Planck 2013 results. XV. CMB power spectra and likelihood

Jan Tauber, J.G. Bartlett, M. Bucher, J.-F. Cardoso, J. Delabrouille, K. Ganga, Y. Giraud-Héraud, M. Le Jeune, G. Patanchon, M. Piat, M. Remazeilles, C. Rosset, G. Roudier, R. Stompor, A. Lähteenmäki, J. León-Tavares, T. Poutanen, M. Kunz, P. Natoli, G. Polenta & 242 others N. Mandolesi, M. Ashdown, M. Bridges, A. Curto, M. Hobson, A. Lasenby, V. Stolyarov, H.C. Chiang, R. Kneissl, J.R. Bond, D. Hanson, P.G. Martin, M.-A. Miville-Deschênes, A.J. Banday, J.-P. Bernard, P. Bielewicz, O. Forni, M. Giard, T.R. Jaffe, L. Montier, E. Pointecouteau, I. Ristorcelli, J.J. Bock, O. Doré, G. Helou, S.R. Hildebrandt, G. Prézeau, G. Rocha, M.D. Seiffert, A. Challinor, E.P.S. Shellard, C. Hernández-Monteagudo, J. Borrill, R. Keskitalo, R. Rebolo, A. Chamballu, D. Yvon, Allan Hornstrup, Michael Linden-Vørnle, Hans Ulrik Nørgaard-Nielsen, Carol Anne Oxborrow, M. Tucci, F. Atrio-Barandela, L. Toffolatti, C.B. Netterfield, J.P. Rachen, D. Scott, L.P.L. Colombo, E. Pierpaoli, A. Benoit-Lévy, K.M. Huffenberger, M. Juvela, E. Keihänen, K. Kiiveri, H. Kurki-Suonio, V. Lindholm, A.-S. Suur-Uski, J. Valiviita, A.A. Fraisse, J.E. Gudmundsson, W.C. Jones, A. Rahlin, M. White, L. Knox, M. Millea, P.M. Lubin, P.R. Meinhold, A. Zonca, B.D. Wandelt, M. Liguori, S. Matarrese, D. Molinari, C. Burigana, M. Lattanzi, P. De Bernardis, S. Masi, A. Melchiorri, E. Menegoni, F. Nati, L. Pagano, F. Piacentini, M. Bersanelli, D. Maino, A. Mennella, A. Gregorio, D. Tavagnacco, P. Mazzotta, N. Vittorio, D. Marinucci, P.R. Christensen, P. Naselsky, J.A. Rubinõ-Martín, X. Dupac, R. Leonardi, L. Mendes, G. Giardino, R.J. Laureijs, J.A. Tauber, B. Partridge, G. De Zotti, M. Frailis, S. Galeotta, M. Maris, F. Pasian, A. Zacchei, M. Massardi, R.C. Butler, F. Cuttaia, A. De Rosa, F. Finelli, E. Franceschi, A. Gruppuso, G. Morgante, D. Paoletti, S. Ricciardi, M. Sandri, L. Terenzi, L. Valenziano, F. Villa, S. Donzelli, M. Tomasi, F.-X. Désert, N. Ponthieu, M. Türler, Susanta Mitra, D.L. Clements, A.H. Jaffe, D. Mortlock, D. Novikov, M. Rowan-Robinson, R. Paladini, B. Rusholme, A. Benoît, H. Dole, N. Aghanim, J. Aumont, F. Boulanger, M. Douspis, G. Hurier, G. Lagache, Fernand Pajot, J.-L. Puget, K. Benabed, F.R. Bouchet, S. Colombi, J.-M. Delouis, F. Elsner, S. Galli, E. Hivon, A. Moneti, F. Orieux, S. Prunet, C. Ringeval, J.-F. Sygnet, L. Popa, L.-Y. Chiang, G. Efstathiou, S. Gratton, D. Harrison, M. Migliaccio, D. Sutton, H.K. Eriksen, E. Gjerløw, F.K. Hansen, P.B. Lilje, R.B. Barreiro, L. Bonavera, J.M. Diego, J. González-Nuevo, D. Herranz, M. López-Caniego, E. Martínez-González, P. Vielva, B.P. Crill, T.C. Gaier, K.M. Górski, W.A. Holmes, J. Jewell, C.R. Lawrence, I.J. O'dwyer, D. Pietrobon, L.A. Wade, I.K. Wehus, A. Bonaldi, R.D. Davies, R.J. Davis, C. Dickinson, J.P. Leahy, B. Maffei, F. Noviello, F. Couchot, S. Henrot-Versillé, O. Perdereau, S. Plaszczynski, M. Tristram, A. Catalano, A. Coulais, J.-M. Lamarre, M. Arnaud, J. Bobin, D.J. Marshall, P. Paykari, G.W. Pratt, J.-L. Starck, F. Sureau, C. Combet, J.F. Maciás-Pérez, L. Perotto, C. Renault, L. Sanselme, D. Santos, B. Van Tent, T.S. Kisner, T.A. Enßlin, W. Hovest, J. Knoche, F. Matthai, M. