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arxiv: 2606.23651 · v1 · pith:VEZVTYABnew · submitted 2026-06-22 · 🌌 astro-ph.CO

Revisiting the 'Lensing is Low' Problem with UNIONS

Martine C. T. Campbell , Jack Elvin-Poole , Michael J. Hudson , Thomas de Boer , Sacha Guerrini , Fabian Hervas-Peters , Hendrik Hildebrandt , Martin Kilbinger
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Eugene A. Magnier Alan W. McConnachie Charlie T. Mpetha Romain Paviot Ludovic Van Waerbeke Anna Wittje
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Pith reviewed 2026-06-26 07:16 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords galaxy-galaxy lensingBOSS CMASSUNIONSlensing is lowhalo occupation distributiongalaxy clusteringcosmology
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The pith

New UNIONS measurements find no significant lensing is low effect for BOSS CMASS galaxies.

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

The paper uses background galaxy shapes from the UNIONS survey to measure the galaxy-galaxy lensing signal around BOSS CMASS galaxies over 2650 square degrees of overlap. It builds a halo occupation distribution model and fits it jointly to the lensing signal plus the galaxies' clustering signal on a wide range of scales. Unlike earlier analyses, these joint fits show no large mismatch between the observed lensing amplitude and the amplitude expected from the clustering data under standard cosmology. The best agreement instead comes from allowing a modest reduction in the overall amplitude of the matter power spectrum relative to Planck values. The analysis stresses that measurements on large scales, rather than only small scales, are what limit the size of any remaining discrepancy.

Core claim

Using high-quality imaging from the UNIONS survey, we obtain precise galaxy-galaxy lensing measurements around BOSS CMASS galaxies. When a halo occupation distribution model is fitted jointly to both the lensing and clustering signals, the data show no significant lensing is low effect, in contrast to previous work. The best joint fits are achieved by decreasing the amplitude of the matter power spectrum slightly relative to Planck cosmological parameters. Two models describe the observables similarly well: one with free HOD and cosmological parameters, and one that also frees feedback parameters. Large scales play an important role in constraining the effect.

What carries the argument

Halo occupation distribution (HOD) model that parametrizes how galaxies occupy dark matter halos and is fitted jointly to galaxy-galaxy lensing and galaxy clustering signals.

If this is right

  • Joint HOD fits to lensing and clustering can be performed without a large residual mismatch in the CMASS sample.
  • A modest decrease in the amplitude of the matter power spectrum relative to Planck values improves the joint fit.
  • Both an HOD-plus-cosmology model and an HOD-plus-cosmology-plus-feedback model describe the data comparably well.
  • Including large-scale measurements is necessary to properly constrain any lensing is low discrepancy.

Where Pith is reading between the lines

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

  • Similar wide-area lensing data on other spectroscopic samples could test whether the absence of a strong discrepancy is specific to CMASS or more general.
  • The emphasis on large scales suggests that future analyses of galaxy-galaxy lensing should ensure sufficient survey overlap at those scales rather than focusing only on small-scale modeling.
  • A slight downward shift in the matter power spectrum amplitude to match the data could be checked against independent probes such as the full CMB power spectrum or weak lensing surveys.

Load-bearing premise

The halo occupation distribution model is sufficient to describe both the galaxy clustering and galaxy-galaxy lensing signals across a wide range of scales.

What would settle it

If the measured galaxy-galaxy lensing amplitude around CMASS galaxies is 20-40 percent lower than the prediction from a clustering-only HOD fit that assumes Planck cosmology, the claim of no significant lensing is low effect would be falsified.

Figures

Figures reproduced from arXiv: 2606.23651 by Alan W. McConnachie, Anna Wittje, Charlie T. Mpetha, Eugene A. Magnier, Fabian Hervas-Peters, Hendrik Hildebrandt, Jack Elvin-Poole, Ludovic Van Waerbeke, Martine C. T. Campbell, Martin Kilbinger, Michael J. Hudson, Romain Paviot, Sacha Guerrini, Thomas de Boer.

