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    Planck 2013 results. XV. CMB power spectra and likelihood


    Ade, P.A.R. and Aghanim, N. and Armitage-Caplan, C. and Arnaud, M. and Ashdown, M. and Atrio-Barandela, F. and Aumont, J. and Baccigalupi, C. and Banday, A.J. and Barreiro, R.B. and Bartlett, J.G. and Battaner, E. and Benabed, K. and Benoit, A. and Benoit-Lévy, A. and Bernard, J.-P. and Bersanelli, M. and Bielewicz, P. and Bobin, J. and Bock, J.J. and Bonaldi, A. and Bonavera, L. and Bond, J.R. and Borrill, J. and Bouchet, F.R. and Boulanger, F. and Bridges, M. and Bucher, M. and Burigana, C. and Butler, R.C. and Calabrese, E. and Cardoso, J.-F. and Catalano, A. and Challinor, A. and Chamballu, A. and Chiang, H.C. and Chiang, L.-Y. and Christensen, P.R. and Church, S. and Clements, D.L. and Colombi, S. and Colombo, L.P.L. and Combet, C. and Couchot, F. and Coulais, A. and Crill, B.P. and Curto, A. and Cuttaia, F. and Danese, L. and Davies, R.D. and Davis, R.J. and De Bernardis, P. and de Rosa, A. and de Zotti, G. and Delabrouille, J. and Delouis, J.-M. and Desert, F.-X. and Dickinson, C. and Diego, J.M. and Dole, H. and Donzelli, S. and Dore, O. and Douspis, M. and Dunkley, J. and Dupac, X. and Efstathiou, G. and Elsner, F. and Enßlin, T.A. and Eriksen, H.K. and Finelli, F. and Forni, O. and Frailis, M. and Fraisse, A.A. and Franceschi, E. and Gaier, T. and Galeotta, S. and Galli, S. and Ganga, K. and Giard, M. and Giardino, G. and Giraud-Héraud, Y. and Gjerløw, E. and Gonzalez-Nuevo, J. and Gorski, K.M. and Gratton, S. and Gregorio, A. and Gruppuso, A. and Gudmundsson, J.E. and Hansen, F.K. and Hanson, D. and Harrison, D. and Helou, G. and Henrot-Versille, S. and Hernandez-Monteagudo, C. and Herranz, D. and Hildebrandt, S.R. and Hivon, E. and Hobson, M. and Holmes, W.A. and Hornstrup, A. and Hovest, W. and Huffenberger, K.M. and Hurier, G. and Jaffe, A.H. and Jaffe, T.R. and Jewell, J. and Jones, W.C. and Juvela, M. and Keihanen, E. and Keskitalo, R. and Kiiveri, K. and Kisner, T.S. and Kneissl, R. and Knoche, J. and Knox, L. and Kunz, M. and Kurki-Suonio, H. and Lagache, G. and Lahteenmaki, A. and Lamarre, J.-M. and Lasenby, A. and Lattanzi, M. and Laureijs, R.J. and Lawrence, C.R. and Le Jeune, M. and Leach, S. and Leahy, J.P. and Leonardi, R. and Leon-Tavares, J. and Lesgourgues, J. and Liguori, M. and Lilje, P.B. and Linden-Vornle, M. and Lindholm, V. and Lopez-Caniego, M. and Lubin, P.M. and Macias-Perez, J.F. and Maffei, B. and Maino, D. and Mandolesi, N. and Marinucci, D. and Maris, M. and Marshall, D.J. and Martin, P.G. and Martinez-Gonzalez, E. and Masi, S. and Massardi, M. and Matarrese, S. and Matthai, F. and Mazzotta, P. and Meinhold, P.R. and Melchiorri, A. and Mendes, L. and Menegoni, E. and Mennella, A. and Migliaccio, M. and Millea, M. and Mitra, S. and Miville-Deschenes, M.-A. and Molinari, D. and Moneti, A. and Montier, L. and Morgante, G. and Mortlock, D. and Moss, A. and Munshi, D. and Murphy, J.Anthony and Naselsky, P. and Nati, F. and Natoli, P. and Netterfield, C.B. and Norgaard-Nielsen, H.U. and Noviello, F. and Novikov, D. and Novikov, I. and O'Dwyer, I.J. and Orieux, F. and Osborne, S. and Oxborrow, C.A. and Paci, F. and Pagano, L. and Pajot, F. and Paladini, R. and Paoletti, D. and Partridge, B. and Pasian, F. and Patanchon, G. and Paykari, P. and Perdereau, O. and Perotto, L. and Perrotta, F. and Piacentini, F. and Piat, M. and Pierpaoli, E. and Pietrobon, D. and Plaszczynski, S. and Pointecouteau, E. and Polenta, G. and Ponthieu, N. and Popa, L. and Poutanen, T. and Pratt, G.W. and Prezeau, G. and Prunet, S. and Puget, J.-L. and Rachen, J.P. and Rahlin, A. and Rebolo, R. and Reinecke, M. and Remazeilles, M. and Renault, C. and Ricciardi, S. and Riller, T. and Ringeval, C. and Ristorcelli, I. and Rocha, G. and Rosset, C. and Roudier, G. and Rowan-Robinson, M. and Rubino-Martin, J.A. and Rusholme, B. and Sandri, M. and Sanselme, L. and Santos, D. and Savini, G. and Scott, D. and Seiffert, M.D. and Shellard, E.P.S. and Spencer, L. and Starck, J.-L. and Stolyarov, V. and Stompor, R. and Sudiwala, R. and Sureau, F. and Sutton, D. and Suur-Uski, A.-S. and Sygnet, J.-F. and Tauber, J.A. and Tavagnacco, D. and Terenzi, L. and Toffolatti, L. and Tomasi, M. and Tristram, M. and Tucci, M. and Tuovinen, J. and Turler, M. and Valenziano, L. and Valiviita, J. and Van Tent, B. and Varis, J. and Vielva, P. and Villa, F. and Vittorio, N. and Wade, L.A. and Wandelt, B.D. and Wehus, I. and White, M. and White, S.D.M. and Yvon, D. and Zacchei, A. and Zonca, A. (2014) Planck 2013 results. XV. CMB power spectra and likelihood. Astronomy & Astrophysics, 571 (A15). ISSN 0004-6361

