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Description
High-z submillimetre galaxies can be used as a background sample for gravitational lensing studies thanks to their magnification bias. In particular, 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. A pseudo-tomographic analysis shows that the tomographic approach should improve the parameter estimation. 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, as well as the cosmological parameter {Omega}_M_, {sigma}_8_ and H_0_ for the lambda cold dark matter ({Lambda}CMD). Moreover, we explore the possible time evolution of the dark energy density introducing the {omaga}_0_ and {omage}_a_ parameters in the joint analysis ({omega}_0_CDM and {omega}_0_{omega}_a_CDM). The CCF was measured between a foreground spectroscopic sample of Galaxy And Mass Assembly galaxies and a background sample of Herschel Astrophysical Terahertz Large Area Survey (H-ATLAS) galaxies. The foreground sample was divided into four redshift bins (0.1-0.2, 0.2-0.3, 0.3-0.5, and 0.5-0.8) and the sample of H-ATLAS galaxies has photometric redshifts >1.2. The CCF was modelled using a halo model description that depends on HOD and cosmological parameters. Then a Markov chain Monte Carlo method was used to estimate the parameters for 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 a more general {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_. The results on Mmin show a trend towards higher values at higher redshift confirming recent findings. The tomographic analysis presented in this work improves the constraints in the {sigma}_8_-{Omega}_M_ plane with respect to previous findings exploiting the magnification bias and it confirms that magnification bias results do not show the degeneracy found with cosmic shear measurements. Moreover, related to dark energy, we found a trend of higher {omega}_0_ values for lower H_0_ values.
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