## Summary

The Hyper Suprime-Cam Year 3 (HSC-Y3) cosmology analyses are based on a shear catalog covering 416 deg^{2} of the sky with exquisite depth and seeing. The HSC-Y3 cosmology effort has been led by a group of primarily early-career scientists, who have prepared the shear catalog, developed redshift distribution inference methods, studied potential contamination from systematics, measured data vectors and carried out the cosmological analyses. This work is described in a set of 8 papers, each of which is described below.

All of the blinded cosmology analyses were carried out in a coordinated fashion to ensure an appropriate degree of consistency on common elements such as catalog-level systematics, and common decision criteria to define model choices. However, the actual results were produced independently, and consistency of the cosmological constraints assessed only after all analysis choices were complete. This approach to the scientific results lends robustness to the analysis results.

When referring to the HSC Y3 cosmic shear results in papers, please cite both Dalal et al. and Li et al., as these together are considered our primary cosmic shear results. When referring to the HSC Y3 3x2pt results in papers, please cite all 3 of More et al., Miyatake et al., and Sugiyama et al. The HSC-Y3 weak lensing products (including the galaxy shape catalog) will be released after the key cosmology papers are accepted. As further cosmological analyses with HSC-Y3 data are completed, we will add them to this webpage.

## Webinar

We held a webinar to present our latest results on April 3rd, 2023. The recording and presentation slides are available below.

## List of papers

- The three-year shear catalog of the Subaru Hyper Suprime-Cam SSP Survey
- A General Framework for Removing Point Spread Function Additive Systematics in Cosmological Weak Lensing Analysis
- Weak Lensing Tomographic Redshift Distribution Inference for the Hyper Suprime-Cam Subaru Strategic Program three-year shape catalogue
- Hyper Suprime-Cam Year 3 Results: Cosmology from Cosmic Shear Two-Point Correlation Functions

- Hyper Suprime-Cam Year 3 Results: Cosmology from Cosmic Shear Power Spectra

- Hyper Suprime-Cam Year 3 Results: Measurements of the Clustering of SDSS-BOSS galaxies, galaxy-galaxy lensing and cosmic shear

- Hyper Suprime-Cam Year 3 Results: Cosmology from Galaxy Clustering and Weak Lensing with HSC and SDSS using the Minimal Bias Model

- Hyper Suprime-Cam Year 3 Results: Cosmology from Galaxy Clustering and Weak Lensing with HSC and SDSS using the Emulator Based Halo Model

The galaxy number density map of the HSC-Y3 shear catalog that is used in the Y3 cosmology analyses.

This paper presents the galaxy shear catalog that is used for the HSC-Y3 cosmological weak gravitational lensing analyses. The galaxy shapes are measured from the *i*-band imaging data in the Wide layer of the survey, acquired from 2014 to 2019. The shapes are calibrated with image simulations that resemble the observing conditions of the survey based on training galaxy images from the Hubble Space Telescope in the COSMOS region. The catalog covers an area of 433.48 sq. deg. of the northern sky, split into six subfields. The mean i-band seeing is 0.59 arcsec. With conservative galaxy selection criteria (e.g., i-band magnitude brighter than 24.5), the observed raw galaxy number density is 22.9 arcmin^{-2}, and the effective galaxy number density is 19.9 arcmin^{-2}. The calibration removes the galaxy property-dependent shear estimation bias to a level: δm < 9 x 10^{-3}. The bias residual δm shows no dependence on redshift in the range 0<z<3. We define the requirements for cosmological weak lensing science for this shear catalog, and quantify potential systematics in the catalog using a series of internal null tests for systematics related to point-spread function modeling and shear estimation. A majority of the null tests are statistically consistent with zero or within requirements. The shear catalogs for the HSC-Y3 cosmological analyses are subsets of this shear catalog.

## A General Framework for Removing Point Spread Function Additive Systematics in Cosmological Weak Lensing Analysis (Tianqing Zhang et al.)

