Cosmology with the sub-millimetre galaxies magnification bias: Tomographic Analysis

As in Gonzalez-Nuevo et al. 2017 and Bonavera et al. 2019, the high-z sub-millimetre galaxies can be used as background sample for gravitational lensing studies thanks to their magnification bias. In particular, as in Bonavera et al. 2020 the magnification bias can be exploited in order to constrain the free parameters of a Halo Occupation Distribution (HOD) model and some of the main cosmological parameters. In this work the magnification bias has been evaluated as cosmological tool in a tomographic set up. The cross-correlation function (CCF) data have been used to jointly constrain the astrophysical parameters $M_{min}$, $M_{1}$ and $\alpha$ in each one of the selected redshift bins and the $\Omega_{M}$, $\sigma_{8}$, and $H_0$ cosmological ones ($\Lambda$CDM). Moreover, we explore the possible time evolution of the dark energy density introducing also the $\omega_0, \omega_a$ parameters in the joint analysis ($\omega_0$CDM and $\omega_0\omega_a$CDM). The CCF has been measured between a foreground spectroscopic sample of GAMA galaxies that has been divided into four redshift bins (0.1-0.2, 0.2-0.3, 0.3-0.5 and 0.5-0.8) and a sample of H-ATLAS galaxies with photometric redshifts >1.2. The CCF is modelled using a description that depends on HOD and cosmological parameters that are estimated with MCMC in different cases. For the $\Lambda$CDM model, the analysis yields a maximum posterior value at 0.26 with $[0.17,0.41]$ 68\% C.I. for $\Omega_M$ and at 0.87 with $[0.75,1]$ 68\% C.I. for $\sigma_8$. With our current results $H_0$ is not yet constrained. With the $\omega_0$CDM model, the constraints on $\Omega_M$ and $\sigma_8$ are similar, but we found a maximum posterior value for $\omega_0$ at -1 with $[-1.56, -0.47]$ 68\% C.I. In the $\omega_0\omega_a$CDM model, the results are -1.09 with $[-1.72, -0.66]$ 68\% C.I. for $\omega_0$ and -0.19 with $[-1.88, 1.48]$ 68\% C.I. for $\omega_a$.