2021A&A...656A..99B

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 M_min, M₁, and α in each of the selected redshift bins as well as the cosmological parameters Ω_M, 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, ω_a parameters in the joint analysis (ω₀CDM and ω₀ω_aCDM).
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 Ω_M 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 Ω_M 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 ω₀ω_aCDM 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 ω_a.
Conclusions. The results on M_min 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 - Ω_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 ω₀ values for lower H₀ values.