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Nonparametric Forecasts of the CMB Angular Power Spectra for the Planck Mission

The Planck mission, designed for making measurements of the cosmic microwave background (CMB) radiation with unprecedented accuracy and angular resolution, is expected to release its first data set in the near future. For the first time in the CMB history, extensive measurements of the CMB polarization will be made available for the entire sky. Such precise and rich data are expected to contain a great wealth of information about the Universe. The information in the CMB data is conveniently represented in terms of angular power spectra for temperature and polarization. A proper estimation of these CMB power spectra from data is the first step in making inferences about the Universe and, in particular, cosmological parameters that govern the Universe. In this paper, we provide forecasts for the $TT$, $EE$, and $TE$ angular power spectra for the Planck mission. Our forecasts are made using synthetic data based on the best-fit $Λ$CDM model while conforming to the characteristics and parameters of the Planck mission. We have analysed such synthetic data sets using a nonparametric function estimation formalism that is otherwise asymptotically model-independent. Indeed, the power spectra estimated from such synthetic data turn out to be sufficiently close to the corresponding $Λ$CDM spectra. Our analysis further indicates that the three angular power spectra are determined sufficiently well for $2 \le l \lesssim l_{max}$, where $l_{max} = 2500 {($TT$),} 1377 {($EE$), and} 1727 {($TE$)}$ respectively. A signature of reionization is evident in the $EE$ and $TE$ power spectra in the form of a bump at low $l$s ...