Hyper Suprime-Cam Year 3 results: Cosmology from galaxy clustering and weak lensing with HSC and SDSS using the emulator based halo model

We present cosmology results from a blinded joint analysis of cosmic shear, ξ_±(ϑ ), galaxy-galaxy weak lensing, Δ Σ (R ), and projected galaxy clustering, w_p(R ), measured from the Hyper Suprime-Cam three-year (HSC-Y3) shape catalog and the Sloan Digital Sky Survey (SDSS) DR11 spectroscopic galaxy catalog—a 3 ×2 pt cosmology analysis. We define luminosity-cut, and therefore nearly volume-limited, samples of SDSS galaxies to serve as the tracers of w_p and as the lens samples for Δ Σ in three spectroscopic redshift bins spanning the range 0.15 <z <0.7 . For the ξ_± and Δ Σ measurements, we use a single sample of about seven million source galaxies over 416 deg² , selected from HSC-Y3 based on having photometric redshifts (photo-z ) greater than 0.75. The deep, high-quality HSC-Y3 data enable significant detections of the Δ Σ signals, with integrated signal-to-noise ratio S /N ∼24 in the range 3 ≤R /[h^-1 Mpc ]≤30 over the three lens samples. ξ_± has S /N ∼19 in the range 8^'≤ϑ ≤5 0^' and 30^'≤ϑ ≤15 0^' for ξ₊ and ξ_-, respectively. For cosmological parameter inference, we use the Dark Emulator package, combined with a halo occupation distribution prescription for the relation between galaxies and halos, to model w_p and Δ Σ down to quasinonlinear scales, and we estimate cosmological parameters after marginalizing over nuisance parameters. In our baseline analysis we employ an uninformative flat prior of the residual photo-z error, given by Π (Δ z_ph)=U (-1 ,1 ) , to model a residual bias in the mean redshift of HSC source galaxies. Comparing the relative lensing amplitudes for Δ Σ in the three redshift bins and for ξ_± with the single HSC source galaxy sample allows us to calibrate the photo-z parameter Δ z_ph to the precision of σ (Δ z_ph)≃0.09 . With these methods, we obtain a robust constraint on the cosmological parameters for the flat Λ CDM model: S₈=σ₈(Ω_m/0.3 )^0.5=0.763_-0.036^+0.040 , or the best-constrained parameter given by S₈^'=σ₈(Ω_m/0.3 )^0.22=0.721 ±0.028 , determined with about 4% fractional precision. Based on multidimensional tension metrics, HSC-Y3 data exhibits about 2.5 σ tension with the cosmological constraint inferred by Planck for the Λ CDM model, and hints at a nonzero residual photo-z bias implying that the true mean redshift of the HSC galaxies at z ≳0.75 is higher than that implied by the original photo-z estimates.