Planck 2018 results. VIII. Gravitational lensing

TL;DR

Planck 2018 presents the final CMB lensing analysis, delivering a robust polarization-based detection at 9σ and a combined 40σ when temperature information is included. The analysis introduces an optimized polarization reconstruction, a joint CIB+lensing approach to extend the lensing signal to small scales, and a clear demonstration of delensing that sharpens acoustic peaks and reduces B-mode power. Across extensive null tests, the lensing results largely agree with ΛCDM predictions, yielding precise constraints on σ8 and Ωm, especially when combined with BAO data, while highlighting a curious curl feature whose origin remains to be resolved. The work provides public data products and paves the way for high-redshift lensing baselines, informing future CMB and large-scale structure studies and delensing efforts.

Abstract

We present measurements of the cosmic microwave background (CMB) lensing potential using the final $\textit{Planck}$ 2018 temperature and polarization data. We increase the significance of the detection of lensing in the polarization maps from $5\,σ$ to $9\,σ$. Combined with temperature, lensing is detected at $40\,σ$. We present an extensive set of tests of the robustness of the lensing-potential power spectrum, and construct a minimum-variance estimator likelihood over lensing multipoles $8 \le L \le 400$. We find good consistency between lensing constraints and the results from the $\textit{Planck}$ CMB power spectra within the $\rm{ΛCDM}$ model. Combined with baryon density and other weak priors, the lensing analysis alone constrains $σ_8 Ω_{\rm m}^{0.25}=0.589\pm 0.020$ ($1\,σ$ errors). Also combining with baryon acoustic oscillation (BAO) data, we find tight individual parameter constraints, $σ_8=0.811\pm0.019$, $H_0=67.9_{-1.3}^{+1.2}\,\text{km}\,\text{s}^{-1}\,\rm{Mpc}^{-1}$, and $Ω_{\rm m}=0.303^{+0.016}_{-0.018}$. Combining with $\textit{Planck}$ CMB power spectrum data, we measure $σ_8$ to better than $1\,\%$ precision, finding $σ_8=0.811\pm 0.006$. We find consistency with the lensing results from the Dark Energy Survey, and give combined lensing-only parameter constraints that are tighter than joint results using galaxy clustering. Using $\textit{Planck}$ cosmic infrared background (CIB) maps we make a combined estimate of the lensing potential over $60\,\%$ of the sky with considerably more small-scale signal. We demonstrate delensing of the $\textit{Planck}$ power spectra, detecting a maximum removal of $40\,\%$ of the lensing-induced power in all spectra. The improvement in the sharpening of the acoustic peaks by including both CIB and the quadratic lensing reconstruction is detected at high significance (abridged).

Figures (30)

• Figure 1: Mollweide projection in Galactic coordinates of the lensing-deflection reconstruction map from our baseline minimum-variance (MV) analysis. We show the Wiener-filtered displacement-like scalar field with multipoles $\hat{\alpha}^{\rm MV}_{LM} = \sqrt{L (L + 1) }\hat{\phi}^{\rm MV}_{LM}$, corresponding to the gradient mode (or $E$ mode) of the lensing deflection angle. Modes with $L<8$ have been filtered out.
• Figure 2: Noise-variance maps (shown as noise rms in $$K$$μ$\hbox{K}\textrm{-arcmin}$) that we use to filter the SMICA CMB maps that are fed into the quadratic estimators when performing inhomogeneous filtering. The upper panel shows the temperature noise map, with median over our unmasked sky area of $27$K$$μ$\hbox{K}\textrm{-arcmin}$. We use a common noise map for $Q$ and $U$ polarization, also neglecting $Q$ and $U$ noise correlations, shown in the lower panel, which spans an entire order of magnitude, with median $52$K$$μ$\hbox{K}\textrm{-arcmin}$ (larger than $\sqrt{2}$ times the temperature noise because not all the Planck detectors are polarized). In temperature, the variance map has a homogeneous (approximately $5$K$$μ$\hbox{K}\textrm{-arcmin}$) contribution from the isotropic additional Gaussian power that we add to the simulations to account for residual foreground contamination.
• Figure 3: Monte Carlo-derived multiplicative normalization corrections for the polarization reconstruction, using inhomogeneous filtering (blue points). Band powers are divided by these numbers to provide our final estimates. This correction is not small, and is sourced by the large spatial variation of the estimator response; however, it is very well reproduced by the approximate analytic model of Eq. \ref{['eq:MCcorr']}, shown as the dashed blue line. The correction for our baseline MV band powers using homogeneous filtering is shown as the orange points.
• Figure 4: Planck 2018 lensing reconstruction band powers (values and multipole ranges are listed in Table \ref{['table:BPMV']}). Left: The minimum-variance (MV) lensing band powers, shown here using the aggressive (blue, $8 \le L \le 2048$) and conservative (orange, $8 \le L \le 400$) multipole ranges. The dots show the weighted bin centres and the fiducial lensing power spectrum is shown as the black line. Right: Comparison of polarization-only band powers using homogeneous map filtering (blue boxes, with dots showing the weighted bin centres) and the more optimal inhomogeneous filtering (orange error bars). The inhomogeneous filtering gives a scale-dependent increase in S/N, amounting to a reduction of 30% in the error on the amplitude of the power spectrum over the conservative multipole range shown. The black line is the fiducial lensing power spectrum.
• Figure 5: Planck 2018 lensing power-spectrum band powers (pink boxes) over the aggressive multipole range. The 2015 analysis band powers (green) were calculated assuming a slightly different fiducial model and have not been (linearly) corrected to the 2018 model. Also shown are recent measurements by the ACTPol Sherwin:2016tyf, SPTpol Story:2014hni, and SPT-SZ Simard:2017xtw collaborations. The SPT-SZ measurement is not completely independent, since the SPT-SZ reconstruction also uses temperature data from Planck, but with subdominant weight over the smaller sky area used. The black line shows the lensing potential power spectrum for the $\rm{\Lambda CDM}$ best-fit parameters to the Planck 2018 likelihoods (Planck TT,TE,EE+ lowE, which excludes the lensing reconstruction).