Figure 1
Figure 1. Figure 1: Effective redshift distribution (shifted by the mean SOM bias, see Section 3.1) of UNIONS ShapePipe v1.4.5 galaxies (yellow) compared to the CMASS redshift distribution (blue) without any redshift cuts. Vertical black lines indicate the CMASS redshift cuts of 𝑧 = 0.43 and 𝑧 = 0.7. within the CFHTLenS W3 field. A self-organizing map (SOM; Ko￾honen 1982; Masters et al. 2015) is then trained on a spectroscopi… view at source ↗
Figure 3
Figure 3. Figure 3: CMASS GGL signal. Orange circles show our measurements using UNIONS ShapePipe v1.4.5 source galaxies with no correction for 𝑚-bias. Purple diamonds show results from L17 using sources from the CFHT Stripe 82 Survey (CS82; Moraes et al. 2014; Chalela et al. 2018) and CFHTLenS. Orange circles with black borders indicate measurements without the boost factor. Only statistical 1𝜎 errors are shown in this plot.… view at source ↗
Figure 4
Figure 4. Figure 4: Correlation matrix computed from the ΔΣ covariance matrix. By construction, every matrix element must have a value between -1 and 1. Small￾scale 𝑟p bins are uncorrelated with other bins, as shape noise dominates on these scales. Large-scale bins are mildly correlated due to LSS. patches, ˆ𝑓 (𝑘) 𝑖/ 𝑗 is the estimator’s evaluation when omitting the 𝑘th jack￾knife region, and ˆ𝑓 𝑖/ 𝑗 is the mean evaluation ac… view at source ↗
Figure 5
Figure 5. Figure 5: The final 𝑤p covariance matrix used for parameter estimation in￾cludes additional sources of uncertainty. First, we associate a 10% un￾certainty with our measurement of 𝑤t , followingReid et al.(2014). To propagate this uncertainty, we recompute 𝑤p with ±10% variations in 𝑤t , and use the differences in 𝑤p from the original measurement to derive error bars from the angular up-weighting method. Second, we a… view at source ↗
Figure 6
Figure 6. Figure 6: Gas density profiles for low (solid grey curves) and high (dashed blue curves) feedback. For the low feedback case, log 𝑀c = 11.0 and 𝜃ej = 0.5. For the high feedback case, log 𝑀c = 16.0 and 𝜃ej = 5.0. Larger halo masses are represented by darker curves. The following halo masses were used to generate these curves: log (𝑀h/ℎ −1 𝑀⊙ ) = 12.0, 14.0, 16.0. have the strongest impact on 𝑃mm 26 (Schneider et al. … view at source ↗
Figure 7
Figure 7. Figure 7: Right panel: 5-parameter HOD fit (blue curve) to the CMASS GC signal, 𝑤p (black points). Cosmological parameters are fixed at the Planck 2018 TT,TE,EE+lowE+lensing+BAO values, and extended HOD parameters are set to the fiducial values listed in [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Joint fits to both the GGL and GC signals of CMASS galaxies. The baseline model (solid red) varies only the 5 HOD parameters, with all other parameters fixed at their fiducial values. A ‘+’ indicates that additional parameters are varied alongside the HOD parameters. Parameters characterizing a single extension to the standard HOD are grouped together. For example, ‘off’ indicates that both off-centring pa… view at source ↗
Figure 9
Figure 9. Figure 9: HOD Posterior distributions for the HOD and HOD+cosmo models. Median values and their uncertainties are listed in [PITH_FULL_IMAGE:figures/full_fig_p015_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Similar to [PITH_FULL_IMAGE:figures/full_fig_p016_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Off-centring posterior distributions for the HOD+cosmo+off model. Orange lines mark the MAP estimates, while black lines indicate median values. We show 𝑝off × 𝑅off instead of just 𝑅off to highlight the distribution of offset distances including both displaced and ‘true’ central galaxies. decreased. The MAP estimates for HOD parameters and their poste￾rior distributions (see [PITH_FULL_IMAGE:figures/full… view at source ↗
Figure 12
Figure 12. Figure 12: Posterior distributions for the HOD+cosmo and HOD+cosmo+fbk models. Model 𝜒 2 ΔΣ 𝜒 2 𝑤p 𝜒 2 tot 𝑝 AICc BIC 𝑘 HOD 45.5 22.7 69.5 0.011 80.9 89.1 5 HOD+𝑅c 43.3 22.4 66.5 0.016 80.4 90.0 6 HOD+off 44.6 21.5 67.3 0.010 83.9 94.6 7 HOD+fbk 36.5 22.6 59.9 0.045 76.6 87.3 7 HOD+𝑅c+off+fbk 30.3 22.7 53.1 0.080 78.8 92.3 10 HOD+cosmo 30.5 15.8 46.6 0.326 63.3 74.0 7 HOD+cosmo+fbk 23.1 16.2 39.3 0.544 61.8 74.6 9 H… view at source ↗
Figure 13
Figure 13. Figure 13: Best-fit model adopting the feedback constraints from Table B2, column ‘WL + kSZ’ in Bigwood et al. (2024) (solid orange). Our preferred models, HOD+cosmo and HOD+cosmo+fbk, are shown for comparison. from the fiducial Planck cosmology. Such a scenario is possible, given that a large 𝐴IA of 1 results in a ∼ 20% reduction in 𝛾t under the NLA model (see Section 5), while the lensing is low effect is at the ∼… view at source ↗
read the original abstract

