Cosmological constraints with the sub-millimetre galaxies Magnification Bias after large scale bias corrections

The study of the magnification bias produced on high z sub-mm galaxies by foreground galaxies through the analysis of the cross-correlation function was recently demonstrated as an interesting independent alternative to the weak lensing shear as a cosmological probe. In the case of the proposed observable, most of the cosmological constraints depends mainly on the largest angular separation measurements. Therefore, we aim at studying and correcting the main large scale biases that affect foreground and background galaxy samples in order to produce a robust estimation of the cross-correlation function (CCF). Then we analyse the corrected signal in order to derive updated cosmological constraints. The large scale bias corrected CCFs are measured using a background sample of H-ATLAS galaxies with photometric redshift > 1.2 and two different foreground samples (GAMA galaxies with spectroscopic redshift or SDSS galaxies with photometric ones, both in the range 0.2 < z < 0.8). They are modelled using the traditional halo model description that depends on both HOD and cosmological parameters. These parameters are then estimated by performing a MCMC under different scenarios to study the performance of this observable and the way to further improve its results. After the large scale bias corrections, we get only minor improvements with respect to the Bonavera et al. 2020 results, mainly confirming their conclusions: a lower bound on $\Omega_m > 0.22$ at $95\%$ C.L. and an upper bound $\sigma_8 < 0.97$ at $95\%$ C.L. (results from the $z_{spec}$ sample). However, by combining both foreground samples into a simplified tomographic analysis, we were able to obtain interesting constraints on the $\Omega_m$-$\sigma_8$ plane: $\Omega_m= 0.42_{- 0.14}^{+ 0.08}$ and $\sigma_8= 0.81_{- 0.09}^{+ 0.09}$ at 68\% CL.