**Link to paper: ****arXiv**

This figure describes the contamination on the cosmic shear two point correlation function by the PSF additive bias. We compare two models for the PSF systematics error, the red line includes both PSF second and fourth moments contribution, while the orange line only includes the former. We show that the contamination from the PSF fourth moment systematics is statistically significant compared to the statistical uncertainty of the shear-shear signal (shown in the dashed line.) Therefore, it is vital to model the PSF systematics using both PSF second and fourth moments in the HSC-Y3 cosmic shear analysis.

This work demonstrates a general framework for detecting and modeling the impact of PSF systematics on the cosmic shear two-point correlation function (2PCF), and mitigating their impact on cosmological analyses. Our framework can detect PSF leakage and modeling error from all spin-2 quantities contributed by the PSF second and higher moments, rather than just the second moments, using the cross-correlation of galaxy shape and PSF moments. We interpret null tests using the HSC-Y3 catalogs with this formalism, and find that leakage from the spin-2 combination of PSF fourth moments is the leading contributor to additive shear systematics, with a total contamination that is an order of magnitude higher than that contributed by PSF second moments alone. We conduct a mock cosmic shear analysis for HSC-Y3, and find that, if uncorrected, PSF systematics can bias the cosmological parameters Ω_{m} and S_{8} by ~0.3σ. The traditional second moment-based model can only correct for a 0.1σ bias, leaving the contamination largely uncorrected. We conclude that it is necessary to model both PSF second and fourth moment contamination for HSC-Y3 cosmic shear analysis. We also reanalyze the HSC-Y1 cosmic shear analysis with our updated systematics model, and identify a 0.07σ bias on Ω_{m} when using the more restricted second moment model from the original analysis. We demonstrate how to self-consistently use the method in both real space and Fourier space, assess shear systematics in tomographic bins, and test for PSF model overfitting.

## Weak Lensing Tomographic Redshift Distribution Inference for the Hyper Suprime-Cam Subaru Strategic Program three-year shape catalogue (Markus Rau et al. )

**Link to paper: ****arXiv**

Sample redshift distribution (p_{samp}(z)) posteriors for the four tomographic redshift bins of the HSC-Y3 source sample derived to include information from the photometry (`PhotZ (DNNz)’, gray area), spatial clustering (`WX (0.1 – 1.0 Mpc)’, black dots) and the combination of spatial information and photometry (`PhotZ & WX’, red area). The blue dots denote the standard deviation on the mean of WX (i.e., clustering redshift) measurements. The CAMIRA LRG sample has a limited redshift coverage to z < 1.2, due to which the high redshift tomographic bin does not include a cross-correlation data vector. The inference includes the lensing weights consistently in all likelihood terms. The piecewise intervals denote the ±1σ errors.

This work presents posterior sample redshift distributions for the HSC-Y3 cosmology analyses. Using the galaxies’ photometry and spatial cross-correlations, we conduct a combined Bayesian Hierarchical Inference of the sample redshift distributions. The spatial cross-correlations are derived using a subsample of Luminous Red Galaxies (LRGs) with accurate redshift information available up to a photometric redshift of z < 1.2. We derive the photometry-based constraints using a combination of two empirical techniques calibrated on spectroscopic- and multiband photometric data that cover a spatial subset of the shear catalog. The limited spatial coverage induces a cosmic variance error budget that we include in the inference. Our cross-correlation analysis models the photometric redshift error of the LRGs to correct for systematic biases and statistical uncertainties. We demonstrate consistency between the sample redshift distributions derived using the spatial cross-correlations, the photometry, and the posterior of the combined analysis. Based on this assessment, we recommend conservative priors for residual errors in the sample redshift distributions of tomographic bins used in the HSC-Y3 cosmological weak lensing analyses.

## Hyper Suprime-Cam Year 3 Results: Cosmology from Cosmic Shear Two-Point Correlation Functions (Xiangchong Li et al.)

Link to paper: arXiv

The HSC-Y3 cosmological constraints from cosmic shear 2PCFs (blue, solid), compared to the results from *Planck*-2018 (orange, dashed), as well as DES-Y3 (green, dotted) and KiDS-1000 (red, dash-dotted).