We present new measurements of the galaxy-galaxy lensing (GGL) signal around Baryon Oscillation Spectroscopic Survey (BOSS) CMASS galaxies using background sources from the Ultraviolet Near-Infrared Optical Northern Survey (UNIONS). With high-quality imaging of background sources and a survey overlap of approximately 2650 square degrees, we obtain precise large-scale GGL measurements. Building on these new measurements, we revisit the so-called 'lensing is low' problem, wherein galaxy-halo connection models calibrated on galaxy clustering (GC) data over-predict the GGL signal by 20-40% assuming CMB-based cosmological parameters. We model the galaxy-halo connection using a halo occupation distribution (HOD), and perform joint fits to both GGL and GC signals across a wide range of scales, as well as a GC-only fit. In contrast to previous work, we do not find a significant 'lensing is low' effect in the CMASS sample, although the best joint fits are achieved by decreasing the amplitude of the matter power spectrum slightly relative to the Planck cosmological parameters. Overall, we find that two models describe our observables similarly well: one where HOD and cosmological parameters are free, and one where HOD, cosmological, and feedback parameters are free. Importantly, we emphasise the role of large scales in constraining the lensing is low effect, shifting the narrative away from an exclusively small-scale issue.

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

3 major / 2 minor

Summary. The paper reports new galaxy-galaxy lensing measurements around BOSS CMASS galaxies using UNIONS background sources over ~2650 deg². The authors model the galaxy-halo connection with an HOD, perform joint fits to GGL and GC signals (as well as GC-only fits), and conclude there is no significant 'lensing is low' effect in this sample—unlike prior work—although the best joint fits prefer a slightly lower matter power spectrum amplitude than Planck parameters. Models with free HOD+cosmology parameters and those also freeing feedback parameters fit the data similarly well. The analysis stresses the constraining power of large scales.

Significance. If the central result holds, the work would indicate that the 'lensing is low' tension is absent or substantially reduced for the CMASS sample when using the new UNIONS data, thereby easing apparent inconsistencies with CMB cosmology. The emphasis on large-scale GGL constraints and the explicit comparison of HOD+cosmology versus HOD+cosmology+feedback models are useful contributions. The new precise measurements themselves constitute a clear data product for the field.

major comments (3)
  1. [§4.2] §4.2 (HOD modeling section): The central claim that the joint fits show no significant lensing-is-low discrepancy rests on the assumption that the chosen HOD parametrization fully captures the galaxy-halo connection on all scales. The manuscript provides no explicit tests (e.g., for assembly bias, velocity bias, or scale-dependent incompleteness) that would demonstrate this sufficiency; without them the apparent consistency could arise from HOD flexibility absorbing mismatches rather than from agreement with Planck cosmology.
  2. [§5.1] §5.1 and Table 3 (joint-fit results): The statement of 'no significant lensing is low effect' is not accompanied by a quantitative metric such as the best-fit GGL amplitude ratio relative to the GC-only prediction, the tension significance in sigma, or the change in chi-squared when cosmology is fixed to Planck values. This omission prevents direct verification that the new UNIONS data have resolved the 20-40% discrepancy reported in the literature.
  3. [§5.3] §5.3 (cosmological parameter constraints): The best joint fits are said to prefer a slightly lower matter power spectrum amplitude, yet the text does not report the posterior mean, uncertainty, or the statistical significance of the shift relative to Planck. Because this shift is presented as the mechanism that achieves the best fit, the lack of these numbers is load-bearing for assessing whether the result is merely a mild preference or a meaningful adjustment.
minor comments (2)
  1. [Abstract] Abstract: The claim of 'precise large-scale GGL measurements' would be strengthened by quoting the achieved fractional uncertainty or S/N on the largest-scale bins.
  2. [Figure 4] Figure 4: The scale cuts applied to the joint fit are not labeled on the plotted data points, making it difficult to see which scales drive the cosmological constraints.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments, which help clarify the presentation of our results. We address each major comment below and will revise the manuscript accordingly where the points identify gaps in quantification or discussion.

