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Abstract We compare multiple foreground-cleaning pipelines for estimating the tensor-to-scalar ratio,r, using simulated maps of the planned CMB-S4 experiment within the context of the South Pole Deep Patch. To evaluate robustness, we analyze bias and uncertainty onracross various foreground suites using map-based simulations. The foreground-cleaning methods include: a parametric maximum likelihood approach applied to auto- and cross-power spectra between frequency maps; a map-based parametric maximum-likelihood method; and a harmonic-space internal linear combination using frequency maps. We summarize the conceptual basis of each method to highlight their similarities and differences. To better probe the impact of foreground residuals, we implement an iterative internal delensing step, leveraging a map-based pipeline to generate a lensingB-mode template from the large aperture telescope frequency maps. Our results show that the performance of the three approaches is comparable for simple and intermediate-complexity foregrounds, withσ(r) ranging from 3–5 ×10⁻⁴. However, biases at the 1σ–2σlevel appear when analyzing more complex forms of foreground emission. By extending the baseline pipelines to marginalize over foreground residuals, we demonstrate that contamination can be reduced to within statistical uncertainties, albeit with a pipeline-dependent impact onσ(r), which translates to a detection significance between 2σand 4σfor an input value ofr= 0.003. These findings suggest varying levels of maturity among the tested pipelines, with the auto- and cross-spectra-based approach demonstrating the best stability and overall performance. Moreover, given the extremely low noise levels, mutual validation of independent foreground-cleaning pipelines is essential to ensure the robustness of any potential detection. 

Abstract The tightest constraints on the tensor-to-scalar ratiorcan only be obtained after removing a substantial fraction of the lensingB-mode sample variance. The planned Cosmic Microwave Background (CMB)-S4 experiment (cmb-s4.org) will remove the lensingB-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 onr, 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 lensingB-mode templates, which are then included in a parametric small-aperture map cross-spectra-based likelihood forr. We find that the lensing reconstruction and framework achieve the expected performance, compatible with the targetσ(r) ≃ 5 · 10⁻⁴in the absence of a tensor signal, after an effective removal of 92%–93% of the lensingB-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.