# Mass bias and cosmological constraints from Planck cluster clustering

## TL;DR

This study uses the clustering of Planck SZ galaxy clusters to estimate the mass bias and constrain cosmological parameters, confirming the importance of clustering data in cosmological analyses.

## Contribution

It provides the first measurement of the Planck mass bias from cluster clustering and demonstrates its impact on cosmological parameter estimation.

## Key findings

- Estimated mass bias $(1-b_{SZ})=0.62^{+0.14}_{-0.11}$ consistent with CMB-cluster count reconciliation.
- Cluster clustering constrains $ ext{Ω}_m$ effectively when priors on mass bias are used.
- Clustering data alone does not constrain $ ext{σ}_8$.

## Abstract

We analysed the 3D clustering of the Planck sample of Sunyaev-Zeldovich (SZ) selected galaxy clusters, focusing on the redshift-space two-point correlation function (2PCF). We compared our measurements to theoretical predictions of the standard $\Lambda$ cold dark matter ($\Lambda$CDM) cosmological model, deriving an estimate of the Planck mass bias, $b_{\mathrm SZ}$, and cosmological parameters. We measured the 2PCF of the sample in the cluster-centric radial range $r\in[10,150]$ $h^{-1}$Mpc, considering 920 galaxy clusters with redshift $z\leq0.8$. A Markov chain Monte Carlo analysis has been performed to constrain $b_{\mathrm SZ}$, assuming priors on cosmological parameters from Planck Cosmic Microwave Background (CMB) results. We also adopted priors on $b_{\mathrm SZ}$ from external data sets to constrain the cosmological parameters $\Omega_{\mathrm m}$ and $\sigma_8$. We obtained $(1-b_{\mathrm SZ})=0.62^{+0.14}_{-0.11}$, which is in agreement with the value required to reconcile primary CMB and cluster count observations. By adopting priors on $(1-b_{\mathrm SZ})$ from external data sets, we derived results on $\Omega_{\mathrm m}$ that are fully in agreement and competitive, in terms of uncertainties, with those derived from cluster counts. This confirms the importance of including clustering in cosmological studies, in order to fully exploit the information from galaxy cluster statistics. On the other hand, we found that $\sigma_8$ is not constrained.