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Cosmic Shear constraints from HSC Year 3 with clustering calibration of the tomographic redshift distributions from DESI

By reanalyzing Hyper Suprime-Cam Year 3 cosmic shear data using improved clustering redshift calibrations from DESI spectroscopy, this study achieves a 1.8-fold reduction in uncertainty for the growth of structure parameter $S_8$ , shifting its central value closer to Planck cosmology and bringing HSC's constraining power on par with recent KiDS and DES results.

Original authors: J. Choppin de Janvry, B. Dai, S. Gontcho A Gontcho, U. Seljak, T. Zhang

Published 2026-05-01

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CC BY 4.0

Original authors: J. Choppin de Janvry, B. Dai, S. Gontcho A Gontcho, U. Seljak, T. Zhang

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

Imagine the universe as a giant, invisible web of invisible matter (dark matter) that stretches across space. When light from distant galaxies travels through this web, the gravity of the dark matter acts like a funhouse mirror, slightly stretching and distorting the shapes of those galaxies. This phenomenon is called Cosmic Shear or Weak Gravitational Lensing.

By measuring these tiny distortions in millions of galaxies, astronomers can map the invisible web and figure out how the universe is growing and evolving.

Here is what this paper did, explained simply:

1. The Problem: A "Blurry" Map

To make a good map, you need to know exactly how far away each galaxy is. If you think a galaxy is close when it's actually far away, your map of the universe's structure will be wrong.

The Hyper Suprime-Cam (HSC) telescope took a massive picture of the sky (the "Year 3" survey). However, the original analysis had a problem: it wasn't entirely sure about the distances of the galaxies. It had to guess a lot, using a wide range of possibilities. Because of this uncertainty, the final result was a bit "fuzzy" (large error bars), and the calculated amount of structure in the universe seemed lower than what other methods (like looking at the afterglow of the Big Bang) suggested. This disagreement was known as the " $S_8$ tension."

2. The Solution: A New GPS for Galaxies

The authors of this paper brought in a new, super-accurate tool: DESI (Dark Energy Spectroscopic Instrument).

The Old Way: Imagine trying to guess how far away a car is at night just by looking at its headlights. You might guess "maybe 100 meters, maybe 200."
The New Way: Imagine the car has a GPS that tells you its exact distance.

DESI acts like that GPS. It uses spectroscopy (splitting light into a rainbow) to measure the exact distance of millions of galaxies. The authors used DESI to "calibrate" the HSC data. They matched the HSC galaxies with the DESI "GPS" data to create a much sharper, more accurate map of where the galaxies really are.

3. The Experiment: Re-doing the Math

The team took the original HSC data and re-ran the calculations using this new, sharper distance map. They did this in two ways to make sure they were right:

Full Re-run: They calculated everything from scratch with the new data.
Re-weighting: They took the original results and adjusted them mathematically to fit the new distance information (like adjusting a recipe without cooking the whole meal again).

Both methods gave the same answer.

4. The Results: A Clearer Picture

The new analysis changed the story in two big ways:

Sharper Precision: The "fuzziness" (error bars) of the measurement shrunk by nearly half (a 1.8x improvement). The map is now much clearer.
A Shift in Value: The calculated value for the growth of structure ( $S_8$ ) moved up. It went from 0.769 to 0.805.

5. The Big Takeaway: The Mystery is Solved?

Previously, the HSC data suggested the universe was growing slower than the standard model of cosmology (based on the Big Bang) predicted. This was a major mystery.

However, with this new, sharper distance map, the HSC result now matches perfectly with the predictions from the Big Bang (Planck data).

The Analogy:
Think of the "S8 tension" like two people measuring the height of a building.

Person A (Old HSC) used a blurry tape measure and said, "It's 100 feet tall."
Person B (Big Bang) used a laser and said, "It's 105 feet tall."
They argued about who was right.

This paper gave Person A a brand new, high-tech laser tape measure (calibrated by DESI). When Person A measured again, they said, "Oh, it's actually 105 feet tall." The argument is over; they agree.

Summary

The paper claims that the previous disagreement between galaxy surveys and the Big Bang model wasn't because the laws of physics were broken, but because the "distance map" used by the HSC telescope was slightly off. By using DESI to fix the distance map, the HSC data now aligns perfectly with the standard model of the universe, suggesting that the "tension" was just a measurement error, not new physics.

1. Problem Statement

Weak gravitational lensing (WL) surveys, such as the Hyper Suprime-Cam (HSC) Year 3 (Y3) survey, are powerful probes for constraining cosmological parameters, specifically the matter density ( $\Omega_m$ ) and the amplitude of matter fluctuations ( $\sigma_8$ ). These are often combined into the growth-of-structure parameter $S_8 \equiv \sigma_8 \sqrt{\Omega_m/0.3}$ .

However, a persistent tension exists between $S_8$ values derived from WL surveys (which tend to be lower) and those inferred from Cosmic Microwave Background (CMB) measurements (e.g., Planck) under the standard $\Lambda$ CDM model. This "S8 tension" could indicate new physics or, more likely, unaccounted-for systematic errors.

