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Revisiting the 'Lensing is Low' Problem with UNIONS

Using high-quality imaging from the UNIONS survey, this study revisits the 'lensing is low' problem with BOSS CMASS galaxies and finds no significant discrepancy between galaxy-galaxy lensing and clustering data, suggesting the issue may be less pronounced than previously thought when large scales are properly included in the analysis.

Original authors: Martine C. T. Campbell, Jack Elvin-Poole, Michael J. Hudson, Thomas de Boer, Sacha Guerrini, Fabian Hervas-Peters, Hendrik Hildebrandt, Martin Kilbinger, Eugene A. Magnier, Alan W. McConnachie, Charli

Published 2026-06-23

📖 6 min read🧠 Deep dive

CC BY 4.0

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

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Picture: A Cosmic Tug-of-War

Imagine the universe is a giant, invisible trampoline made of dark matter. Galaxies are like heavy bowling balls sitting on this trampoline. They bend the fabric, creating "dips" or "wells."

Astronomers have two main ways to study these bowling balls and the dips they create:

Galaxy Clustering (GC): Counting how many bowling balls are close together. This tells us about the "clumpiness" of the universe.
Galaxy-Galaxy Lensing (GGL): Looking at how the light from distant background stars gets distorted as it passes through the dips created by the foreground bowling balls. This tells us about the actual mass (weight) of the dips.

For years, astronomers have been playing a game of "compare and contrast" with these two methods. They use the "clumpiness" data to predict what the "mass" data should look like, based on our best understanding of the universe (the "Planck" model).

The Problem: "Lensing is Low"

In 2017, a team of scientists noticed a glitch. When they used the "clumpiness" data to predict the "mass" (lensing) data, the prediction was too high. The actual mass measured by lensing was 20–40% lower than expected.

They called this the "Lensing is Low" problem. It was like if you weighed a bowling ball by looking at how much it sank into a trampoline, and it turned out to be much lighter than the scale said it was.

Scientists wondered: Is our scale broken (the cosmology is wrong)? Or is our understanding of how bowling balls sit on the trampoline wrong (the physics of galaxy formation)?

The New Experiment: A Better Camera

This paper by Campbell et al. (2026) revisits this problem using a new, high-definition camera called UNIONS.

The Lenses: They used a specific group of bright, red galaxies from the BOSS survey (the "bowling balls").
The Sources: They used a massive new catalog of background galaxies from UNIONS (the "distant stars" whose light gets distorted).
The Advantage: UNIONS covers a huge area of the sky (about 2,650 square degrees) and provides incredibly sharp images. This allowed the team to measure the "mass" of the galaxies with much higher precision, especially on large scales (far away from the center of the galaxy).

The Investigation: Testing the Models

The team tried to fix the "Lensing is Low" problem by testing different theories, like a mechanic trying to tune a car engine. They used a computer model called the Halo Occupation Distribution (HOD), which is basically a rulebook for how galaxies live inside their dark matter "homes" (halos).

They tested four main scenarios:

The Standard Rulebook: They used the basic rules with the standard Planck universe settings.
- Result: The prediction was still slightly too high (about 7% too high). The "Lensing is Low" problem was still there, but smaller than before.
Changing the Universe (Cosmology): They asked, "What if the universe is slightly less 'clumpy' than we thought?" They tweaked the parameters to lower the amount of matter in the universe.
- Result: This made the prediction fit the data much better. It suggested that the universe might have slightly less matter than the Planck model predicts.
Adding "Feedback" (The Galaxy's Internal Engine): They added rules for how galaxies push gas around (feedback from supernovas and black holes). Usually, this pushes gas away, making the galaxy lighter.
- Result: Surprisingly, in their specific setup, the feedback actually helped boost the signal on small scales, helping to fix the mismatch there.
The "Off-Center" Galaxy: They considered that the main galaxy in a halo might not sit perfectly in the middle, but might be slightly off-center.
- Result: This didn't significantly improve the fit.

The Key Discovery: It's About the Big Picture

The most important finding of this paper is about scale.

