wherever a reconstructed peculiar-velocity covariance is available.","Because the mocks use one 2M++ realisation as truth and the mean field for analysis, the method's success depends on the reconstruction's resolution; surveys that resolve smaller-scale velocity dispersion could reveal a larger bias than reported here.","The patch decomposition hints that any residual velocity systematic would show up first in the directions of massive superclusters, where the weighted $H_0$ offsets are largest."],"forward_implications":["Supernovae below $z=0.023$ can be included in $H_0$ analyses instead of being cut, reducing sample variance.","Ignoring peculiar velocities biases $H_0$ by only $0.4\\pm0.5$ km s$^{-1}$ Mpc$^{-1}$ at $0.023<z<0.046$, so velocity systematics do not account for the reported Hubble tension.","The per-host SNIa rate model is a secondary ingredient for velocity studies, since uniform rates give the same $H_0$ shift.","More velocity realisations from future reconstructions will allow the contribution of individual superclusters, such as Hydra-Centaurus and Shapley, to be pinned down precisely."],"supporting_citations":[{"why":"Supplies the Bayesian 2M++ reconstruction whose non-linear velocity mean and covariance drive both the mocks and the analysis.","marker":"Jasche & Lavaux 2019"},{"why":"Provides the constrained SIBELIUS simulation whose initial conditions reproduce the local large-scale structure used to host the mock SNe.","marker":"Sawala et al. 2022"},{"why":"Supplies the SIBELIUS-DARK galaxy catalogue and GALFORM star-formation histories from which SNIa rates are derived.","marker":"McAlpine et al. 2022"},{"why":"Gives the delay-time distribution and Poisson sampling scheme used to place mock supernovae in galaxies.","marker":"Wiseman et al. 2021"},{"why":"Provides the debiased covariance estimate that converts the sample velocity covariance into the invertible matrix used in the posterior.","marker":"Hartlap et al. 2007"},{"why":"Establishes the linear peculiar-velocity correlation effect on alpha_B that this paper extends to the non-linear field level.","marker":"Carreres et al. 2024"},{"why":"Quantifies the impact of non-linear velocities in random N-body simulations, the comparison point for the constrained-simulation result.","marker":"Odderskov et al. 2016"},{"why":"Earlier framework marginalising peculiar velocities in H0 inference; the paper's Equation 14 is compared against its Equation 10.","marker":"Peterson et al. 2022"}],"fun_headline_variants":["Peculiar velocities don't explain Hubble tension","Field-level velocity model recovers true H0 in mocks","Low-redshift SNe included with new velocity model","H0 intact: non-linear velocities rule out as tension source","Simulated SNe show negligible velocity bias on H0"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole argument rests on the 2M++ Bayesian reconstruction being an accurate description of the true non-linear peculiar velocity field at its 2.65 Mpc/h resolution, with a covariance that faithfully captures the reconstruction's uncertainty.","fun_headline_variants_meta":{"raw":{"variants":["Peculiar velocities don't explain Hubble tension","Field-level velocity model recovers true H0 in mocks","Low-redshift SNe included with new velocity model","H0 intact: non-linear velocities rule out as tension source","Simulated SNe show negligible velocity bias on H0"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000683,"raw_usage":{"total_tokens":3125,"prompt_tokens":992,"completion_tokens":2133,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":608,"completion_tokens_details":{"reasoning_tokens":2052}},"tokens_in":608,"tokens_out":2133,"duration_ms":16664,"temperature":1.0,"reasoning_tokens":2052,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-08T05:17:11.573723+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Apply the same pipeline to real low-redshift SNeIa with independent peculiar-velocity measurements, such as host-galaxy distances from other distance indicators; if including $z<0.023$ supernovae moves the inferred $H_0$ by substantially more than the $\\sim 0.5$ km s$^{-1}$ Mpc$^{-1}$ implied by the mocks, the reconstruction is not capturing the relevant velocity field.","supporting_citations":[{"cited_title":"H., Frenk C","cited_arxiv_id":null,"evidence_quote":"Provides the constrained SIBELIUS simulation whose initial conditions reproduce the local large-scale structure used to host the mock SNe."},{"cited_title":"M., Hannestad S., 2016, @doi [ ] 10.1088/1475-7516/2016/02/001 , https://ui.adsabs.harvard.edu/abs/2016JCAP...02..001O 2016, 001","cited_arxiv_id":null,"evidence_quote":"Quantifies the impact of non-linear velocities in random N-body simulations, the comparison point for the constrained-simulation result."}],"review_version":1}