This work presents the HSC-Y3 cosmological constraints using cosmic shear two-point correlation functions (2PCFs). The analysis is coordinated with the cosmology analysis using power spectra (Dalal et. al 2023). We measure 2PCFs measured from galaxies in the HSC-Y3 shear catalog in four tomographic redshift bins ranging from 0.3 to 1.5 and in the angular range: 7.1 < θ /arcmin < 56.6 for ξ_{+} and 31.2 < θ / arcmin < 248 for ξ_{–}, with a total signal-to-noise ratio 26.6. By fitting a flat LambdaCDM model prediction to the 2PCFs after marginalizing over astrophysical and systematic uncertainties, we find Ω_{m}=0.256^{+0.056}_{-0.044} (68% CI) and S_{8} = σ_{8} (Ω_{m}/0.3)^{0.5}=0.769^{+0.031}_{-0.034} (68% CI).

We study the effect that various modeling choices and systematic errors could have on this value, and find that they can shift the best-fit values of S_{8} by no more than ~0.5σ, indicating that our result is robust to such systematics. The constraint on S_{8} is ~2σ lower than the constraint from *Planck*-2018.

## Hyper Suprime-Cam Year 3 Results: Cosmology from Cosmic Shear Power Spectra (Roohi Dalal et al.)

Link to paper: arXiv

The HSC-Y3 cosmological constraints from cosmic shear power spectra (blue, solid), compared to the results from *Planck* 2018 (orange, dashed), as well as DES-Y3 (green, dotted) and KiDS-1000 (red, dash-dotted), 2 other Stage III cosmic shear experiments.

This work presents the HSC-Y3 cosmological constraints using cosmic shear power spectra. The analysis in this paper is conducted in coordination with Li et al. (2023), which uses cosmic shear two point correlation functions. We use the Pseudo-Cl method to obtain an unbiased and high-significance measurement of the cosmic shear power spectrum, with a signal-to-noise ratio of approximately 26.4 in the multipole range 300<ℓ<1800. We then fit a cosmological model to the spectra while marginalizing over uncertainties in astrophysical models, such as baryonic feedback and intrinsic alignments, as well as systematics in our data, including, most significantly, uncertainties in our source redshift distribution inference. For a flat LambdaCDM model, we find S_{8}= 0.776^{+0.032}_{-0.033} (68% CI), which is in excellent agreement with the constraints from the other HSC Year 3 cosmology analyses, as well as those from a number of other cosmic shear experiments. This result is in ~2σ tension with the constraint from *Planck* 2018. We study the effect that various systematic errors and modeling choices could have on this value, and find that they can shift the best-fit values of S_{8} by no more than ~0.5σ, indicating that our result is robust to such systematics.

## Hyper Suprime-Cam Year 3 Results: Measurements of the Clustering of SDSS-BOSS galaxies, galaxy-galaxy lensing and cosmic shear (Surhud More et al.)

Link to paper: arXiv

The high signal-to-noise ratio measurements of the projected correlation functions of the three different subsamples of SDSS galaxies (top panels), their weak lensing signal (middle panels), and the cosmic shear correlations (bottom panels).

This work presents the measurements of the three two-point correlations that form the basis of the cosmological analyses performed in the companion papers, Miyatake et al. and Sugiyama et al. We use three approximately volume limited subsamples of spectroscopic lens galaxies selected by their i-band magnitude from SDSS-BOSS: LOWZ (0.1<z<0.35), CMASS1 (0.43<z<0.55) and CMASS2 (0.55<z<0.7). We present high signal-to-noise ratio measurements of the projected correlation functions of these galaxies. In order to break the degeneracy between the amplitude of the matter correlation and the bias of these spectroscopic galaxies, we measure the galaxy-galaxy lensing signal using background galaxies from the Subaru HSC survey, which probes the projected galaxy-matter cross-correlation function of the SDSS-BOSS galaxies. Finally, we also measure the cosmic shear correlation functions from HSC galaxies which is related to the projected matter correlation function. We demonstrate the robustness of our measurements by subjecting each of these measurements to a variety of systematic tests and present results of null tests. We also describe the construction of a suite of mocks: i) spectroscopic galaxy catalogs which obey the clustering and abundance of each of the three SDSS-BOSS subsamples, and ii) galaxy shape catalogs which obey the footprint of the HSC survey and have been appropriately sheared by the large scale structure expected in a flat LambdaCDM model. These mock catalogs are used to compute the covariance of each of our observables.

