Primordial power spectrum from Planck
  Using modified Richardson-Lucy algorithm we reconstruct the primordial power
spectrum (PPS) from Planck Cosmic Microwave Background (CMB) temperature
anisotropy data. In our analysis we use different combinations of angular power
spectra from Planck to reconstruct the shape of the primordial power spectrum
and locate possible features. Performing an extensive error analysis we found
the dip near $\ell\sim750-850$ represents the most prominent feature in the
data. Feature near $\ell\sim1800-2000$ is detectable with high confidence only
in 217 GHz spectrum and is apparently consequence of a small systematic as
described in the revised Planck 2013 papers. Fixing the background cosmological
parameters and the foreground nuisance parameters to their best fit baseline
values, we report that the best fit power law primordial power spectrum is
consistent with the reconstructed form of the PPS at 2$\sigma$ C.L. of the
estimated errors (apart from the local features mentioned above). As a
consistency test, we found the reconstructed primordial power spectrum from
Planck temperature data can also substantially improve the fit to WMAP-9
angular power spectrum data (with respect to power-law form of the PPS)
allowing an overall amplitude shift of $\sim2.5\%$. In this context low-$\ell$
and 100 GHz spectrum from Planck which have proper overlap in the multipole
range with WMAP data found to be completely consistent with WMAP-9 (allowing
amplitude shift). As another important result of our analysis we do report the
evidence of gravitational lensing through the reconstruction analysis. Finally
we present two smooth form of the PPS containing only the important features.
These smooth forms of PPS can provide significant improvements in fitting the
data (with respect to the power law PPS) and can be helpful to give hints for
inflationary model building.
