Delensing for Precision Cosmology: Optimizing Future CMB B-mode Surveys to Constrain r

TL;DR

This study develops a streamlined delensing framework for precision CMB B-mode cosmology by combining internal CMB lensing reconstruction with external large-scale structure tracers (CIB and Euclid galaxies). It compares two delensing approaches—Gradient-order template and inverse-lensing—and rigorously analyzes biases from foregrounds and lensing reconstruction using simulations, debiasing with transfer functions, and cross-spectral likelihoods. The results show substantial improvements in constraining r: roughly 40% with CMB-only LT and up to ~60% when including LSS tracers, with consistent results across Gaussian and Hamimeche–Lewis likelihoods. A generalized modeling approach that allows for LT biases via an extra parameter improves bias control, though at a modest cost to precision; overall, the framework demonstrates that combining NILC foreground handling, internal reconstruction, and multi-tracer delensing can significantly enhance sensitivity to primordial gravitational waves for future ground-based CMB experiments.

Abstract

The detection of primordial B-modes, a key probe of cosmic inflation, is increasingly challenged by contamination from weak gravitational lensing B-modes induced by large-scale structure (LSS). We present a delensing pipeline designed to enhance the sensitivity to the inflationary parameter r, minimizing reliance on foreground mitigation during lensing reconstruction. Using simulations of Simons Observatory-like CMB observations and Euclid-like LSS surveys in the Northern hemisphere, we demonstrate that excluding low-l modes (l<200) effectively mitigates foreground biases, enabling robust lensing potential reconstruction using observed CMB polarization maps. We reconstruct the lensing potential with a minimum-variance (MV) quadratic estimator (QE) applied to CMB polarization data and combine this with external LSS tracers to improve delensing efficiency. Two complementary methods, the Gradient-order template and the Inverse-lensing approach, are used to generate lensing B-mode templates, which are cross-correlated with observed B-modes. This achieves a 40 percent reduction in the uncertainty of r with CMB-only reconstruction, improving to 60 percent when incorporating external LSS tracers. We validate our results using both the Hamimeche and Lewis likelihood and a Gaussian approximation, finding consistent constraints on r. Our work establishes a streamlined framework for ground-based CMB experiments, demonstrating that synergies with LSS surveys significantly enhance sensitivity to primordial gravitational waves.

Figures (23)

• Figure 1: The B-mode maps of the template (middle panel), constructed from the foreground E-mode and the input foreground at 93 GHz (left panel), are presented. We observe that only a negligible portion of the E-modes is converted to B-modes, and the difference map (right panel)—referred to as the delensed map—shows almost no change compared to the input foreground. The maximum multipole is set to be $\ell_\text{max}=3000$.
• Figure 2: The B-mode power spectra of the template constructed from the foreground E-mode, input foreground, and their difference at 93 GHz is shown. We observe that, at the scales presented, the power of the template constructed from the foreground E-mode is very small, indicating negligible lensing effects (as demonstrated by the perfect overlap of the orange dashed line with the black solid line). It is important to note that the power of the foreground difference is related to the intensity of the input foreground.
• Figure 3: B-mode map comparisons of remapped foreground (middle panel) and input foreground at 93 GHz(left panel) at different multipole ranges. The first column shows the input foreground B-mode maps, the second column displays the remapped foreground B-mode maps, and the third column illustrates their difference. Results are presented for three multipole ranges: $\ell_{\text{max}} = 200$, $1000$, and $6000$. On large scales ($\ell_{\text{max}} = 200$), the differences are negligible, indicating accurate template construction. However, as the multipole range increases, the differences grow, reflecting more significant deviations on smaller angular scales due to lensing effect.
• Figure 4: The plot compares the B-mode power spectra of the remapped foreground, the input foreground, and their difference. The difference foreground is derived by subtracting the remapped foreground from the input foreground at the map level. The results show negligible differences on large scales, while the differences become more pronounced as the multipoles increase. It is important to note that the power of the foreground difference correlates with the intensity of the input foreground.
• Figure 5: The overlap masks of the LAT and SAT utilized in the simulation. The left panel is the apodized mask used for the delensing procedure, and the right one shows the apodized mask used for the calculation of pseudo-Cl with NaMasteralonso2023namaster.