Primordial Power Spectrum reconstruction from CMB Weak Lensing Power Spectrum

We use the modified and improved Richardson-Lucy (IRL) deconvolution algorithm to reconstruct the Primordial Power Spectrum (PPS) from the Weak Lensing Power Spectrum C-L(phi phi) reconstructed from 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 must be addressed during PPS reconstructions. We demonstrate that the physical behaviour of the weak lensing kernel is unique and reconstructs broad features over k. We provide an in-depth analysis of the error propagation using simulated data and Monte-Carlo sampling, using Planck best-fit cosmological parameters to simulate the data with cosmic variance limited error bars. The error and initial condition analyses provide a clear picture of the optimal reconstruction region for the estimator while providing a detailed statistical insight of the results. We also provide an algorithm for P-R(k) sampling sparsity to be used based on the given data and errors, to optimize statistical significance. 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.