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We present a semi-analytical method to investigate the systematic effects and statistical uncertainties of the calculated angular power spectrum when incomplete spherical maps are used. The computed power spectrum suffers in particular a loss of angular frequency resolution, which can be written as , where is the effective maximum extent of the partial spherical maps. We propose a correction algorithm to reduce systematic effects on the estimated , as obtained from the partial map projection on the spherical harmonic basis. We have derived near-optimal bands and weighting functions in -space for the power spectrum calculation using small maps, and a correction algorithm for partially masked spherical maps that contain information on the angular correlations on all scales. [ABSTRACT FROM AUTHOR]

The form of the primordial power spectrum has the potential to differentiate strongly between competing models of perturbation generation in the early universe and so is of considerable importance. The recent release of five years of Wilkinson Microwave Anisotropy Probe observations have confirmed the general picture of the primordial power spectrum as deviating slightly from scale invariance with a spectral tilt parameter of . None the less, many attempts have been made to isolate further features such as breaks and cut-offs using a variety of methods, some employing more than ∼10 varying parameters. In this paper, we apply the robust technique of the Bayesian model selection to reconstruct the optimal degree of structure in the spectrum. We model the spectrum simply and generically as piecewise linear in between ‘nodes’ in k space whose amplitudes are allowed to vary. The number of nodes and their k-space positions are chosen by the Bayesian evidence so that we can identify both the complexity and location of any detected features. Our optimal reconstruction contains, perhaps, surprisingly few features, the data preferring just three nodes. This reconstruction allows for a degree of scale dependence of the tilt with the ‘turn-over’ scale occurring around . More structure is penalized by the evidence as overfitting the data, so there is currently little point in attempting reconstructions that are more complex. [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]

We presentXspect, a method to obtain estimates of the angular power spectrum of the cosmic microwave background (CMB) temperature anisotropies including analytical error bars developed for theArcheopsexperiment. Cross-power spectra are computed from a set of maps and each of them is in itself an unbiased estimate of the power spectrum as long as the detector noises are uncorrelated. Then, the cross-power spectra are combined into a final temperature power spectrum with error bars analytically derived from the cross-correlation matrix.This method presents three main useful properties: (1) no estimation of the noise power spectrum is needed; (2) complex weighting schemes including sky covering and map noise properties can be easily taken into account, and corrected for, for each input map; and (3) error bars are quickly computed analytically from the data themselves with no Monte Carlo simulations involved.Xspectalso permits the study of common fluctuations between maps from different sky surveys such as CMB, Sunyaev–Zel'dovich effect or mass fluctuations from weak lensing observations. [ABSTRACT FROM AUTHOR]