A primary source of systematic uncertainty in WL analyses is the calibration of photometric redshifts ( $z_{ph}$ ). Errors in the redshift distribution $n(z)$ of source galaxies propagate directly into biases in $S_8$ . The original HSC Y3 analysis relied on "self-calibration" methods, which placed wide, uniform priors on redshift biases ( $\Delta z$ ) for higher redshift bins due to a lack of external spectroscopic constraints. This approach accounted for uncertainties but resulted in weak constraints (large error bars) on $S_8$ .

2. Methodology

The authors reanalyze the HSC Y3 cosmic shear data using a significantly improved calibration of the redshift distributions ( $n(z)$ ) derived from the Dark Energy Spectroscopic Instrument (DESI).

DESI Clustering Redshifts: The study utilizes DESI Data Release 1 and 2 spectroscopic data. By measuring the angular cross-correlation between the HSC photometric sample and DESI spectroscopic reference samples, the authors reconstruct the true redshift distributions for the four tomographic bins of HSC Y3. This method leverages the physical clustering of galaxies to calibrate $n(z)$ without relying solely on internal self-calibration.
Two-Pronged Analysis Approach:
1. Full MCMC Re-analysis: The authors re-ran the likelihood analysis using the CosmoSIS pipeline. They replaced the original $n(z)$ and the wide uniform priors on redshift shifts ( $\Delta z$ ) with the new DESI-calibrated $n(z)$ and tighter Gaussian priors derived from the clustering redshift method. They used the pocoMC sampler (Preconditioned Monte Carlo) for efficiency.
2. Importance Weighting: As a consistency check, they applied importance weights to the original HSC Y3 Markov Chain Monte Carlo (MCMC) chains. This re-weighted the original chains based on the new $\Delta z$ priors (specifically for the 3rd and 4th bins where the original priors were uniform).
Modeling Details:
- Scale Cuts: Two scale cuts were tested for the two-point correlation functions: $0.3 - 3 \, h^{-1}\text{Mpc}$ (fiducial) and $1 - 5 \, h^{-1}\text{Mpc}$ .
- Systematics: The analysis includes modeling for intrinsic alignments (using the TATT model), baryonic feedback, shear multiplicative bias, and PSF additive bias.
- Power Spectrum: The matter power spectrum was computed using CAMB (linear emulator) rather than the BACCO emulator used in the original HSC analysis, to avoid potential biases observed in projected 1D modes.

3. Key Contributions

DESI-Calibrated Redshifts: The primary contribution is the application of DESI spectroscopic clustering redshifts to calibrate the HSC Y3 $n(z)$ distributions. This provides the first external, high-precision constraint on the redshift biases for HSC Y3.
Resolution of the S8 Tension for HSC: The study demonstrates that the previously observed low $S_8$ value in HSC Y3 was largely driven by the conservative, wide priors on redshift uncertainties. By tightening these priors with DESI data, the central value shifts upward.
Methodological Validation: The paper validates the results through two independent methods (full MCMC re-sampling and importance weighting), showing consistent outcomes.
Comparison with Other Surveys: The re-analyzed HSC Y3 results are shown to be competitive with the latest results from KiDS-Legacy and DES Y6.

4. Key Results

$S_8$ Constraint: The re-analyzed HSC Y3 data yields:
$S_8 = 0.805 \pm 0.018$
This is compared to the original HSC Y3 result of $S_8 = 0.769^{+0.031}_{-0.034}$ .
Error Reduction: The improved calibration leads to a 1.8-fold reduction in the error bar on $S_8$ .
Shift in Central Value: The central value shifted significantly higher (from 0.769 to 0.805), moving much closer to the Planck CMB measurement ( $S_8 \approx 0.81$ ).
Tension Status: The tension between HSC Y3 and Planck is effectively eliminated. The new result shows no significant deviation from the Planck cosmology.
Redshift Shifts ( $\Delta z$ ): The new calibration found that the original HSC redshift biases were not zero but were within the $1-2\sigma$ range of the self-calibration posteriors. The new priors are significantly tighter (Gaussian) compared to the original wide uniform priors.
Combined Constraints: When naively combined with KiDS-Legacy and DES Y3 (assuming independence), the joint WL constraint reaches $S_8 = 0.813 \pm 0.009$ . Further combining with CMB lensing yields a sub-percent constraint of $S_8 = 0.818 \pm 0.007$ , comparable to the precision of CMB-only measurements.

5. Significance

Systematics vs. New Physics: The results strongly suggest that the "S8 tension" observed in Stage III weak lensing surveys is primarily driven by systematic uncertainties in photometric redshift calibration, rather than new physics beyond the standard $\Lambda$ CDM model.
Role of Spectroscopic Surveys: The paper highlights the critical necessity of spectroscopic surveys (like DESI) for calibrating photometric redshifts in future weak lensing missions.
Future Outlook: The methodology and results provide a blueprint for upcoming Stage III (DES Y6, HSC PDR4) and Stage IV (Euclid, Rubin LSST) surveys. It suggests that with reliable clustering redshift calibration, these surveys will achieve percent-level constraints on structure growth, further validating the standard cosmological model.
Data Availability: The authors have made the code, chains, and data publicly available to ensure reproducibility and facilitate future combination studies.