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Forecast for growth-rate measurement using peculiar velocities from LSST supernovae

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read This paper forecasts that LSST supernova peculiar velocities alone can measure the cosmic growth rate to 10 percent precision at low redshift, even when typing is photometric.

desk verdict A solid and honest LSST forecast paper whose headline 10% growth-rate precision is plausible but rests on a photometric classifier trained and tested on the same simulation, which no current test validates against real data. read the letter →

arxiv 2507.00157 v1 pith:LNEANPPP submitted 2025-06-30 astro-ph.CO

Damiano Rosselli , Bastien Carreres , Corentin Ravoux , Julian E. Bautista , Dominique Fouchez , Alex G. Kim , Benjamin Racine , Fabrice Feinstein
show 3 more authors
Bruno Sánchez Aurelien Valade The LSST Dark Energy Science Collaboration
This is my paper
classification astro-ph.CO PACS 98.80.-k
keywords peculiarvelocitiesgrowthratefσ8TypeIasupernovaeLSSTforecastmaximumlikelihoodphotometricclassificationstructuretestsofgravity
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

The paper's central claim is that the ten-year LSST supernova sample, used on its own, can measure the cosmic growth rate $f\sigma_8$ — the product of the linear growth rate of structure and the amplitude of matter fluctuations — to 10% precision in the low-redshift range $0.02 < z < 0.14$, using only the peculiar velocities of Type Ia supernovae. This is the forecast for the most realistic scenario, in which supernovae are typed photometrically by a neural network and the sample retains some contamination from non-Ia events. The authors build an end-to-end simulation — galaxy mocks with a correlated large-scale velocity field, the LSST observing strategy, detection and selection effects, light-curve fitting, and photometric classification — and recover the input $f\sigma_8$ without bias in every scenario they consider. The result matters because peculiar-velocity measurements give their strongest growth signal at low redshift, exactly where galaxy-clustering estimates of $f\sigma_8$ are limited by cosmic variance; if the forecast holds, LSST becomes an independent low-redshift probe of gravity and dark energy.

What carries the argument

The load-bearing object is the maximum-likelihood estimator for the peculiar-velocity field: a multivariate Gaussian likelihood whose covariance matrix adds per-supernova measurement errors to an analytical velocity covariance $C^{vv}$, built from the velocity-divergence power spectrum $P_{\theta\theta}$, a nonlinear model fitted to N-body simulations, and a small-scale damping term that models redshift-space distortions. Individual velocities are extracted from Hubble-diagram residuals through a first-order expansion that converts standardized distance-modulus residuals into line-of-sight peculiar velocities. Feeding this likelihood is a simulation stack — galaxy mocks from the Uchuu simulation supplying a correlated large-scale velocity field, the LSST Operations Simulator providing the ten-year observing calendar, difference-imaging detection efficiencies, and the SuperNNova classifier for photometric typing — which is what makes the forecast conditional on realistic survey behavior.

What would settle it

Apply the same classifier, the same quality cuts, and the same maximum-likelihood fit to the first years of real LSST data and measure the contamination fraction from a spectroscopically typed subsample. If the real contamination exceeds roughly 2%, or if the recovered $f\sigma_8$ in $0.02 < z < 0.14$ deviates from the value expected under the fiducial cosmology by more than the forecast uncertainty, the central claim fails.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is that realistic survey selections do not erase the peculiar-velocity signal carried by LSST supernovae. After adding saturation limits, a detection-efficiency model for difference imaging, host-galaxy spectroscopic redshift completeness from the DESI and 4MOST surveys, SALT3 light-curve fitting with quality cuts, and neural-network photometric classification, the maximum-likelihood analysis recovers the fiducial $f\sigma_8$ over $0.02 < z < 0.14$ without bias: 8% precision for an idealized fully spectroscopic sample, 9% when host redshifts come from DESI and 4MOST, and 10% in the most realistic photo-typed scenario, with per-bin errors near 14–18% in tomographic bins. The paper further maps where the method breaks: contamination below roughly 2% leaves the estimate unbiased, while above that level the Gaussian likelihood is no longer valid, the fitted standardization parameters drift, and some realizations return $f\sigma_8 \simeq 0$.

