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It has been long recognised that, besides being a formidable experiment to observe the primordial CMB anisotropies, Planck will also have the capability to detect galaxy clusters via their SZ imprint. In this paper constraints on cosmological parameters derivable from the Planck cluster candidate sample are examined for the first time as a function of cluster sample selection and purity obtained from realistic simulations of the microwave sky at the Planck observing frequency bands, observation process modelling and a cluster extraction pipeline. In particular, we employ a multi-frequency matched filtering (MFMF) method to recover clusters from mock simulations of Planck observations. Obtainable cosmological constraints under realistic assumptions of priors and knowledge about cluster redshifts are discussed. Just relying on cluster redshift abundances without making use of recovered cluster fluxes, it is shown that from the Planck cluster catalogue cosmological constraints comparable to the ones derived from recent primordial CMB power spectrum measurements can be achieved. For example, for a concordance $\Lambda$CDM model and a redshift binning of $\Delta z = 0.1$, the $1\sigma$ uncertainties on the values of $\Omega_m$ and $\sigma_8$ are $\Delta \Omega_m \approx 0.031$ and $\Delta \sigma_8 \approx 0.014$ respectively. Furthermore, we find that the constraint of the matter density depends strongly on the prior which can be imposed on the Hubble parameter by other observational means., Comment: 20 pages, 9 figures, submitted to MNRAS

We examine the ability of the future Planck mission to provide a catalogue of galaxy clusters observed via their SZ distortion in the cosmic microwave background. For this purpose we produce full-sky SZ maps based on N-body simulations and scaling relations between cluster properties for several cosmological models. We extrapolate the N-body simulations by a mass function to high redshifts in order to obtain a realistic SZ background. The simulated Planck observations include, besides the thermal and kinematic SZ effects, contributions from the primordial CMB, extragalactic point sources as well as Galactic dust, free-free and synchrotron emission. A HSMEM method is used to separate the SZ signal from contaminating components in combination with a cluster detection algorithm based on thresholding and flux integration to identify clusters and to obtain their fluxes. We estimate a survey sensitivity limit (depending on the quality of the recovered cluster flux) and provide cluster survey completeness and purity estimates. We find that given our modelling and detection algorithm Planck will reliably detect at least several thousands of clusters over the full sky. The exact number depends on the particular cosmological model (up to 10000 cluster detections in a concordance LCDM model with sigma_8=0.9). We show that the Galaxy does not significantly affect the cluster detection. Furthermore, the dependence of the thermal SZ power spectrum on the matter variance on scales of 8 Mpc/h and the quality of its reconstruction by the employed method are investigated. Our simulations suggest that the Planck cluster sample will not only be useful as a basis for follow-up observations, but also will have the ability to provide constraints on cosmological parameters., Comment: 19 pages, 14 figures, submitted to MNRAS