Cosmic Insights from Galaxy Clusters: Exploring Magnification Bias on Sub-millimeter Galaxies

Magnification bias, an observational effect of gravitational lensing in the weak regime, allows testing the cosmological model through angular correlations of sources at different redshifts. This effect has been observed in various contexts, particularly with sub-millimeter galaxies (SMGs), offering astrophysical and cosmological insights. The study aims to investigate the magnification bias effect exerted by galaxy clusters on SMGs and its implications for astrophysical and cosmological parameters within the ΛCDM model. Magnification bias was explored through quantifying the cross-correlation function, utilised to derive constraints on cosmological and astrophysical parameters with a Markov Chain Monte Carlo algorithm. Two distinct galaxy cluster samples were used to assess result robustness and understand the influence of sample characteristics. Cluster samples show higher cross-correlation values than galaxies, with an excess at larger scales suggesting contributions from additional large-scale structures. The parameters obtained, while consistent with galaxies, are less constrained due to broader redshift distributions and limited cluster statistics. Results align with weak lensing studies, hinting at slightly lower σ_8 and Ω_m values than Planck's CMB data, emphasizing the need for enhanced precision and alternative low-redshift universe tests. While yielding constraints compatible with the ΛCDM model, limitations include broader redshift distributions and a limited number of lenses, resulting in less constrained parameters compared to previous galaxy studies. Nonetheless, the study underscores the potential of using galaxy clusters as lenses for magnification bias studies, capitalising on their elevated mass, providing a promising avenue to test current Cosmology theories. Further progress can be made by expanding the lens sample size.