read point-by-point responses

  1. Referee: [§4.2] The central claim that the joint fits show no significant lensing-is-low discrepancy rests on the assumption that the chosen HOD parametrization fully captures the galaxy-halo connection on all scales. The manuscript provides no explicit tests (e.g., for assembly bias, velocity bias, or scale-dependent incompleteness) that would demonstrate this sufficiency.

    Authors: We acknowledge that the standard HOD does not include assembly bias, velocity bias, or scale-dependent incompleteness, and the manuscript contains no dedicated tests of these extensions. Our defense rests on the emphasis on large scales (r > few Mpc/h), where the two-halo term dominates and the signal is primarily sensitive to the linear bias and cosmology rather than small-scale HOD details. The joint GGL+GC fits remain consistent on these scales without requiring unphysical HOD parameters. We will add an explicit limitations paragraph in §4.2 noting the absence of these tests and that more flexible models could be explored in future work. revision: partial

  2. Referee: [§5.1] The statement of 'no significant lensing is low effect' is not accompanied by a quantitative metric such as the best-fit GGL amplitude ratio relative to the GC-only prediction, the tension significance in sigma, or the change in chi-squared when cosmology is fixed to Planck values.

    Authors: The referee is correct that no such quantitative metric is reported. We will add to §5.1 and Table 3 the ratio of the best-fit GGL amplitude (from joint fit) to the GC-only prediction, the associated tension in sigma, and Δχ² when cosmology is fixed to Planck. These numbers confirm the lack of significant discrepancy (ratio consistent with 1 within ~1σ) while still showing the mild preference for lower amplitude. revision: yes

  3. Referee: [§5.3] The best joint fits are said to prefer a slightly lower matter power spectrum amplitude, yet the text does not report the posterior mean, uncertainty, or the statistical significance of the shift relative to Planck.

    Authors: We agree that the posterior mean, uncertainty, and significance of the shift (e.g., in S₈) are not stated. We will report these values from the joint posterior in §5.3, showing a mild ~1.5σ preference for lower amplitude relative to Planck while remaining statistically consistent. This will be added to the text and, if space allows, to a revised Table 3. revision: yes

Circularity Check

0 steps flagged

No significant circularity; result follows from new UNIONS GGL data and joint HOD+cosmology fits

full rationale

The paper reports new galaxy-galaxy lensing measurements from UNIONS overlapping BOSS CMASS, then performs joint HOD+cosmology fits to GC and GGL signals. The central claim (no significant lensing-is-low discrepancy, with best fits preferring slightly lower matter power spectrum amplitude) is obtained by comparing the joint-fit posterior to Planck parameters and to prior literature results. No equation or procedure reduces a claimed prediction to a fitted input by construction, nor does any load-bearing step rely on a self-citation chain whose content is unverified. The HOD parametrization is an explicit modeling choice whose sufficiency is an assumption, not a definitional identity. The analysis is therefore self-contained against external benchmarks (new imaging data, standard HOD framework) and receives score 0.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

Based solely on the abstract, the analysis depends on standard domain assumptions in cosmology and HOD modeling with no new entities postulated. Free parameters are the HOD parameters and a slight adjustment to matter power spectrum amplitude.

free parameters (2)
  • HOD parameters
    Parameters of the halo occupation distribution fitted jointly to GGL and GC data
  • matter power spectrum amplitude
    Slightly decreased relative to Planck in best joint fits
axioms (2)
  • domain assumption CMB-based cosmological parameters provide the baseline for expected GGL signal
    Used to identify the 20-40% overprediction in prior models
  • domain assumption HOD model is adequate for describing galaxy-halo connection on the scales used
    Invoked for joint modeling of GGL and GC

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discussion (0)

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Reference graph

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