Load-bearing premise

The forecast stands or falls on whether the simulated LSST survey faithfully represents the real one — especially the assumed rates of different supernova types and the photometric classifier's real-world performance — because after quality cuts the simulated Photo-typed sample has only 0.02% contamination, which the paper itself notes is lower than previously seen and leaves uninvestigated, while its own contamination study shows the maximum-likelihood measurement becomes biased above roughly 2%.

Editorial extensions

If this is right

  • In the most realistic (Photo-typed) scenario, LSST supernova peculiar velocities measure $f\sigma_8$ at 10% precision over $0.02 < z < 0.14$, giving a low-redshift growth probe that complements redshift-space distortion constraints from DESI and Euclid.
  • Because the Spec-z scenario reaches 9% precision, host-galaxy spectroscopy from DESI and 4MOST improves the measurement only marginally, implying the probe does not require spectroscopic follow-up of every supernova.
  • The contamination study sets a concrete requirement for the analysis: keep non-Ia contamination below about 2%, beyond which the maximum-likelihood estimate becomes biased.
  • Tomographic bins with roughly 14–18% errors allow the growth index $\gamma$ to be constrained, offering a direct test of general relativity against alternative gravity models.
  • The survey-duration forecast shows precision improving from about 20% after the first year to roughly 12% after five years in the $0.02 < z < 0.14$ bin, making the probe competitive within the survey's nominal lifetime.

Reading between the lines

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

  • If the forecast holds, the same velocity field could be cross-correlated with galaxy density fields from DESI and 4MOST — a step the paper lists as future work — probably tightening low-redshift growth constraints beyond what velocities alone provide.
  • The 0.02% post-cut contamination is the fragile link: the paper flags it as lower than previously seen and uninvestigated, and its own tests show the method breaks at about 2%. A direct check is to measure the contamination of a spectroscopically confirmed subsample in early LSST data before trusting the 10% number.
  • Because the mocks come from a single $z=0$ snapshot, the forecast implicitly assumes no growth evolution inside $0.02 < z < 0.14$; a tomographic result inconsistent with the fiducial shape would be ambiguous between new growth physics and a limitation of the single-snapshot simulation.
  • The forecast's dependence on assumed supernova rates means first-year LSST rate measurements will likely move the predicted sample size; if the real rates of 91bg-like and Iax events are higher than assumed, contamination after classification rises and the 10% precision would degrade toward the paper's own break point.
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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

3 major / 5 minor

Summary. The paper presents a forecast for measuring the cosmic growth-rate parameter fσ8 using peculiar velocities of Type Ia supernovae from LSST. The authors build simulated LSST supernova light curves on top of the Uchuu UniverseMachine mocks, using a realistic observing strategy (OpSim), DIA detection efficiencies, host-galaxy spectroscopic redshift efficiencies from DESI and 4MOST, and photometric classification with SuperNNova. They consider three scenarios: a pure 'Full' sample, a 'Spec-z' sample with realistic host spectroscopy, and a 'Photo-typed' sample including machine-learning classification and contamination from non-Ia supernovae. Using a maximum-likelihood velocity-field estimator, they recover fσ8 in several redshift bins and report a 10% precision in 0.02<z<0.14 for the Photo-typed sample, 9% for Spec-z, and 8% for Full, with tomographic errors around 12–15%. They also test the effect of contamination and find that above ~2% the estimator becomes biased and can return fσ8≈0.

Significance. If the forecast is correct, LSST SNe Ia would provide an independent low-redshift growth-rate measurement that complements RSD surveys such as DESI and Euclid, and would be competitive with ZTF PV constraints at z<0.06. The paper's controlled recovery tests (Appendix C) are a genuine strength: random PV inputs return null results and true PV inputs recover the injected fσ8, demonstrating that the pipeline is internally consistent. The use of the Uchuu mocks and a realistic survey simulator is also a step beyond Fisher-matrix forecasts. The main weakness is that the headline Photo-typed scenario relies on a post-cut contamination of 0.021% that is produced by training and testing the classifier on the same simulation; the paper's own stress test (Sect. 5) shows the likelihood breaks above ~2% contamination. The realism of the classifier is therefore the load-bearing assumption for the 'most realistic' label.

