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Planck 2015 results. XV. Gravitational lensing

Planck Collaboration, P. A. R. Ade, N. Aghanim, M. Arnaud, M. Ashdown, J. Aumont, C. Baccigalupi, A. J. Banday, R. B. Barreiro, J. G. Bartlett, N. Bartolo, S. Basak, E. Battaner, K. Benabed, A. Benoît, A. Benoit-Lévy, J. -P. Bernard, M. Bersanelli, P. Bielewicz, J. J. Bock, A. Bonaldi, L. Bonavera, J. R. Bond, J. Borrill, F. R. Bouchet, F. Boulanger, M. Bucher, C. Burigana, R. C. Butler, E. Calabrese, J. -F. Cardoso, A. Catalano, A. Challinor, A. Chamballu, H. C. Chiang, P. R. Christensen, S. Church, D. L. Clements, S. Colombi, L. P. L. Colombo, C. Combet, F. Couchot, A. Coulais, B. P. Crill, A. Curto, F. Cuttaia, L. Danese, R. D. Davies, R. J. Davis, P. de Bernardis, A. de Rosa, G. de Zotti, J. Delabrouille, F. -X. Désert, J. M. Diego, H. Dole, S. Donzelli, O. Doré, M. Douspis, A. Ducout, J. Dunkley, X. Dupac, G. Efstathiou, F. Elsner, T. A. Enßlin, H. K. Eriksen, J. Fergusson, F. Finelli, O. Forni, M. Frailis, A. A. Fraisse, E. Franceschi, A. Frejsel, S. Galeotta, S. Galli, K. Ganga, M. Giard, Y. Giraud-Héraud, E. Gjerløw, J. González-Nuevo, K. M. Górski, S. Gratton, A. Gregorio, A. Gruppuso, J. E. Gudmundsson, F. K. Hansen, D. Hanson, D. L. Harrison, S. Henrot-Versillé, C. Hernández-Monteagudo, D. Herranz, S. R. Hildebrandt, E. Hivon, M. Hobson, W. A. Holmes, A. Hornstrup, W. Hovest, K. M. Huffenberger, G. Hurier, A. H. Jaffe, T. R. Jaffe, W. C. Jones, M. Juvela, E. Keihänen, R. Keskitalo, T. S. Kisner, R. Kneissl, J. Knoche, M. Kunz, H. Kurki-Suonio, G. Lagache, A. Lähteenmäki, J. -M. Lamarre, A. Lasenby, M. Lattanzi, C. R. Lawrence, R. Leonardi, J. Lesgourgues, F. Levrier, A. Lewis, M. Liguori, P. B. Lilje, M. Linden-Vørnle, M. López-Caniego, P. M. Lubin, J. F. Macías-Pérez, G. Maggio, D. Maino, N. Mandolesi, A. Mangilli, M. Maris, P. G. Martin, E. Martínez-González, S. Masi, S. Matarrese, P. McGehee, P. R. Meinhold, A. Melchiorri, L. Mendes, A. Mennella, M. Migliaccio, S. Mitra, M. -A. Miville-Deschênes, A. Moneti, L. Montier, G. Morgante, D. Mortlock, A. Moss, D. Munshi, J. A. Murphy, P. Naselsky, F. Nati, P. Natoli, C. B. Netterfield, H. U. Nørgaard-Nielsen, F. Noviello, D. Novikov, I. Novikov, C. A. Oxborrow, F. Paci, L. Pagano, F. Pajot, D. Paoletti, F. Pasian, G. Patanchon, O. Perdereau, L. Perotto, F. Perrotta, V. Pettorino, F. Piacentini, M. Piat, E. Pierpaoli, D. Pietrobon, S. Plaszczynski, E. Pointecouteau, G. Polenta, L. Popa, G. W. Pratt, G. Prézeau, S. Prunet, J. -L. Puget, J. P. Rachen, W. T. Reach, R. Rebolo, M. Reinecke, M. Remazeilles, C. Renault, A. Renzi, I. Ristorcelli, G. Rocha, C. Rosset, M. Rossetti, G. Roudier, M. Rowan-Robinson, J. A. Rubiño-Martín, B. Rusholme, M. Sandri, D. Santos, M. Savelainen, G. Savini, D. Scott, M. D. Seiffert, E. P. S. Shellard, L. D. Spencer, V. Stolyarov, R. Stompor, R. Sudiwala, R. Sunyaev, D. Sutton, A. -S. Suur-Uski, J. -F. Sygnet, J. A. Tauber, L. Terenzi, L. Toffolatti, M. Tomasi, M. Tristram, M. Tucci, J. Tuovinen, L. Valenziano, J. Valiviita, B. Van Tent, P. Vielva, F. Villa, L. A. Wade, B. D. Wandelt, I. K. Wehus, M. White, D. Yvon, A. Zacchei, A. Zonca

