CMB Delensing with Neural Network Based Lensing Reconstruction in the Presence of Primordial Tensor Perturbations

Abstract

The next-generation CMB experiments are expected to constrain the tensor-to-scalar ratio $r$ with high precision. Delensing is an important process as the observed CMB $B$-mode polarization that contains the primordial tensor perturbation signal is dominated by a much larger contribution due to gravitational lensing. To do so successfully, it is useful to explore methods for lensing reconstruction beyond the traditional quadratic estimator (QE) (which will become suboptimal for the next-generation experiments), and the maximum a posterior estimator (which is still currently under development). In Caldeira et al. 2020, the authors showed that a neural network (NN) method using the ResUNet architectrue performs better than the QE and slightly suboptimally compared to the iterative estimator in terms of the lensing reconstruction performance. In this work, we take one step further to evaluate the delensing performance of these estimators on maps with primordial tensor perturbations using a standard delensing pipeline, and show that the \emph{delensing} performance of the NN estimator is optimal, agreeing with that of a converged iterative estimator, when tested on a suite of simulations with $r=0.01$ and $r=0.001$ for $12.7^{\circ} \times 12.7^{\circ}$ maps at a CMB-Stage~4 like polarization noise level $1\,\mu \rm{K\,arcmin}$ and 1' beam. We found that for the purpose of delensing, it is necessary to train and evaluate the NN on a set of CMB maps with $l<l_{\rm{cut}}$ removed, in order to avoid spurious correlations on the scales of interest for the final delensed $B$-mode power spectrum $l<l_{\rm{cut}}$, similar to what was known previously for the QE and the iterative estimator. We also present various NN training techniques that can be extended for a simultaneous treatment of foregrounds and more complex instrumental effects where the modeling is more uncertain.