Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Planck 2013 results. XVII. Gravitational lensing by large-scale structure

Planck Collaboration, P. A. R. Ade, N. Aghanim, C. Armitage-Caplan, M. Arnaud, M. Ashdown, F. Atrio-Barandela, J. Aumont, C. Baccigalupi, A. J. Banday, R. B. Barreiro, J. G. Bartlett, S. Basak, E. Battaner, K. Benabed, A. Benoît, A. Benoit-Lévy, J. -P. Bernard, M. Bersanelli, P. Bielewicz, J. Bobin, J. J. Bock, A. Bonaldi, L. Bonavera, J. R. Bond, J. Borrill, F. R. Bouchet, M. Bridges, M. Bucher, C. Burigana, R. C. Butler, J. -F. Cardoso, A. Catalano, A. Challinor, A. Chamballu, L. -Y Chiang, H. C. Chiang, P. R. Christensen, S. Church, D. L. Clements, S. Colombi, L. P. L. Colombo, 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, T. Déchelette, J. Delabrouille, J. -M. Delouis, F. -X. Désert, C. Dickinson, J. M. Diego, H. Dole, S. Donzelli, O. Doré, M. Douspis, J. Dunkley, X. Dupac, G. Efstathiou, T. A. Enßlin, H. K. Eriksen, F. Finelli, O. Forni, M. Frailis, E. Franceschi, S. Galeotta, K. Ganga, M. Giard, G. Giardino, Y. Giraud-Héraud, J. González-Nuevo, K. M. Górski, S. Gratton, A. Gregorio, A. Gruppuso, J. E. Gudmundsson, F. K. Hansen, D. Hanson, D. Harrison, S. Henrot-Versillé, C. Hernández-Monteagudo, D. Herranz, S. R. Hildebrandt, E. Hivon, S. Ho, M. Hobson, W. A. Holmes, A. Hornstrup, W. Hovest, K. M. Huffenberger, T. R. Jaffe, A. H. Jaffe, W. C. Jones, M. Juvela, E. Keihänen, R. Keskitalo, T. S. Kisner, R. Kneissl, J. Knoche, L. Knox, M. Kunz, H. Kurki-Suonio, G. Lagache, A. Lähteenmäki, J. -M. Lamarre, A. Lasenby, R. J. Laureijs, A. Lavabre, C. R. Lawrence, J. P. Leahy, R. Leonardi, J. León-Tavares, J. Lesgourgues, A. Lewis, M. Liguori, P. B. Lilje, M. Linden-Vørnle, M. López-Caniego, P. M. Lubin, J. F. Macías-Pérez, B. Maffei, D. Maino, N. Mandolesi, A. Mangilli, M. Maris, D. J. Marshall, P. G. Martin, E. Martínez-González, S. Masi, S. Matarrese, F. Matthai, P. Mazzotta, 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, P. Naselsky, F. Nati, P. Natoli, C. B. Netterfield, H. U. Nørgaard-Nielsen, F. Noviello, D. Novikov, I. Novikov, S. Osborne, C. A. Oxborrow, F. Paci, L. Pagano, F. Pajot, D. Paoletti, B. Partridge, F. Pasian, G. Patanchon, O. Perdereau, L. Perotto, F. Perrotta, F. Piacentini, M. Piat, E. Pierpaoli, D. Pietrobon, S. Plaszczynski, E. Pointecouteau, G. Polenta, N. Ponthieu, L. Popa, T. Poutanen, G. W. Pratt, G. Prézeau, S. Prunet, J. -L. Puget, A. R. Pullen, J. P. Rachen, R. Rebolo, M. Reinecke, M. Remazeilles, C. Renault, S. Ricciardi, T. Riller, I. Ristorcelli, G. Rocha, C. Rosset, G. Roudier, M. Rowan-Robinson, J. A. Rubiño-Martín, B. Rusholme, M. Sandri, D. Santos, G. Savini, D. Scott, M. D. Seiffert, E. P. S. Shellard, L. D. Spencer, J. -L. Starck, V. Stolyarov, R. Stompor, R. Sudiwala, R. Sunyaev, F. Sureau, D. Sutton, A. -S. Suur-Uski, J. -F. Sygnet, J. A. Tauber, D. Tavagnacco, L. Terenzi, L. Toffolatti, M. Tomasi, M. Tristram, M. Tucci, J. Tuovinen, G. Umana, L. Valenziano, J. Valiviita, B. Van Tent, P. Vielva, F. Villa, N. Vittorio, L. A. Wade, B. D. Wandelt, M. White, S. D. M. White, D. Yvon, A. Zacchei, A. Zonca

TL;DR

Planck 2013 results XVII reports the first full-sky CMB lensing map and its power spectrum derived from 15 months of Planck data using optimal quadratic estimators. The authors demonstrate a high-significance detection of gravitational lensing, validate the lensing map through simulations and cross-correlations with large-scale structure, and show that the lensing information helps break parameter degeneracies in ΛCDM, notably improving curvature constraints and reducing A_s–τ degeneracy. They provide a public lensing map and a likelihood based on C_L^{φφ} in the range 40 ≤ L ≤ 400, and explore cross-correlations with ISW and various galaxy catalogs, underscoring the cosmological and astrophysical utility of Planck's lensing measurements.