Previous studies focused heavily on the small scales (right next to the galaxy) to solve this problem. They thought the issue was just about how galaxies form or how gas moves.

This paper argues that the large scales matter just as much.
Because UNIONS provided such precise measurements on large scales, the team found that you can't just fix the problem by tweaking the small-scale physics (like gas feedback). The data on the large scales demands that the overall "weight" of the universe (the cosmology) might be slightly different.

They found that two models worked best:

One where they let the rules for how galaxies live in halos change, and the universe's settings change.
One where they also let the "feedback" (gas pushing) change.

Both models pointed to a universe that is slightly less dense than the standard Planck model suggests.

The "But Wait..." (Intrinsic Alignments)

The authors add a crucial warning: We might be missing a trick.

There is a phenomenon called Intrinsic Alignments (IA). Imagine if the bowling balls themselves were slightly squashed or aligned by the wind, rather than just sitting there. This can fake a lensing signal.

The team estimated that if this effect is strong, it could be hiding the true mass of the galaxies.
If they correct for this in the future (using better data that separates galaxies by distance), the "Lensing is Low" problem might disappear entirely without needing to change the universe's settings.

The Conclusion

In simple terms:

The Problem: We thought galaxies were heavier than they looked.
The New Data: With a better camera (UNIONS), we measured the weight more accurately.
The Result: The problem is smaller than we thought, but it's still there.
The Twist: It's not just a small-scale physics issue; the large-scale structure of the universe suggests the universe might be slightly less "clumpy" than the standard model says.
The Caveat: We haven't fully accounted for the "wind" (Intrinsic Alignments) yet. Once we do, the mystery might be solved without changing our view of the universe.

The paper concludes that while we haven't solved the mystery completely, we now have the right tools and the right data to solve it in the future. We've shifted the conversation from "it's just a small-scale glitch" to "we need to look at the whole picture."

Technical Summary: Revisiting the 'Lensing is Low' Problem with UNIONS

Problem Statement
This study addresses the "lensing is low" problem, a tension first identified by Leauthaud et al. (2017; L17) in the Baryon Oscillation Spectroscopic Survey (BOSS) CMASS sample. In this discrepancy, galaxy–halo connection models calibrated on galaxy clustering (GC) data over-predict the galaxy–galaxy lensing (GGL) signal by 20–40% when assuming Planck-based cosmological parameters. Previous investigations have attributed this tension to limitations in standard Halo Occupation Distribution (HOD) models, specifically the neglect of astrophysical effects such as assembly bias (AB), baryonic feedback, and satellite galaxy segregation. Alternatively, the tension has been interpreted as a potential indication of a lower amplitude of matter fluctuations ( $S_8$ ) compared to Cosmic Microwave Background (CMB) constraints. However, distinguishing between astrophysical systematics and cosmological deviations requires precise measurements across a wide range of scales, from the non-linear to the linear regime.

Methodology
The authors present new, high-precision GGL measurements around BOSS CMASS galaxies using background sources from the Ultraviolet Near-Infrared Optical Northern Survey (UNIONS). The analysis leverages a survey overlap of approximately 2,650 square degrees, utilizing UNIONS ShapePipe v1.4.5 catalogues for source shapes and BOSS DR12 CMASS catalogues for lenses.

