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.