Cosmology with the submillimetre galaxies magnification bias: Tomographic analysis

Context. 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. Aims. 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 Mmin, M1, and α in each of the selected redshift bins as well as the cosmological parameters ωM, σ8, and H0 for the lambda cold dark matter (ΛCDM) model. Moreover, we explore the possible time evolution of the dark energy density by also introducing the ω0, ωa parameters in the joint analysis (ω0CDM and ω0ωaCDM). Methods. 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. Results. For the ΛCDM model the analysis yields a maximum posterior value at 0.26 with [0.17, 0.41] 68% C.I. for ωM and at 0.87 with [0.75, 1] 68% C.I. for σ8. With our current results H0 is not yet constrained. With a more general ω0CDM model, the constraints on ωM and σ8 are similar, but we found a maximum posterior value for ω0 at -1 with [ - 1.56, -0.47] 68% C.I. In the ω0ωaCDM model, the results are -1.09 with [ - 1.72, -0.66] 68% C.I. for ω0 and -0.19 with [ - 1.88, 1.48] 68% C.I. for ωa. Conclusions. 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 σ8 - ωM 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 ω0 values for lower H0 values.