Limitations of CMB B-mode template delensing

Abstract

Efforts to detect a primordial B-mode of cosmic microwave background 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 nonperturbatively, 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 nonperturbative 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 nonperturbative 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 nonperturbative remapping.