Abstract
Searches for the imprint of primordial gravitational waves in degree-scale CMB B-mode polarisation data must account for significant contamination from gravitational lensing. Fortunately, the lensing effects can be partially removed by combining high-resolution E-mode measurements with an estimate of the projected matter distribution. In the near future, experimental characteristics will be such that the latter can be reconstructed internally with high fidelity from the observed CMB, with the EB quadratic estimator providing a large fraction of the signal-to-noise. It is a well-known phenomenon in this context that any overlap in modes between the B-field to be delensed and the B-field from which the reconstruction is derived leads to a suppression of delensed power going beyond that which can be attributed to a mitigation of the lensing effects. More importantly, the variance associated with this spectrum is also reduced, posing the question of whether the additional power suppression could help better constrain the tensor-to-scalar ratio, r. In this paper, we show this is not the case, as suggested but not quantified in previous work. We develop an analytic model for the biased delensed B-mode angular power spectrum, which suggests a simple renormalisation prescription to avoid bias on the inferred tensor-to-scalar ratio. With this approach, we learn that the bias necessarily leads to a degradation of the signal-to-noise on a primordial component compared to “unbiased delensing”. Next, we assess the impact of removing from the lensing reconstruction any overlapping B-modes on our ability to constrain r, showing that it is in general advantageous to do this rather than modelling or renormalising the bias. Finally, we verify these results within a maximum-likelihood inference framework applied to simulations.
Highlights
The removal of lensing B-modes cannot be achieved via multi-frequency cleaning, since lensing merely induces a remapping of photons by small deflection angles while preserving the blackbody spectrum of the unlensed CMB
Ref. [19] showed that whenever there is an overlap in modes between the field we wish to delens and the fields from which a lensing reconstruction is derived, the delensed power is subject to a bias that leads to a suppression in power going beyond that which can be attributed to a mitigation of the lensing effects
We expect constraints on r to worsen in this case, which we demonstrate through a simulated maximum-likelihood analysis
Summary
In order to undo the deflections induced by lensing, an estimate of the projected matter distribution on the sky – which determines the lensing potential – is required. The CIB retains a high degree of correlation with the smaller-scale lenses at high redshift that are important for converting E-modes into B-modes, something that is not yet possible with internal lensing reconstruction, which is very noisy on the relevant angular scales This situation will change with planned CMB polarisation surveys, which can provide high signal-to-noise lensing reconstructions on most scales relevant for B-mode delensing [25]. For low enough noise levels, the quadratic estimator involving E and B fields is expected to provide the highest signal-to-noise reconstruction – the reason being that, in this case, the dominant source of reconstruction noise involves the Gaussian contraction EE BB , and the lensing and primordial contributions to BB are small [27] It is because of its relevance in upcoming efforts to delens the CMB that we focus on the EB estimator in this paper. As its effect is negligible for values of r compatible with experimental bounds
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