Quasi-2D Weak Lensing Cosmological Constraints Using the PDF-SYM method

Cosmic shear statistics, such as the two-point correlation function (2PCF), can be evaluated with the PDF-SYM method instead of the traditional weighted-sum approach. It makes use of the full PDF information of the shear estimators, and does not require weightings on the shear estimators, which can in principle introduce additional systematic biases. This work presents our constraints on $S_8$ and $\Omega_m$ from the shear-shear correlations using the PDF-SYM method. The data we use is from the z-band images of the Dark Energy Camera Legacy Survey (DECaLS), which covers about 10000 deg$^2$ with more than 100 million galaxies. The shear catalog is produced by the Fourier\_Quad method, and well tested on the real data itself with the field-distortion effect. Our main approach is called quasi-2D as we do use the photo-$z$ information of each individual galaxy, but without dividing the galaxies into redshift bins. We mainly use galaxy pairs within the redshift interval between 0.2 and 1.3, and the angular range from $4.7$ to $180$ arcmin. Our analysis yields $S_8=0.762 \pm 0.026$ and $\Omega_{\rm m}=0.234 \pm 0.075$, with the baryon effects and the intrinsic alignments included. The results are robust against redshift uncertainties. We check the consistency of our results by deriving the cosmological constraints from auto-correlations of $\gamma_1$ and $\gamma_2$ separately, and find that they are consistent with each other, but the constraints from the $\gamma_1$ component is much weaker than that from $\gamma_2$. It implies a much worse data quality of $\gamma_1$, which is likely due to additional shear uncertainties caused by CCD electronics (according to the survey strategy of DECaLS). We also perform a pure 2D analysis, which gives $S_8=0.81^{+0.03}_{-0.04}$ and $\Omega_{\rm m}=0.25^{+0.06}_{-0.05}$. Our findings demonstrate the potential of the PDF-SYM method for precision cosmology.