## Hyper Suprime-Cam Year 3 Results: Cosmology from Galaxy Clustering and Weak Lensing with HSC and SDSS using the Minimal Bias Model (Sunao Sugiyama et al.)

Link to paper: arXiv

The HSC-Y3 cosmological constraints from the 3x2pt analyses: the joint analyses of cosmic shear, galaxy-galaxy leasing and galaxy clustering, compared to the Planck 2018 CMB result and the external weak lensing surveys’ results, DES Y3 and KiDS 1000.

This work, together with Miyatake & Sugiyama et al. (2023), presents the cosmological parameter constraints from the joint analyses of cosmic shear, galaxy clustering, and galaxy-galaxy lensing, the so-called 3x2pt analyses. We analyze the measurements of these observables from More & Sugiyama et al. (2023), especially focusing on the large-scale signal of the galaxy clustering and the galaxy-galaxy lensing signal above R=8 h^{-1} Mpc and 12 h^{-1} Mpc respectively, using the minimal bias model. We perform the various model validations with mock data vectors and test analysis choices, which are all conducted in the blind fashion. After fixing the analysis choice and unblinding, we find a ~5% fractional precision estimate of the clustering amplitude, S_{8} = 0.775^{+0.043}_{-0.038} (68% C.I.). We assess the tension between our result and Planck 2018 CMB result, and find no significant tension.

## Hyper Suprime-Cam Year 3 Results: Cosmology from Galaxy Clustering and Weak Lensing with HSC and SDSS using the Emulator Based Halo Model (Hironao Miyatake et al.)

Link to paper: arXiv

The HSC-Y3 cosmological constraints from the small-scale 3x2pt analysis: the joint analysis of cosmic shear, galaxy-galaxy leasing, and galaxy clustering, compared to the constraints from the Planck 2018 primary CMB. Red lines show the posterior for the HSC-Y3 3x2pt results when the prior of σ(Ω_{m})=N(0.3,0.01) is added. The parameter Δz_{ph} is a parameter to model residual systematic error of the HSC source galaxies. Our result indicate a non-zero Δz_{ph}.

This work presents the cosmological parameter constraints from the joint analysis of cosmic shear, galaxy-galaxy lensing, and galaxy-galaxy clustering signals measured by More, Sugiyama et al. (2023). While Sugiyama et al. focus on large scales (8 Mpc/h for galaxy-galaxy clustering and 12 Mpc/h for galaxy-galaxy lensing) where the linear bias approximation holds, this analysis uses small scales down to 2 Mpc/h for galaxy-galaxy clustering and 3 Mpc/h for galaxy-galaxy lensing to obtain more signal-to-noise ratio. To robustly model the non-linear regime, we combine Dark Emulator (Nishimichi et al., 2019), the cosmic emulator that computes halo-matter and halo-halo correlation function to a few percent accuracy, and the halo occupation distribution prescription to model the relation between galaxy and halo distributions. We perform a blind analysis while testing the robustness of the model with various analysis choices. After unblinding, we find the constraints on the matter clustering S_{8}=0.763^{+0.040}_{-0.036} (68% C.I.), which exhibits about 2.5-sigma tension with the Planck constraint for a flat LambdaCDM cosmology. We emphasize that we use an uninformative prior for the photo-z residual systematics and fully make use of the self-calibration scheme proposed by Oguri & Takada (2011). Hence this analysis is robust against photo-z uncertainties, which are considered one of the most important systematics in weak lensing analysis.