The study of the magnification bias produced on high-redshift sub-millimetre 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 mainly depend on the largest angular separation measurements. Therefore, we aim to study and correct the main large-scale biases that affect foreground and background galaxy samples to produce a robust estimation of the cross-correlation function. Then we analyse the corrected signal to derive updated cosmological constraintsWe measured the large-scale, bias-corrected cross-correlation functions using a background sample of H-ATLAS galaxies with photometric redshifts > 1.2 and two different foreground samples (GAMA galaxies with spectroscopic redshifts or SDSS galaxies with photometric ones, both in the range 0.2 < z < 0.8). These measurements are modelled using the traditional halo model description that depends on both halo occupation distribution and cosmological parameters. We then estimated these parameters by performing a Markov chain Monte Carlo under multiple scenarios to study the performance of this observable and how to improve its results. After the large-scale bias corrections, we obtain only minor improvements with respect to the previous magnification bias 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 as follows: $Omega_m= 0.50_{- 0.20}^{+ 0.14}$ and $sigma_8= 0.75_{- 0.10}^{+ 0.07}$ at 68% CL.
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