On the tomographic cluster clustering as a cosmological probe

TL;DR

This study compares 2D and 3D galaxy cluster clustering methods using simulations, showing that 2D clustering remains effective for cosmological constraints even with photometric redshift errors, aiding future surveys.

Contribution

It demonstrates that 2D clustering analysis can be competitive with 3D methods for cosmological parameter estimation under realistic observational errors.

Findings

Photometric redshift errors impact 3D clustering more than 2D.

2D clustering provides competitive constraints on cosmological parameters.

Results support using 2D clustering for upcoming photometric surveys.

Abstract

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 \textsc{Pinocchio} simulations, in the redshift range $0.2 < z < 1.0$ and with virial masses $M_\mathrm{vir} > 10^{14} M_\odot \, h^{-1}$, 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 a quarter of the sky. We adopted a linear power spectrum model, accounting for nonlinear corrections at the baryon acoustic oscillations scale, 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, $\xi(r)$, the angular correlation function, $w(\theta)$, and the angular power spectrum, $C_\ell$. We considered observational effects such as redshift-space distortions, produced by the peculiar velocities of tracers, and redshift errors. We found that photometric redshift errors have a more severe consequence on the 3D than on the 2D clustering, as they affect only the radial separation between haloes and not the angular one, 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 $\Omega_m-\sigma_8$ plane, focusing on the summary parameter $S_8\equiv \sigma_8\sqrt{\Omega_m/0.3}$. Our results show that in the presence of large photometric 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.