TL;DR

The Planck 2015 XV paper delivers the most precise all-sky measurement of the CMB lensing potential to date using the full-mission temperature and polarization data, achieving a $40\sigma$ detection and a $10\sigma$ lensing-B-mode detection. By constructing a minimum-variance lensing map from quadratic estimators and validating it with extensive null and consistency tests, the study provides a robust lensing power spectrum $C_{L}^{\phi\phi}$ and a corresponding lensing-likelihood that tightens constraints on key cosmological parameters, notably $\sigma_8\Omega_m^{0.25}$ and curvature when combined with Planck TT/lowP data. The results corroborate the fiducial $\Lambda$CDM model, enable independent estimates of parameters such as $H_0$ and $\tau$, and demonstrate Planck’s capability to probe late-time geometry and structure growth through CMB lensing. Additionally, cross-checks with CIB and ISW-derived signals, along with null tests, reinforce the reliability of the measurements while highlighting areas (curl-mode features) that motivate cautious interpretation and future methodological refinements.

Abstract

We present the most significant measurement of the cosmic microwave background (CMB) lensing potential to date (at a level of 40 sigma), using temperature and polarization data from the Planck 2015 full-mission release. Using a polarization-only estimator we detect lensing at a significance of 5 sigma. We cross-check the accuracy of our measurement using the wide frequency coverage and complementarity of the temperature and polarization measurements. Public products based on this measurement include an estimate of the lensing potential over approximately 70% of the sky, an estimate of the lensing potential power spectrum in bandpowers for the multipole range 40<L<400 and an associated likelihood for cosmological parameter constraints. We find good agreement between our measurement of the lensing potential power spectrum and that found in the best-fitting LCDM model based on the Planck temperature and polarization power spectra. Using the lensing likelihood alone we obtain a percent-level measurement of the parameter combination $σ_8 Ω_m^{0.25} = 0.591\pm 0.021$. We combine our determination of the lensing potential with the E-mode polarization also measured by Planck to generate an estimate of the lensing B-mode. We show that this lensing B-mode estimate is correlated with the B-modes observed directly by Planck at the expected level and with a statistical significance of 10 sigma, confirming Planck's sensitivity to this known sky signal. We also correlate our lensing potential estimate with the large-scale temperature anisotropies, detecting a cross-correlation at the 3 sigma level, as expected due to dark energy in the concordance LCDM model.

Planck 2015 results. XV. Gravitational lensing

TL;DR

The Planck 2015 XV paper delivers the most precise all-sky measurement of the CMB lensing potential to date using the full-mission temperature and polarization data, achieving a detection and a lensing-B-mode detection. By constructing a minimum-variance lensing map from quadratic estimators and validating it with extensive null and consistency tests, the study provides a robust lensing power spectrum and a corresponding lensing-likelihood that tightens constraints on key cosmological parameters, notably and curvature when combined with Planck TT/lowP data. The results corroborate the fiducial CDM model, enable independent estimates of parameters such as and , and demonstrate Planck’s capability to probe late-time geometry and structure growth through CMB lensing. Additionally, cross-checks with CIB and ISW-derived signals, along with null tests, reinforce the reliability of the measurements while highlighting areas (curl-mode features) that motivate cautious interpretation and future methodological refinements.