Abstract

On the arcminute angular scales probed by Planck, the CMB anisotropies are gently perturbed by gravitational lensing. Here we present a detailed study of this effect, detecting lensing independently in the 100, 143, and 217GHz frequency bands with an overall significance of greater than 25sigma. We use the temperature-gradient correlations induced by lensing to reconstruct a (noisy) map of the CMB lensing potential, which provides an integrated measure of the mass distribution back to the CMB last-scattering surface. Our lensing potential map is significantly correlated with other tracers of mass, a fact which we demonstrate using several representative tracers of large-scale structure. We estimate the power spectrum of the lensing potential, finding generally good agreement with expectations from the best-fitting LCDM model for the Planck temperature power spectrum, showing that this measurement at z=1100 correctly predicts the properties of the lower-redshift, later-time structures which source the lensing potential. When combined with the temperature power spectrum, our measurement provides degeneracy-breaking power for parameter constraints; it improves CMB-alone constraints on curvature by a factor of two and also partly breaks the degeneracy between the amplitude of the primordial perturbation power spectrum and the optical depth to reionization, allowing a measurement of the optical depth to reionization which is independent of large-scale polarization data. Discarding scale information, our measurement corresponds to a 4% constraint on the amplitude of the lensing potential power spectrum, or a 2% constraint on the RMS amplitude of matter fluctuations at z~2.

Planck 2013 results. XVII. Gravitational lensing by large-scale structure

TL;DR

Planck 2013 results XVII reports the first full-sky CMB lensing map and its power spectrum derived from 15 months of Planck data using optimal quadratic estimators. The authors demonstrate a high-significance detection of gravitational lensing, validate the lensing map through simulations and cross-correlations with large-scale structure, and show that the lensing information helps break parameter degeneracies in ΛCDM, notably improving curvature constraints and reducing A_s–τ degeneracy. They provide a public lensing map and a likelihood based on C_L^{φφ} in the range 40 ≤ L ≤ 400, and explore cross-correlations with ISW and various galaxy catalogs, underscoring the cosmological and astrophysical utility of Planck's lensing measurements.

Abstract

On the arcminute angular scales probed by Planck, the CMB anisotropies are gently perturbed by gravitational lensing. Here we present a detailed study of this effect, detecting lensing independently in the 100, 143, and 217GHz frequency bands with an overall significance of greater than 25sigma. We use the temperature-gradient correlations induced by lensing to reconstruct a (noisy) map of the CMB lensing potential, which provides an integrated measure of the mass distribution back to the CMB last-scattering surface. Our lensing potential map is significantly correlated with other tracers of mass, a fact which we demonstrate using several representative tracers of large-scale structure. We estimate the power spectrum of the lensing potential, finding generally good agreement with expectations from the best-fitting LCDM model for the Planck temperature power spectrum, showing that this measurement at z=1100 correctly predicts the properties of the lower-redshift, later-time structures which source the lensing potential. When combined with the temperature power spectrum, our measurement provides degeneracy-breaking power for parameter constraints; it improves CMB-alone constraints on curvature by a factor of two and also partly breaks the degeneracy between the amplitude of the primordial perturbation power spectrum and the optical depth to reionization, allowing a measurement of the optical depth to reionization which is independent of large-scale polarization data. Discarding scale information, our measurement corresponds to a 4% constraint on the amplitude of the lensing potential power spectrum, or a 2% constraint on the RMS amplitude of matter fluctuations at z~2.

Paper Structure

This paper contains 12 sections, 31 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Methodology
  3. Lens reconstruction
  4. Lensing power spectrum estimation
  5. Lensing power spectrum likelihood
  6. Unresolved point-source correction
  7. Data and cuts
  8. Planck sky maps:
  9. Galaxy mask:
  10. CO and extended-object masks:
  11. Point-source masks:
  12. Simulations

Figures (2)

  • Figure 1: Sky-averaged lens reconstruction noise levels for the 100, 143, and 217GHz Planck channels (red, green, and blue solid, respectively), as well as for experiments that are cosmic-variance limited to a maximum multipole $\ell_{\rm max}=1000$, $1500$, and $1750$ (upper to lower solid grey lines). A fiducial $\Lambda$CDM lensing potential using best-fit parameters to the temperature power spectrum from planck2013-p11 is shown in dashed black. The noise level for a minimum-variance ("MV") combination of $143+217$GHz is shown in black (the gain from adding 100GHz is negligible).
  • Figure 2: Overview of forecasted contributions to the detection significance as a function of lensing multipole $L$ for the $C_L^{\phi\phi}$ power spectrum (solid black), as well as for several other mass tracers, at the noise levels of our MV lens reconstruction. Our measurement of the power spectrum $C_L^{\phi\phi}$ is presented in Sect. \ref{['sec:results']}, The ISW-$\phi$ correlation believed to be induced by dark energy is studied in Sect. \ref{['sec:results:iswlensing']}. The NVSS-$\phi$ correlation is studied (along with other galaxy correlations) in Sect. \ref{['subsec:xcorr']}. The CIB-$\phi$ prediction (dashed cyan) uses the linear SSED model of Hall:2009rv, assuming no noise or foreground contamination. A full analysis and interpretation of the CIB-$\phi$ correlation is performed in planck2013-p13.