Data Processing: Source galaxy shapes were measured using NGMIX and calibrated via the Metacalibration framework. Due to the lack of photometric redshifts in the UNIONS sample, an effective redshift distribution, $n(z_s)$ , was constructed using a Self-Organizing Map (SOM) trained on CFHTLenS spectroscopic data. The GGL signal ( $\Delta\Sigma$ ) was measured over scales of $0.15\text{--}62 \, h^{-1}\text{Mpc}$ , while the GC signal ( $w_p$ ) was measured over $0.15\text{--}80 \, h^{-1}\text{Mpc}$ . Systematic uncertainties, including intrinsic alignments (IA) and magnification bias, were modeled, with a specific focus on the impact of $n(z_s)$ uncertainty on the covariance matrix.
Theoretical Framework: The analysis employs the Dark Emulator, a fast emulation tool based on Dark Quest N-body simulations, to model the galaxy–halo connection. The study utilizes a standard 5-parameter HOD (Zheng et al. 2005) and extends it with several physical modifications:
- Off-centring: Allowing central galaxies to be offset from halo centers.
- Satellite Concentration: Modifying the concentration of satellite galaxies relative to their host halos ( $R_c$ ).
- Baryonic Feedback: Implementing a semi-analytic "baryonic correction" (BC) model to simulate the redistribution of matter due to feedback processes (gas ejection and cooling).
Parameter Estimation: Joint fits to $\Delta\Sigma$ and $w_p$ were performed using Bayesian inference (MCMC). The study tested various configurations: a baseline HOD with fixed Planck cosmology, models with free cosmological parameters ( $\Omega_{m,0}$ and $\ln(10^{10}A_s)$ ), and models incorporating feedback and off-centring parameters. Goodness-of-fit was evaluated using the Corrected Akaike Information Criterion (AICc) and Bayesian Information Criterion (BIC).

Key Contributions and Results

New GGL Measurements: The paper provides precise large-scale GGL measurements for the CMASS sample, significantly reducing statistical errors compared to previous studies (e.g., Amon et al. 2023) at large scales ( $r_p \sim 50 \, h^{-1}\text{Mpc}$ ).
Re-evaluation of the Tension: Contrary to previous findings in CMASS samples, the authors do not find a significant "lensing is low" effect when using the UNIONS data and a standard HOD with Planck cosmology. While the standard HOD over-predicts the GGL signal by approximately 13% relative to the raw measurements, correcting for the multiplicative shear bias ( $m$ -bias) reduces this discrepancy to roughly 7%, which is within the estimated 3–4% uncertainty.
Role of Large Scales: The study emphasizes that large-scale data is critical for constraining the lensing is low effect. The best joint fits are achieved not by small-scale modifications alone, but by models that allow for flexibility in cosmological parameters.
Preferred Models: Two models describe the observables similarly well:
- HOD + Cosmology: A model where HOD and cosmological parameters are free. This model favors a slightly lower $S_8$ ( $S_8 \approx 0.743$ ) compared to Planck ( $S_8 \approx 0.824$ ), though the authors note this is a lower limit due to the assumption of zero intrinsic alignment amplitude ( $A_{IA}=0$ ).
- HOD + Cosmology + Feedback: A model including feedback parameters. Interestingly, in this configuration, feedback enhances the small-scale GGL signal (via contraction of collisionless matter shells) rather than suppressing it, helping to fit the small-scale data without compromising the large-scale fit.
Astrophysical Constraints: The analysis yields robust estimates for the minimum halo mass hosting CMASS galaxies ( $\log M_{min} \sim 13$ ) and the satellite fraction ( $f_s \sim 8.5\text{--}9.8\%$ ), consistent with previous literature.

Significance and Claims
The paper claims that the "lensing is low" problem is not exclusively a small-scale issue but is heavily influenced by large-scale modeling and cosmological assumptions. By combining high-precision large-scale GGL measurements with GC data, the authors demonstrate that the tension can be alleviated by slightly lowering the matter fluctuation amplitude ( $S_8$ ) or by incorporating flexible astrophysical models, without requiring a radical departure from the $\Lambda$ CDM framework.

The authors explicitly state that their results should not be interpreted as definitive evidence for a low $S_8$ tension. They highlight that intrinsic alignments (IAs), which were fixed to zero in the fiducial analysis, could introduce a $\sim 20\%$ bias in the shear signal if significant. Consequently, the current results serve as a proof-of-concept for the UNIONS survey's capability to deliver competitive cosmological constraints. The study establishes the methodology for future work where tomographic binning (enabled by future photometric redshifts in UNIONS) will allow for the marginalization of IA uncertainties, potentially resolving the lensing is low problem and providing robust $S_8$ constraints.