major comments (3)
  1. [Sect. 2.7.3 and Sect. 5] The headline 10% precision in the Photo-typed scenario rests on a post-cut contamination of 0.021 ± 0.007% (Sect. 2.7.3). The paper's own contamination test (Sect. 5, Fig. 9) shows that the maximum-likelihood fit becomes biased above ~2% contamination and sometimes drives fσ8 to zero. The SNN classifier was trained and tested on the same simulation (Sect. 2.5), and the Parsnip cross-check (Appendix B) is also evaluated in-sample. The paper explicitly flags that the 0.02% contamination is 'lower than has been seen before' and that a 'proper investigation of this is beyond the scope of this work' (Sect. 2.7.3), while Sect. 2.3.4 states that all results 'strongly depend on the assumptions made for the simulation, especially on the rates for the different SN types'. Since a modest degradation of classifier performance to a contamination of ~0.5–2% would materially change the forecast, the central claim is not yet robust to out-of-sample classification. I recommend adding an out-of-sample validation (e.g., train on one Uchuu realization and test on another, or calibrate against DES/ZTF photometric classification performance) and, following the method of Sect. 5, presenting the expected fσ8 precision as a function of contamination.
  2. [Sect. 4.1 and Table 1] The redshift window 0.02<z<0.14 is chosen after inspecting the PV residuals shown in Fig. 6, and the same window is then applied to all samples. The low-redshift cut avoids saturation and the local peculiar-velocity field; the high-redshift cut avoids the growing PV bias. However, because the window is selected from the same simulated data that are used to quote the forecast, the paper should either justify the window from independent considerations (such as the saturation limit, the Hubble-flow criterion, and a pre-specified bias threshold from simulations) or quantify the sensitivity of the headline precision to the exact window boundaries. Additionally, the persistent recovery ratio of about 0.93 in the 0.06<z<0.10 bin across all three samples, with mean reduced chi-squared values around 1.2–1.3, is suggestive of a small uncorrected systematic (possibly a residual Malmquist-bias effect at z≈0.08) rather than pure sample variance; eight realizations are insufficient to distinguish these explanations.
  3. [Sect. 5] The contamination stress test constructs contaminated samples by applying SALT quality cuts to non-Ia SNe, rather than by using the photometric classifier (SNN). This is a reasonable first-order test, but it does not reproduce the redshift- and type-dependent misclassification patterns of a machine-learning classifier, which may preferentially retain faint 91bg-like or core-collapse SNe at particular redshifts. The ~2% threshold should therefore be understood as a property of the likelihood under a specific contamination composition, not as a universal guarantee that any contaminant fraction below 2% is safe. The statement in Sect. 4.4 that a 'low percentage of contamination in the HD does not bias fσ8 from PVs' would be stronger if supported by a contamination test that uses the actual SNN-selected contaminants at varying thresholds.
minor comments (5)
  1. [Sect. 3.2] The phrase 'Assuming that the velocity field is irrational' should read 'irrotational'; the intended meaning is that the velocity field is curl-free so that it can be written in terms of a divergence scalar.
  2. [Sect. 2.7.3] The sentence 'The low contamination can be a results of the fact that we are analyzing only low-redshift SNe' contains a grammatical error ('a results'), and the claimed explanation is not tested. Please rephrase and, if possible, provide a brief diagnostic (e.g., contamination as a function of redshift or SALT-fit properties).
  3. [Sect. 4.2 and Table 1] The text says 'the averages are always compatible with the fiducial value, except for the redshift range 0.06<z<0.1' and then repeats similar phrasing in Sects. 4.3 and 4.4. This repetition is unnecessary; a single statement that the same 0.06–0.1 bin shows a sub-2σ offset in all scenarios would be clearer.
  4. [Eq. (20) and surrounding text] The notation 'σ2 8,f id' and '(f σ8)/(f σ8)fid' is typeset awkwardly; please use a consistent subscript convention (e.g., 'fid') in both the equation and the text. Also, 'kmax = 1 hMpc−1' should include a space before 'hMpc−1'.
  5. [Appendix A] The approximation of the Roman K213 magnitude as WISE W1 for the 4MOST color cuts is stated and then dismissed with a test that changes the color cuts. Please report the outcome of that test quantitatively (e.g., the change in Rhost or in the final Spec-z sample size) so that the reader can assess the impact.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the paper is a self-contained Monte Carlo recovery forecast, with the input growth rate used only as fiducial normalization and recovery target.

