Tomographic cluster clustering as a cosmological probe

The spatial distribution of galaxy clusters is a valuable probe for inferring fundamental cosmological parameters. We measured the clustering properties of dark matter haloes from the PINOCCHIO simulations in the redshift range 0.2 < z < 1.0 and with virial masses Mvir > 1014 M⊙ h-1, which reproduce the expected mass selection of galaxy cluster samples. The past light cones we analysed have an angular size of 60 degrees, which approximately corresponds to one-quarter of the sky. We adopted a linear power spectrum model, accounting for non-linear corrections at the scale of baryon acoustic oscillations, to perform a comparative study between 3D and 2D tomographic clustering. For this purpose, we modelled the multipoles of the 3D two-point correlation function, ξ(s); the angular correlation function, w(θ); and the angular power spectrum, Cℓ. We considered observational effects such as redshift-space distortions produced by the peculiar velocities of tracers, and redshift errors. We found that photo-z errors have a more severe consequence on 3D clustering than on 2D clustering, as they affect only the radial separation between haloes and not the angular separation, with a relevant impact on the 3D multipoles. Using a Bayesian analysis, we explored the posterior distributions of the considered probes with different tomographic strategies, in the Ωm - σ8 plane, focusing on the summary parameter S8 ≡ σ8 √Ωm/0.3. Our results show that in the presence of large photo-z errors the 2D clustering can provide competitive cosmological constraints with respect to the full 3D clustering statistics, and can be successfully applied to analyse the galaxy cluster catalogues from the ongoing and forthcoming Stage III and Stage IV photometric redshift surveys.