CMB-S4: Foreground-Cleaning Pipeline Comparison for Measuring Primordial Gravitational Waves

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 on r across 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 lensing B-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. However, biases at the 1 − 2σ level appear when analyzing more complex foreground emissions. 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 on σ(r). At these extremely low noise levels, consistency of results across multiple foreground cleaning pipelines must be demonstrated to ensure robustness of detections.