  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.