Abstract

We present the most significant measurement of the cosmic microwave background (CMB) lensing potential to date (at a level of 40 sigma), using temperature and polarization data from the Planck 2015 full-mission release. Using a polarization-only estimator we detect lensing at a significance of 5 sigma. We cross-check the accuracy of our measurement using the wide frequency coverage and complementarity of the temperature and polarization measurements. Public products based on this measurement include an estimate of the lensing potential over approximately 70% of the sky, an estimate of the lensing potential power spectrum in bandpowers for the multipole range 40<L<400 and an associated likelihood for cosmological parameter constraints. We find good agreement between our measurement of the lensing potential power spectrum and that found in the best-fitting LCDM model based on the Planck temperature and polarization power spectra. Using the lensing likelihood alone we obtain a percent-level measurement of the parameter combination . We combine our determination of the lensing potential with the E-mode polarization also measured by Planck to generate an estimate of the lensing B-mode. We show that this lensing B-mode estimate is correlated with the B-modes observed directly by Planck at the expected level and with a statistical significance of 10 sigma, confirming Planck's sensitivity to this known sky signal. We also correlate our lensing potential estimate with the large-scale temperature anisotropies, detecting a cross-correlation at the 3 sigma level, as expected due to dark energy in the concordance LCDM model.

Paper Structure

This paper contains 22 sections, 35 equations, 15 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Data and methodology
  3. Results
  4. Lensing potential
  5. Lensing $B$-mode power spectrum
  6. Lensing-ISW bispectrum
  7. Lensing potential power spectrum
  8. Likelihoods and cosmological parameter constraints
  9. Constraints from CMB lensing alone
  10. Joint parameter constraints
  11. Constraints on extensions to the $\Lambda$CDM model
  12. Sensitivity to $L$-range
  13. Consistency and null tests
  14. Individual estimator crosses
  15. Foreground tests
  16. ...and 7 more sections

Figures (15)

  • Figure 1: Lens reconstruction noise levels $N_{L}^{\phi\phi}$ for the $TT$, $TE$, $EE$, $EB$, and $TB$ estimators applied to the SMICA full-mission CMB map. The noise level for their minimum-variance combination (MV) is also shown. The fiducial $\Lambda$CDM theory power spectrum $C_{L}^{\phi\phi,{\rm fid}}$ used in our Monte Carlo simulations is plotted as the black solid line.
  • Figure 2: Lensing potential estimated from the SMICA full-mission CMB maps using the MV estimator. The power spectrum of this map forms the basis of our lensing likelihood. The estimate has been Wiener filtered following Eq. \ref{['eqn:phiwf']}, and band-limited to $8 \le L \le 2048$.
  • Figure 3: Simulation of a Wiener-filtered MV lensing reconstruction (upper) and the input $\phi$ realization (lower), filtered in the same way as the MV lensing estimate. The reconstruction and input are clearly correlated, although the reconstruction has considerable additional power due to noise.
  • Figure 4: Measurement of the lensing $B$-mode power spectrum, using cross-correlation with estimates of the lensing potential as discussed in Sect. \ref{['sect:lensing_bmode_power_spectrum']}. The theoretical lensing $B$-mode power spectrum, for the parameters of the fiducial cosmological model of Sect. \ref{['sec:data_and_methodology']}, is plotted as dashed black. Green squares and blue triangles are results using the $TT$ and MV $\phi$ reconstructions, respectively, to construct the lens-induced $B$-mode template, while red circles use the CIB (from the Planck$545 {\rm GHz}$ channel) to construct a proxy for $\phi$. Lensing $B$-mode power is detected with the expected scale dependence and amplitude at a significance level of approximately $10\sigma$.
  • Figure 5: Lensing-ISW bispectrum on large angular scales. The cross-spectrum between the MV lensing potential estimate and the temperature anisotropy is plotted for bins of width $\Delta L = 15$, covering the multipole range $L = 8$--$98$. The dashed line shows the predicted cross-spectrum in the fiducial model. The lensing-ISW bispectrum is detected at just over $3\sigma$ significance.
  • ...and 10 more figures