full rationale

This paper is a forecasting and recovery study, not a claim to have measured f_sigma8 from real data, and its central result does not reduce to its inputs by construction. A peculiar-velocity field is injected into the LSST SN light-curve simulations from the Uchuu UniverseMachine N-body simulation (Sect. 2.1), with the input growth rate appearing only as the fiducial normalization (f_sigma8)_fid in Eq. (20) and as the recovery target in Table 1. The maximum-likelihood analysis of Sect. 3 fits the ratio (f_sigma8)/(f_sigma8)_fid together with the Hubble-diagram and nuisance parameters; the analytic covariance uses the external Bel et al. (2019) velocity-divergence power-spectrum model and Koda et al. (2014) RSD damping, not the Uchuu velocity field itself, so the recovery is a genuine test of the model against an independent N-body realization. Appendix C strengthens this by showing that random velocities return zero signal and true velocities recover the input. The photometric-classification step is the only place where the same simulation inputs are used on both sides: SNN is trained on a simulation built with the same SED templates, rates, and selections as the test sample (Sect. 2.5), and the resulting 0.021% contamination is an in-sample validation. That is a realism and calibration risk for the forecast, not a circular reduction of the f_sigma8 measurement, because the classifier output feeds only the sample selection and the f_sigma8 likelihood does not reuse the classifier as an input. Self-citations to Carreres et al. (2023, 2024, 2025) and Ravoux et al. (2025) supply the likelihood, covariance, and FLIP machinery, but the underlying derivations are also given in external references (Hui & Greene 2006; Johnson et al. 2014) and the method is independently exercised in Appendix C. No equation in the paper is equivalent to its own input by construction, and no fitted parameter is renamed as a prediction.

Assumptions & free parameters 4 free parameters · 8 assumptions · 0 invented entities

The paper is a simulation-based forecast; it introduces no new physical entities. The analysis fits standard nuisance parameters (sigma_v, sigma_M, sigma_u, alpha, beta, M0) and relies on several domain assumptions about the fidelity of the simulations, most notably the photometric classification performance and the Uchuu velocity field.

free parameters (4)
  • sigma_v (velocity scatter nuisance) = not quoted in the paper; shown in Fig. D.1
    Added to the diagonal of the covariance matrix (Eq. 12) to absorb imperfect modeling of nonlinear scales; its fitted value affects the total error budget and thus the forecast precision.
  • sigma_M (SN intrinsic scatter) = 0.12 mag input; fitted per bin
    Intrinsic scatter in the distance modulus used in Eq. (9) for PV errors; fitted simultaneously with fσ8 and affects the recovered uncertainties.
  • sigma_u (RSD damping scale) = prior-dominated (Carreres et al. 2023)
    Scale in the Koda et al. (2014) damping function (Eq. 19) in the velocity covariance; reported as prior-dominated, but its choice affects the covariance amplitude.
  • alpha, beta, M0 (Tripp standardization) = alpha=0.14, beta=2.9, M0=-19.12 input; fitted per bin
    Tripp standardization parameters used to estimate PVs from distance-modulus residuals; fitted in the likelihood in each redshift bin, and their bias at high z (Appendix D) is checked but not propagated into the forecast.
assumptions (8)
  • domain assumption The peculiar velocity field is drawn from a multivariate Gaussian distribution (Eq. 7).
    The likelihood in Sect. 3 assumes Gaussianity; Appendix C validates recovery on mocks but does not test Gaussianity against non-Gaussian velocity fields.
  • domain assumption The nonlinear velocity-divergence power spectrum Pθθ of Bel et al. (2019) describes the velocity field on the scales used (kmax=1 h/Mpc).
    Used in Eq. (20) to build the covariance; coefficients are fitted to simulations in the cited work, and validation is inherited from Carreres et al. (2023).
  • domain assumption The RSD damping function Du(k) of Koda et al. (2014), Eq. (19), correctly models the effect of using observed rather than cosmological redshifts.
    Adopted in the covariance model; any mismatch alters the predicted signal amplitude and hence the forecast error.
  • domain assumption The Uchuu UniverseMachine z=0 snapshot provides a representative galaxy and velocity field for observers in 8 sub-boxes out to z~0.14.
    Single snapshot with no redshift evolution (Sect. 2.1); used for host galaxies and true PVs.
  • domain assumption SN Ia light curves and standardization follow SALT3 and the Tripp relation with the stated inputs (alpha=0.14, beta=2.9, M0=-19.12, sigma_M=0.12).
    Sect. 2.3.1; the same model is used to generate and fit the light curves, which may overstate the realism of the distance estimates.
  • ad hoc to paper SuperNNova trained on the simulation pipeline will achieve similar efficiency and contamination on real LSST data.
    Sect. 2.7.3 reports 0.02% contamination after quality cuts, acknowledged as lower than previously seen and not investigated; the paper's own Sect. 5 shows >2% contamination biases the measurement.
  • ad hoc to paper DESI BGS and 4MOST host-spectroscopic efficiencies computed from cosmoDC2/OpenUniverse are accurate, including approximating Roman K213 as WISE W1 for 4MOST color cuts.
    Appendix A; the approximation is stated as minor compared to magnitude cuts but is a simulation-based assumption.
  • domain assumption Spectroscopic redshifts have negligible uncertainty for PV estimation (Sect. 2.6).
    Stated at the start of Sect. 2.6; if host-redshift errors are non-negligible, the PV errors in Eq. (11) are underestimated.

