Primordial Power Spectrum from Lensed CMB Temperature Spectrum using Iterative Delensing

We address a current caveat in the deconvolution of the Primordial Power Spectrum (PPS), from observed Cosmic Microwave Background (CMB) temperature anisotropy, in the presence of weak lensing of the CMB by the large scale structure (LSS) in the Universe. Richardson-Lucy (RL) deconvolution algorithm has been used in the context of reconstructing a free-form PPS, $P_R(k)$ from the observed lensed CMB temperature anisotropy power spectrum $\widetilde{C}_{\ell}^{TT}$. We propose and demonstrate that the RL algorithm works in the context of a non-linear convolution where the non-linear contribution is small, such as the effect of weak lensing of the $\widetilde{C}_{\ell}^{TT}$, for the deconvolution of the PPS from it. The Non-Linear Iterative Richardson-Lucy (NIRL) algorithm is successful at both convergence, as well as fidelity, in reconstructing features in some underlying PPS. This makes PPS reconstruction efforts more robust in accounting for the weak lensing effect in the CMB temperature observations. No prior assumptions on the PPS are involved during the iterative delensing process, and distinct improvement is noted over a power-law template based delensing approach used earlier, at the cost of moderately increased computational cost due to the NIRL reconstruction kernel.