CMB-S4: Iterative Internal Delensing and r Constraints

The tightest constraints on the tensor-to-scalar ratio r can only be obtained after removing a substantial fraction of the lensing B-mode sample variance. The planned Cosmic Microwave Background (CMB)-S4 experiment (cmb-s4.org) will remove the lensing B-mode signal internally by reconstructing the gravitational lenses from high-resolution observations. We document here a first lensing reconstruction pipeline able to achieve this optimally for arbitrary sky coverage. We make it part of a map-based framework to test CMB-S4 delensing performance and its constraining power on r, including inhomogeneous noise and two non-Gaussian Galactic polarized foreground models. The framework performs component separation of the high-resolution maps, followed by the construction of lensing B-mode templates, which are then included in a parametric small-aperture map cross-spectra-based likelihood for r. We find that the lensing reconstruction and framework achieve the expected performance, compatible with the target sigma(r) similar or equal to 5 10(-4) in the absence of a tensor signal, after an effective removal of 92%-93% of the lensing B-mode variance, depending on the simulation set. The code for the lensing reconstruction can also be used for cross-correlation studies with large-scale structures, lensing spectrum reconstruction, cluster lensing, or other CMB lensing-related purposes. As part of our tests, we also demonstrate the joint optimal reconstruction of the lensing potential with the lensing curl potential mode at second order in the density fluctuations.