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This paper introduces a technique called needlet Karhunen–Loéve (NKL), which cleans both polarized and unpolarized foregrounds from H i intensity maps by applying a Karhunen–Loéve transform on the needlet coefficients. In NKL, one takes advantage of correlations not only along the line of sight, but also between different angular regions, referred to as ‘chunks’. This provides a distinct advantage over many of the standard techniques applied to map space that one finds in the literature, which do not consider such spatial correlations. Moreover, the NKL technique does not require any priors on the nature of the foregrounds, which is important when considering polarized foregrounds. We also introduce a modified version of Generalized Needlet Internal Linear Combination (GNILC), referred to as MGNILC, which incorporates an approximation of the foregrounds to improve performance. The NKL and MGNILC techniques are tested on simulated maps which include polarized foregrounds. Their performance is compared to the GNILC, generalized morphological component analysis, independent component analysis, and principal component analysis techniques. Two separate tests were performed. One at 1.84 < z < 2.55 and the other at 0.31 < z < 0.45. NKL was found to provide the best performance in both tests, providing a factor of 10–50 improvement over GNILC at $k \lt 0.1\, {\rm hMpc^{-1}}$ in the higher redshift case and $k \lt 0.03 \, {\rm hMpc^{-1}}$ in the lower redshift case. However, none of the methods were found to recover the power spectrum satisfactorily at all baryon acoustic oscillations scales.

 

Abstract CMB-S4—the next-generation ground-based cosmic microwave background (CMB) experiment—is set to significantly advance the sensitivity of CMB measurements and enhance our understanding of the origin and evolution of the universe. Among the science cases pursued with CMB-S4, the quest for detecting primordial gravitational waves is a central driver of the experimental design. This work details the development of a forecasting framework that includes a power-spectrum-based semianalytic projection tool, targeted explicitly toward optimizing constraints on the tensor-to-scalar ratio, r , in the presence of Galactic foregrounds and gravitational lensing of the CMB. This framework is unique in its direct use of information from the achieved performance of current Stage 2–3 CMB experiments to robustly forecast the science reach of upcoming CMB-polarization endeavors. The methodology allows for rapid iteration over experimental configurations and offers a flexible way to optimize the design of future experiments, given a desired scientific goal. To form a closed-loop process, we couple this semianalytic tool with map-based validation studies, which allow for the injection of additional complexity and verification of our forecasts with several independent analysis methods. We document multiple rounds of forecasts for CMB-S4 using this process and the resulting establishment of the current reference design of the primordial gravitational-wave component of the Stage-4 experiment, optimized to achieve our science goals of detecting primordial gravitational waves for r > 0.003 at greater than 5 σ , or in the absence of a detection, of reaching an upper limit of r < 0.001 at 95% CL.