Methodological refinement of the submillimeter galaxy magnification bias. I. Cosmological analysis with a single redshift bin

The main goal of this work, the second in a three-paper series, is to test the impact of a methodological improvement in measuring the magnification bias signal on a sample of submillimeter galaxies and its implications for constraining cosmological parameters. The analysis considers the angular cross-correlation function between a foreground sample of GAMA galaxies ($0.2<z<0.8$) and a background sample of H-ATLAS submillimeter galaxies ($1.2<z<4.0$). A refined methodology, discussed extensively in Paper I, is used. By interpreting the weak lensing signal within the halo model and employing an MCMC algorithm, the posterior distribution of the halo occupation distribution (HOD) and cosmological parameters is obtained for a flat $\Lambda$CDM model. The analysis incorporates the foreground angular auto-correlation function to account for galaxy clustering. The results demonstrate a remarkable improvement in uncertainties for both HOD and cosmological parameters compared to previous studies. However, when using the cross-correlation data alone, the estimation of $\sigma_8$ depends on prior knowledge of $\beta$, the logarithmic slope of the background number counts. Assuming a physically motivated prior distribution for $\beta$, mean values of $\Omega_m=0.18^{+0.03}{-0.03}$ and $\sigma_8=1.04^{+0.11}{-0.07}$ are obtained. These results may however be subject to an inherent bias in the data due to anomalous behavior observed in the G15 field. After excluding the G15 region, the mean values shift to $\Omega_m=0.30^{+0.05}{-0.06}$ and $\sigma_8=0.92^{+0.07}{-0.07}$. This becomes more apparent when adding the clustering of the foreground sample, but the dependence on $\beta$ information disappears, mitigating the aforementioned issue. Excluding the G15 region, the joint analysis yields mean values of $\Omega_m=0.36^{+0.03}{-0.07}$, $\sigma_8=0.90^{+0.03}{-0.03}$, and $h=0.76^{+0.14}_{-0.14}$.