Planck 2013 results. XV. CMB power spectra and likelihood
  We present the Planck likelihood, a complete statistical description of the
two-point correlation function of the CMB temperature fluctuations. We use this
likelihood to derive the Planck CMB power spectrum over three decades in l,
covering 2 <= l <= 2500. The main source of error at l <= 1500 is cosmic
variance. Uncertainties in small-scale foreground modelling and instrumental
noise dominate the error budget at higher l's. For l < 50, our likelihood
exploits all Planck frequency channels from 30 to 353 GHz through a physically
motivated Bayesian component separation technique. At l >= 50, we employ a
correlated Gaussian likelihood approximation based on angular cross-spectra
derived from the 100, 143 and 217 GHz channels. We validate our likelihood
through an extensive suite of consistency tests, and assess the impact of
residual foreground and instrumental uncertainties on cosmological parameters.
We find good internal agreement among the high-l cross-spectra with residuals
of a few uK^2 at l <= 1000. We compare our results with foreground-cleaned CMB
maps, and with cross-spectra derived from the 70 GHz Planck map, and find broad
agreement in terms of spectrum residuals and cosmological parameters. The
best-fit LCDM cosmology is in excellent agreement with preliminary Planck
polarisation spectra. The standard LCDM cosmology is well constrained by Planck
by l <= 1500. For example, we report a 5.4 sigma deviation from n_s /= 1.
Considering various extensions beyond the standard model, we find no indication
of significant departures from the LCDM framework. Finally, we report a tension
between the best-fit LCDM model and the low-l spectrum in the form of a power
deficit of 5-10% at l <~ 40, significant at 2.5-3 sigma. We do not elaborate
further on its cosmological implications, but note that this is our most
puzzling finding in an otherwise remarkably consistent dataset. (Abridged)
