CMB lensing from Planck PR4 maps

TL;DR

This work reanalyzes Planck CMB data using PR4 (NPIPE) maps to produce a more-optimal full-sky lensing reconstruction with joint T–E filtering and a generalized minimum-variance estimator (GMV). It introduces κ-filtering to down-weight noise-dominated regions, employs a realization-dependent covariance scheme, and accounts for point-source and other biases, yielding a 20% improvement in lensing S/N over PR3. The resulting CMB-lensing amplitude is tightly constrained, with A_lensing = 1.004 ± 0.024 relative to the Planck 2018 best-fit, and the derived ΛCDM constraints are sharpened when combined with BAO data (e.g., σ8 = 0.814 ± 0.016, H0 = 68.1 ± 1.0 km/s/Mpc). Polarization-only lensing constraints remain weaker but still informative, and the ISW–lensing detection is reinforced. Overall, PR4 advances the precision of Planck lensing analyses and provides a robust framework for future, more sensitive measurements.

Abstract

We reconstruct the Cosmic Microwave Background (CMB) lensing potential on the latest Planck CMB PR4 (NPIPE) maps, which include slightly more data than the 2018 PR3 release, and implement quadratic estimators using more optimal filtering. We increase the reconstruction signal to noise by almost $20\%$, constraining the amplitude of the CMB-marginalized lensing power spectrum in units of the Planck 2018 best-fit to $1.004 \pm 0.024$ ($68\%$ limits), which is the tightest constraint on the CMB lensing power spectrum to date. For a base $Λ$CDM cosmology we find $σ_8 Ω_m^{0.25} = 0.599\pm 0.016$ from CMB lensing alone in combination with weak priors and element abundance observations. Combination with baryon acoustic oscillation data gives tight $68\%$ constraints on individual $Λ$CDM parameters $σ_8 = 0.814\pm 0.016$, $H_0 = 68.1^{+1.0}_{-1.1}$km s$^{-1}$ Mpc$^{-1}$, $Ω_m = 0.313^{+0.014}_{-0.016}$. Planck polarized maps alone now constrain the lensing power to $7\%$.

Figures (7)

• Figure 1: Top panel: the foreground model map input to the cleanest CMB channel $143$GHz PR4 simulation maps on the lensing mask (all panels in $\mu$K, with different scales). Middle panel: approximate residuals after foreground cleaning using our SMICA weighting of the frequency channels, where the most visible features are a handful of bright sources leaking slightly out of the point-source mask, and zodiacal emission dust bands. Bottom panel: the difference of the middle panel to the PR4 simulations average, sourced by the data processing.
• Figure 2: The large-scale effective lensing convergence reconstruction noise variance map, $N^\kappa_{0,{\rm eff}}$, obtained by averaging the approximately flat convergence noise spectrum across the range $8 \leq L \leq 100$. After applying the same mask as for CMB filtering, and condensing this map into a simpler one with 64 homogeneous noise patches, this map is used to perform the filtering of the quadratic estimator convergence maps that are then used for our Minimum Variance estimate. This $\kappa$-filtering operation down-weights regions where the lensing reconstruction is poorest (the ecliptic equator), decreasing the bandpower errors. The overall gain remains limited, since it is CMB fluctuations, which are isotropically distributed across the sky, that dominate the reconstruction noise rather than instrumental noise.
• Figure 3: Top panel: Error bars on our reconstructed lensing power spectrum bandpower amplitudes $_{\rm fid}A$ relative to the FFP10 fiducial model, over the conservative range $8 \leq L \leq 400$. The inhomogeneously CMB-filtered and $\kappa$-filtered GMV bandpowers, with $\kappa$-filtering (our best result, red), and without $\kappa$ filtering (green), are shown compared to the published MV Aghanim:2018oex reconstruction (blue). The orange line shows the results of applying the same 2018 pipeline to the NPIPE maps. Bottom panel: The ratio of these errors to those of the Aghanim:2018oex reconstruction. The reconstruction without $\kappa$-filtering, but using improved CMB-filtering with respect to PR3 (green), performs worse at low multipoles than the PR3-like analysis in agreement with purely analytic predictions. This is because using inverse reconstruction noise $N^{(0)}$ weighting for power spectrum estimation, as implied without $\kappa$-filtering, is suboptimal on large scales where the first couple of bins are now highly signal dominated. This is corrected by $\kappa$-filtering, which produces a reconstruction with (very) slightly higher $N^{(0)}$ bias but smaller error bars by effectively using more of the sky.
• Figure 4: The left panel shows our most precise bandpower estimates over the conservative multipole range (green), together with the Planck 2018 (PR3) Minimum Variance bandpowers (blue). The black line is the lensing power spectrum best-fit to the Planck 2018 CMB spectra data (without lensing). The right panel focuses on lensing multipoles close to the $\Lambda$CDM lensing power spectrum peak, and also shows as the dotted lines the corresponding realization-dependent $N^{(0)}$ biases (without residual Monte-Carlo correction). Many more modes are now signal dominated. All bandpowers are built with the same approximate inverse-variance multipole weighting scheme given in Aghanim:2018oex. The orange points show the results of implementing the PR3 reconstruction analysis on the NPIPE maps by using a homogeneous noise sky model as well as independent temperature to polarization filtering. The bottom panel shows the relative deviation to the fiducial FFP10 cosmology amplitude on the entire range.
• Figure 5: Lensing temperature-only bandpowers in units of the fiducial FFP10 lensing spectrum for each bin of the conservative range (without point-source subtraction), with the PR3 points in blue, and several test reconstructions on PR4 maps. All of the reconstructions used here use the same filtering and main analysis choices as PR3, with the orange points showing the PR4 result corresponding to the blue points. The filtering deprojects the residual foreground model to give the green points. The point-source component of the analysis mask is extended for the red points. The purple points exclude a range of 20 CMB multipoles centred on 1240, for reasons given in the text. The brown points show the reconstruction bias-hardened against point sources. The shifts seen in these cases are all compatible with the expected variance obtained from differencing simulations. Finally, the last four sets of points show results from the A and B splits, namely $\hat{\kappa}^{AA}\cdot \hat{\kappa}^{AA}$, $\hat{\kappa}^{BB}\cdot \hat{\kappa}^{BB}$, $\hat{\kappa}^{AA}\cdot \hat{\kappa}^{BB}$ and $\hat{\kappa}^{AB}\cdot \hat{\kappa}^{AB}$ respectively.