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It has been long recognized that, besides being a formidable experiment to observe the primordial cosmic microwave background (CMB) anisotropies, Planck will also have the capability to detect galaxy clusters via their Sunyaev–Zel'dovich (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 multifrequency 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 Λ cold dark matter (ΛCDM) model and a redshift binning of , the 1σ uncertainties on the values of Ωm and σ8 are and , 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. [ABSTRACT FROM AUTHOR]

We develop the pseudo- Cℓ method for reconstructing the cosmic microwave background (CMB) temperature and polarization auto- and cross-power spectra, and estimate the pseudo- Cℓ covariance matrix for a realistic experiment on the cut sky. We calculate the full coupling equations for all six possible CMB power spectra, relating the observed pseudo- Cℓ values to the underlying all-sky Cℓ values, and test the reconstruction on both full-sky and cut-sky simulated CMB data sets. In particular we consider the reconstruction of the Cℓ from upcoming ground-based polarization experiments covering areas of a few hundred deg2 and find that the method is fast, unbiased and performs well over a wide range of multipoles from to . We then calculate the full covariance matrix between the modes of the pseudo-temperature and polarization power spectra, assuming that the underlying CMB fields are Gaussian randomly distributed. The complexity of the covariance matrix prohibits its rapid calculation, required for parameter estimation. Hence we present an approximation for the covariance matrix in terms of convolutions of the underlying power spectra. The coupling matrices in these expressions can be estimated by fitting to numerical simulations, circumventing direct and slow calculation, and further, inaccurate analytic approximations. We show that these coupling matrices are mostly independent of cosmology, and that the full covariance matrix for all six pseudo- Cℓ power spectra can be quickly and accurately calculated for any given cosmological model using this method. We compare these semi-analytic covariance matrices against simulations and find good agreement, the accuracy of which depends mainly on survey area and the range of cosmological parameters considered. [ABSTRACT FROM AUTHOR]