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Cite this review

Pith. "Pith review of Forecast for growth-rate measurement using peculiar velocities from LSST supernovae." pith.science (2026). https://pith.science/paper/LNEANPPP

@misc{pith2026250700157,
  author       = {Pith},
  title        = {Pith review of: Forecast for growth-rate measurement using peculiar velocities from LSST supernovae},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LNEANPPP}},
  note         = {Machine review of arXiv:2507.00157}
}
abstract

In this work, we investigate the feasibility of measuring the cosmic growth-rate parameter, $f\sigma_8$, using peculiar velocities (PVs) derived from Type Ia supernovae (SNe Ia) in the Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST). We produce simulations of different SN types using a realistic LSST observing strategy, incorporating noise, photometric detection from the Difference Image Analysis (DIA) pipeline, and a PV field modeled from the Uchuu UniverseMachine simulations. We test three observational scenarios, ranging from ideal conditions with spectroscopic host-galaxy redshifts and spectroscopic SN classification, to more realistic settings involving photometric classification and contamination from non-Ia supernovae. Using a maximum-likelihood technique, we show that LSST can measure $f\sigma_8$ with a precision of $10\%$ in the redshift range $ 0.02 < z < 0.14 $ in the most realistic case. Using three tomographic bins, LSST can constrain the growth-rate parameter with errors below $18\%$ up to $z = 0.14$. We also test the impact of contamination on the maximum likelihood method and find that for contamination fractions below $\sim 2\%$, the measurement remains unbiased. These results highlight the potential of the LSST SN Ia sample to complement redshift-space distortion measurements at high redshift, providing a novel avenue for testing general relativity and dark energy models.

Figures

Figures reproduced from arXiv: 2507.00157 by the authors.

Figure 1
Figure 1. LSST survey footprint showing the number of visits [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. SN/host redshift efficiencies, Rhost, as a function of redshift for each type of SN in the simulation. The top panel shows the efficiencies for DESI BGS survey, the cen￾tral panel shows the ones for 4MOST CRS BG survey and the bottom panel shows the efficiencies for 4MOST 4HS surveys. The gray shaded area shows the redshift range of interest for LSST PV measurement. ing sample. We define t0 as the time of the observ… view at source ↗
Figure 4
Figure 4. Redshift distribution (top panel), comoving density [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figures from the paper (5 more)
Figure 6
Figure 6. Figure 6: Difference between estimated PVs (vp) and true PVs (vp,true) as a function of the observed redshift for the Full sample. The solid line grey lines shows the residual for each of the 8 LSST realizations, the red points are the means over the 8 mocks, and the blue points…
Figure 5
Figure 5. Figure 5: Hubble diagram residuals as a function of the ob [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]
Figure 7
Figure 7. Figure 7: Results of fσ8 measurements for all the scenarios in different redshift bins. Left: Full sample, centre: Spec-z sample, and right: Photo-typed sample. For each scenario, the top panel shows the results of the fit for each of the 8 LSST realizations together with the me…
Figure 9
Figure 9. Figure 9: fσ8 fit results (top panel) and relative error (bottom panel) as a function of the sample contamination fraction for the redshift bin 0.02 < z < 0.14. The blue points show the results for the Spec-z sample, the orange ones for the Photo-typed sample, and the red ones f…
Figure 10
Figure 10. Figure 10: Growth-rate parameter as a function of redshift. [PITH_FULL_IMAGE:figures/full_fig_p014_10.png]

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    2025 arXiv

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