Constraining $σ_8$ with Lensing Statistics in Low and High Density Regions

TL;DR

This work tests the standard cosmology by including lensing signals from low-density regions (LDPs) along with galaxy-galaxy lensing (GGL) and galaxy clustering to constrain $\sigma_8$. Using DECaLS data for LDPs and GGL, paired with SHAM-based mocks and mass/photometric-redshift uncertainties, the authors perform a joint Bayesian analysis guided by simulations (CosmicGrowth) and low-resolution $\sigma_8$-varying runs. They report $\sigma_8=0.824^{+0.015}_{-0.015}$, with LDP lensing enhancing the constraint by about 14% over GGL+2PCF alone, and provide constrained values for $\sigma_{\lg M}$ and $\sigma_z$ that reflect parameter degeneracies. The results illustrate the value of incorporating low-density lensing to test $\Lambda$CDM, while highlighting modeling limitations and directions for improved error treatment in future work.

Abstract

Lensing studies are typically carried out around high density regions, such as groups and clusters, where the lensing signals are significant and indicative of rich density structures. However, a more comprehensive test of the cosmological model should also include the lensing effect in low density regions. In this work, we incorporate the stacked weak lensing signals around the low density positions, alongside galaxy-galaxy lensing and galaxy-galaxy two point correlation function to perform a joint cosmological analysis on $σ_8$. The low density positions are constructed from the DR9 data release of the DESI legacy imaging survey, using galaxies with r-band absolute magnitude cut M$<$-21.5 and in the redshift range of 0.18$<$z$<$0.28. In doing so, we simultaneously parameterize photometric redshift errors and halo mass uncertainties while building mock catalogs from simulations using the method of SubHalo Abundance Matching (SHAM). For the weak lensing measurements, we use the shear estimators derived from the DECaLS DR8 imaging data, processed by the Fourier_Quad pipeline. The survey boundaries and masks are fully taken into account. Our analysis achieves a total significance of $31.1σ$ detection for lensing in the low density positions, which significantly improve the $σ_8$ constraint compared to galaxy-galaxy lensing and galaxy-galaxy two point correlation function by 14$\%$. For flat $Λ$CDM model, we constrain $σ_8$ =$0.824^{+0.015}_{-0.015}$, which shows a good agreement with the PLANCK result. Additionally, the halo mass uncertainty $σ_{\lg M}$ and photometric redshift error $σ_z$ are constrained to be $0.565^{+0.086}_{-0.070}$ and $0.004^{+0.004}_{-0.003}$ respectively, which are somewhat different from our expectations due to the significant degeneracy of the two parameters.

Figures (15)

• Figure 1: The absolute magnitude distribution of galaxies in the redshift range between 0.18 and 0.28. The grey dotted line refers to the cut at -21.5 for FBGs.
• Figure 2: Footprint of the DECaLS galaxy samples within the redshift range between 0.18 and 0.28, and with absolute magnitude smaller than -21.5.
• Figure 3: The distribution of the DECaLS galaxy sample (blue points, M$<$-21.5, $0.18 < z < 0.28$) and the LDPs (orange points) with the critical radius $R_s$ being $5^{\prime}$. The white areas are either masks or the neighborhood of galaxies.
• Figure 4: Flow chart of selecting FBGs in simulation.
• Figure 5: The (sub)halo mass function from redshift 0.18 to 0.28 in CG (orange) and the small simulation with $\sigma_8$=0.829 (blue) respectively. The grey-dotted line shows the FBGs’ cut with the lowest mass of about $10^{12.8}M_{\odot}/h$.