Spherical needlets for cosmic microwave background data analysis

We discuss spherical needlets and their properties. Needlets are a form of spherical wavelets which do not rely on any kind of tangent plane approximation and enjoy good localization properties in both pixel and harmonic space; moreover needlet coefficients are asymptotically uncorrelated at any fixed angular distance, which makes their use in statistical procedures very promising. In view of these properties, we believe needlets may turn out to be especially useful in the analysis of cosmic microwave background (CMB) data on the incomplete sky, as well as of other cosmological observations. As a final advantage, we stress that the implementation of needlets is computationally very convenient and may rely completely on standard data analysis packages such as healp ix.     

Separation of instrumental and astrophysical foregrounds for mapping cosmic microwave background anisotropies

For the most sensitive present and future experiments dedicated to cosmic microwave background (CMB) anisotropy observations, the identification and separation of signals coming from different sources is an important step in the data analysis. This problem of the restitution of signals from the observation of their mixture is classically called 'component separation' in CMB mapping. In this paper, we address the general problem of separating, for millimetre-wave sky-mapping applications, components which include not only astrophysical emissions in two-dimensional maps, but also one-dimensional instrumental effects in the data streams. We show that component separation methods can be adapted to separate simultaneously both astrophysical emissions and components coming from time-dependent foreground signals which originate from the instrument itself. Such general methods can be used for the optimal processing of low-redundancy observations where multi-channel observations are a precious tool to remove systematic effects, as may be the case for the Planck mission.     

Circular scans for cosmic microwave background anisotropy observation and analysis

A number of experiments for measuring anisotropies of the cosmic microwave background (CMB) use scanning strategies in which temperature fluctuations are measured along circular scans on the sky. It is possible, from a large number of such intersecting circular scans, to build two-dimensional sky maps for subsequent analysis. However, since instrumental effects — especially the excess low-frequency 1/ f noise — project on to such two-dimensional maps in a non-trivial way, we discuss the analysis approach which focuses on information contained in the individual circular scans. This natural way of looking at CMB data from experiments scanning on the circles combines the advantages of elegant simplicity of Fourier series for the computation of statistics useful for constraining cosmological scenarios, and superior efficiency in analysing and quantifying most of the crucial instrumental effects.     

Large-scale cosmic microwave background anisotropies and dark energy

In this paper we investigate the effects of perturbations in a dark energy component with a constant equation of state on large-scale cosmic microwave background (CMB) anisotropies. The inclusion of perturbations increases the large-scale power. We investigate more speculative dark energy models with   w < −1  and find the opposite behaviour. Overall the inclusion of perturbations in the dark energy component increases the degeneracies. We generalize the parametrization of the dark energy fluctuations to allow for an arbitrary constant sound speed, and we show how constraints from CMB experiments change if this is included. Combining CMB with large-scale structure, Hubble parameter and supernovae observations we obtain   w =−1.02 ± 0.16 (1σ)  as a constraint on the equation of state, which is almost independent of the sound speed chosen. With the presented analysis we find no significant constraint on the constant speed of sound of the dark energy component.     

Processing and compression of noise-dominated data: application to the cosmic microwave background data on board the Planck satellite

We address the problem of encoding and compressing data dominated by noise. Information is decomposed into 'reference' sequences plus arrays containing noisy differences susceptible to being described by a known probability distribution. One can then give reliable estimates of the optimal compression rates by estimating the corresponding Shannon entropy. As a working example, this idea is applied to an idealized model of the cosmic microwave background (CMB) data on board the Planck satellite. Data reduction is a critical issue in space missions because the total information that can be downloaded to Earth is sometimes limited by telemetry allocation. Similar limitations might arise in remotely operated ground based telescopes. This download-rate limitation could reduce the amount of diagnostics sent on the stability of the instruments and, as a consequence, curb the final sensitivity of the scientific signal. Our proposal for Planck consists of taking differences of consecutive circles at a given sky pointing. To a good approximation, these differences could be made independent of the external signal, so that they are dominated by thermal (white) instrumental noise, which is simpler to model than the sky signal. Similar approaches can be found in other individual applications. Generic simulations and analytical predictions show that high compression rates,     can be obtained with minor or zero loss of sensitivity. Possible effects of digital distortion are also analysed. The proposed scheme is flexible and reliable enough to be optimized in relation to other critical aspects of the corresponding application. For Planck , this study constitutes an important step towards a more realistic modelling of the final sensitivity of the CMB temperature anisotropy maps.     

Map-making methods for cosmic microwave background experiments

The map-making step of cosmic microwave background (CMB) data analysis involves linear inversion problems that cannot be performed by a brute-force approach for the large time-lines of today. In this paper we present optimal vector-only map-making methods, which are an iterative COBE method, a Wiener direct filter and a Wiener iterative method. We apply these methods on diverse simulated data, and we show that they produce very well restored maps, by removing nearly completely the correlated noise that appears as intense stripes on the simply pixel-averaged maps. The COBE iterative method can be applied to any signals, assuming the stationarity of the noise in the time-line. The Wiener methods assume both the stationarity of the noise and the sky, which is the case for CMB-only data. We apply the methods to Galactic signals too, and test them on balloon-borne experiment strategies and on a satellite whole-sky survey.