Characterizing CMB noise anisotropies from CMB delensing

TL;DR

This work identifies and quantifies a delensed-noise mean-field bias that arises when CMB maps are delensed prior to lensing reconstruction. The authors derive a perturbative analytic expression for the mean-field’s response to the lensing convergence and rotation, and systematically evaluate its impact on both quadratic-estimator and maximum-a-posteriori (MAP) lensing reconstructions. They find that the mean-field mainly renormalizes the MAP normalization (by ~15–20% for SO/S4 configurations) but does not degrade reconstruction quality, enabling safe neglect of the MF in MAP searches if the normalization is corrected; neglect can bias cross-correlations with large-scale structure if not accounted. Delensing B-modes remains robust to MF neglect, while caution is advised for modulation-like analyses and foreground-rich skies, where MF will play a non-negligible role. Overall, the work provides practical guidance for incorporating or safely neglecting delensed noise MF in CMB lensing analyses and highlights its potential impact on cross-correlation cosmology and precision delensing efforts.

Abstract

Un-doing the effect of gravitational lensing on the Cosmic Microwave Background (`de-lensing') is essential in shaping constraints on weak signals limited by lensing effects on the CMB, for example on a background of primordial gravitational waves. Removing these anisotropies induced by large-scale structures from the CMB maps also generally helps our view of the primordial Universe by sharpening the acoustic peaks and the damping tail. However, practical implementations of delensing transfer parts of these anisotropies to the noise maps. This will induce a new large scale `mean-field' bias to any anisotropy estimator applied to the delensed CMB, and this bias directly traces large-scale structures. This paper analytically quantifies this delensed noise mean-field and its impact on quadratic (QE) and likelihood-based lensing estimators. We show that for Simons-Observatory-like surveys, this mean-field bias can reach 15\% in cross-correlation with large-scale structures if unaccounted for. We further demonstrate that this delensed noise mean-field can be safely neglected in likelihood-based estimators without compromising the quality of lensing reconstruction or $B$-mode delensing, provided the resulting lensing map is properly renormalized.

Figures (7)

• Figure 1: The top panel shows a randomly selected 7 degrees by 7 degrees patch of Planck effective temperature depth map after SMICA component separation Planck:2018yyeCarron:2022eyg. Delensing using a Wiener-filtered lensing tracer with fidelity similar to that expected from the Planck reconstruction will result in an effective depth given by the middle panel, where the original stripes caused by the scan strategy are modulated by the deflection field magnification. The resulting fluctuations trace the convergence map of the deflection field shown in the bottom panel.
• Figure 2: The blue line shows the contribution per multipole to the large scale (here $L=50$) delensed noise mean-field response to the lensing convergence map, for a SO-like configuration, with a Gaussian beam of $3$-arcmin and white noise. The squeezed approximation in \ref{['eq:squeezk']} is a perfect match, with the orange curve highlighting the contribution from converging rather than shearing effects on the delensed noise map. The green line shows for comparison the standard lensing signal contributions to the $TT$ lensing quadratic estimator (reduced by a factor 5). The delensed noise mean-field is sourced from significantly smaller scales, where noise is relevant but not completely dominating either. This is for temperature reconstruction.
• Figure 3: Delensed-noise mean-field response for the polarized lensing quadratic estimator, for a configuration approaching crudely the planned CMB-S4 wide survey, with equal power in the $E$ and $B$ noise spectra. All curves were computed using the lensed CMB spectra. In contrast to standard lensing, the $EB$ mean-field response is essentially zero (green), owing to the symmetry in unlensed $E$ and $B$ noise power, and $EE$ (blue) dominate the response, followed by $BB$ in orange. Dashed green shows the standard lensing response in the same configuration for comparison.
• Figure 4: Estimation of the delensed noise mean-field $\kappa^{\rm MF}$ in real space, at the first iteration of the MAP estimator from temperature. Simulations are with CMB-S4 like noise level. The left panel shows the predicted delensed noise mean-field at first order in the deflection field. The central panel shows the delensed noise mean-field estimated from a set of 20 simulations at fixed deflection field. The right panel shows the negative of the Wiener filtered true convergence field of the simulation. Patches are 200x200 pixels, with 1.5 arcmin per pixel, cutouts from full-sky simulations.
• Figure 5: Upper panel: Predicted correlation coefficients for the temperature only MAP (teal) and QE (golden) reconstruction for Planck, SO and CMB-S4 like noise levels, respectively in dotted, dash-doted and plain lines. Lower panels: Correlation coefficient after 10 iterations of our lensing reconstruction divided by the fiducial correlation coefficient, for Planck, SO and CMB-S4 noise levels from top to bottom. Note that the range of $L$ value is not the same in each panel. In teal we show the case without mean-field subtraction, in pink it is using the perturbative mean-field prediction and in purple it is with the MF estimated from simulations. The QE case is shown in golden for comparison. We see that for all recipes we find very similar correlation coefficients: neglecting the delensed noise mean-field has no impact on the quality of the lensing potential reconstruction. We also see that the predicted correlation coefficients are accurate at $\sim 2 \%$.