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    Abstract

    This paper presents the Planck 2013 likelihood, a complete statistical description of the two-point correlation function of the CMB temperature fluctuations that accounts for all known relevant uncertainties, both instrumental and astrophysical in nature. We use this likelihood to derive our best estimate of the CMB angular power spectrum from Planck over three decades in multipole moment, ℓ, covering 2 ≤ ℓ ≤ 2500. The main source of uncertainty at ℓ ≲ 1500 is cosmic variance. Uncertainties in small-scale foreground modelling and instrumental noise dominate the error budget at higher ℓs. For ℓ < 50, our likelihood exploits all Planck frequency channels from 30 to 353 GHz, separating the cosmological CMB signal from diffuse Galactic foregrounds through a physically motivated Bayesian component separation technique. At ℓ ≥ 50, we employ a correlated Gaussian likelihood approximation based on a fine-grained set of angular cross-spectra derived from multiple detector combinations between the 100, 143, and 217 GHz frequency channels, marginalising over power spectrum foreground templates. We validate our likelihood through an extensive suite of consistency tests, and assess the impact of residual foreground and instrumental uncertainties on the final cosmological parameters. We find good internal agreement among the high-ℓ cross-spectra with residuals below a few μK2 at ℓ ≲ 1000, in agreement with estimated calibration uncertainties. We compare our results with foreground-cleaned CMB maps derived from all Planck frequencies, as well as with cross-spectra derived from the 70 GHz Planck map, and find broad agreement in terms of spectrum residuals and cosmological parameters. We further show that the best-fit ΛCDM cosmology is in excellent agreement with preliminary PlanckEE and TE polarisation spectra. We find that the standard ΛCDM cosmology is well constrained by Planck from the measurements at ℓ ≲ 1500. One specific example is the spectral index of scalar perturbations, for which we report a 5.4σ deviation from scale invariance, ns = 1. Increasing the multipole range beyond ℓ ≃ 1500 does not increase our accuracy for the ΛCDM parameters, but instead allows us to study extensions beyond the standard model. We find no indication of significant departures from the ΛCDM framework. Finally, we report a tension between the Planck best-fit ΛCDM model and the low-ℓ spectrum in the form of a power deficit of 5–10% at ℓ ≲ 40, with a statistical significance of 2.5–3σ. Without a theoretically motivated model for this power deficit, we do not elaborate further on its cosmological implications, but note that this is our most puzzling finding in an otherwise remarkably consistent data set.

    Item Type: Article
    Keywords: Planck Collaboration; cosmic background radiation; cosmological parameters; cosmology: observations; methods: data analysis;
    Academic Unit: Faculty of Science and Engineering > Experimental Physics
    Item ID: 14200
    Identification Number: https://doi.org/10.1051/0004-6361/201321573
    Depositing User: Dr. Anthony Murphy
    Date Deposited: 16 Mar 2021 17:10
    Journal or Publication Title: Astronomy & Astrophysics
    Publisher: EDP Sciences
    Refereed: Yes
    URI:

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