Primordial Power Spectrum Reconstruction From CMB Weak Lensing Power
  Spectrum
  We use the modified Richardson-Lucy deconvolution algorithm to reconstruct
the Primordial Power Spectrum from the Weak Lensing Power spectrum
reconstructed from the CMB anisotropies. This provides an independent window to
observe and constrain the PPS $P_R(k)$ along different $k$ scales as compared
to CMB Temperature Power Spectrum. The Weak Lensing Power spectrum does not
contain secondary variations in power and hence is cleaner, unlike the
Temperature Power spectrum which suffers from lensing which is visible in its
PPS reconstructions. We demonstrate that the physical behaviour of the weak
lensing kernel is different from the temperature kernel and reconstructs broad
features over $k$. We provide an in-depth analysis of the error propagation
using simulated data and Monte-Carlo sampling, based on Planck best-fit
cosmological parameters to simulate the data and cosmic variance limited error
bars. The error and initial condition analysis provides a clear picture of the
optimal reconstruction region for the estimator and we provide and algorithm
for $P_R(k)$ sampling to be used based on the given data, errors and its
binning properties. Eventually we plan to use this method on actual mission
data and provide a cross reference to PPS reconstructed from other sectors and
any possible features in them.
