Planck 2015 results. XI. CMB power spectra, likelihoods, and robustness
  of parameters
  This paper presents the Planck 2015 likelihoods, statistical descriptions of
the 2-point correlations of CMB data, using the hybrid approach employed
previously: pixel-based at $\ell<30$ and a Gaussian approximation to the
distribution of spectra at higher $\ell$. The main improvements are the use of
more and better processed data and of Planck polarization data, and more
detailed foreground and instrumental models, allowing further checks and
enhanced immunity to systematics. Progress in foreground modelling enables a
larger sky fraction. Improvements in processing and instrumental models further
reduce uncertainties. For temperature, we perform an analysis of end-to-end
instrumental simulations fed into the data processing pipeline; this does not
reveal biases from residual instrumental systematics. The $\Lambda$CDM
cosmological model continues to offer a very good fit to Planck data. The slope
of primordial scalar fluctuations, $n_s$, is confirmed smaller than unity at
more than 5{\sigma} from Planck alone. We further validate robustness against
specific extensions to the baseline cosmology. E.g., the effective number of
neutrino species remains compatible with the canonical value of 3.046. This
first detailed analysis of Planck polarization concentrates on E modes. At low
$\ell$ we use temperature at all frequencies and a subset of polarization. The
frequency range improves CMB-foreground separation. Within the baseline model
this requires a reionization optical depth $\tau=0.078\pm0.019$, significantly
lower than without high-frequency data for explicit dust monitoring. At high
$\ell$ we detect residual errors in E, typically O($\mu$K$^2$); we recommend
temperature alone as the high-$\ell$ baseline. Nevertheless, Planck high-$\ell$
polarization allows a separate determination of $\Lambda$CDM parameters
consistent with those from temperature alone.
