Limitations of CMB B-mode template delensing

Abstract

Efforts to detect a primordial $B$-mode of CMB polarization generated by inflationary gravitational waves ought to mitigate the large variance associated with the $B$-modes produced by gravitational lensing, a process known as delensing. A popular approach to delensing entails building a lensing $B$-mode template by mimicking the lensing operation, either at gradient order or non-perturbatively, using high-resolution $E$-mode observations and some proxy of the lensing potential. By explicitly calculating all contributions to two-loop order in lensing to the power spectrum of $B$-modes delensed with such a template in the noise-free limit, we are able to show that: (i) corrections to the leading-order calculation of the lensing $B$-mode power spectrum only enter at the $O(1)\%$ level because of extensive cancellations between large terms at next-to-leading order; (ii) these cancellations would disappear if a gradient-order template were to be built from unlensed or delensed $E$-modes, giving rise to a residual delensing floor of $O(10)\%$ of the original power; (iii) new cancellations arise when the lensed $E$-modes are used in the gradient-order template, allowing for the delensing floor to be as low as $O(1)\%$ of the original power in practical applications of this method; and (iv) these new cancellations would disappear for a non-perturbative template constructed from the lensed $E$-modes, reintroducing a residual delensing floor of $O(10)\%$. We further show that the gradient-order template outperforms the non-perturbative one in realistic scenarios with noisy estimates of the $E$-mode polarization and lensing potential. We therefore recommend that in practical applications of $B$-mode template delensing, where the template is constructed directly from the (filtered) observed $E$-modes, the gradient-order approach should be used rather than a non-perturbative remapping.

12 pages + references. 5 Figures. Published in PRD as an "Editor's suggestion"

References in corpus (4)

• CMB-S4 Science Case, Reference Design, and Project Plan
• Detectability of CMB tensor B modes via delensing with weak lensing galaxy surveys
• Lensing reconstruction from a patchwork of polarization maps
• Emission-angle and polarization-rotation effects in the lensed CMB

Cited by in corpus (16)

• The Simons Observatory: Constraining inflationary gravitational waves with multi-tracer B-mode delensing
• CMB-S4: Iterative Internal Delensing and $r$ Constraints
• Foreground Separation and Constraints on Primordial Gravitational Waves with the PICO Space Mission
• LiteBIRD Science Goals and Forecasts: Improving Sensitivity to Inflationary Gravitational Waves with Multitracer Delensing
• Delensing the CMB with the cosmic infrared background: the impact of foregrounds
• The impact of extragalactic foregrounds on internal delensing of CMB B-mode polarization
• A numerical study of observational systematic errors in lensing analysis of CMB polarization
• A halo model of extragalactic contamination to CMB lensing, delensing, and cross-correlations
• The parity-odd Intrinsic Bispectrum
• Model independent variance cancellation in CMB lensing cross-correlations
• Stage IV CMB forecasts for warm inflation
• Enhancing Primordial B-mode Detection: Comprehensive Delensing Pipelines for Improved Sensitivity to $r$
• Delensing for Precision Cosmology: Optimizing Future CMB B-mode Surveys to Constrain r
• LiteBIRD science goals and forecasts: improved full-sky reconstruction of the gravitational lensing potential through the combination of Planck and LiteBIRD data
• Delensing CMB B-modes using galaxy surveys: the effect of galaxy bias and matter clustering non-linearities
• Characterizing CMB noise anisotropies from CMB delensing