Abstract
Precise reconstruction of the cosmic microwave background lensing potential can be achieved with deep polarization surveys by iteratively removing lensing-induced $B$ modes. We introduce a lensing spectrum estimator and its likelihood for such optimal iterative reconstruction. Our modeling shares similarities to the state-of-the-art likelihoods for quadratic estimator (QE)-based lensing reconstruction. In particular, we generalize the ${N}^{(0)}$ and ${N}^{(1)}$ lensing biases, and design a realization-dependent spectrum debiaser, making this estimator robust to uncertainties in the data modeling. We demonstrate unbiased recovery of the cosmology using map-based reconstructions, focussing on lensing-only cosmological constraints and neutrino mass measurement in combination with CMB spectra and acoustic oscillation data. We find this spectrum estimator is essentially optimal and with a diagonal covariance matrix. For a CMB-S4 survey, this likelihood can double the constraints on the lensing amplitude compared to the QE on a wide range of scales, while at the same time keeping numerical cost under control and being robust to errors.
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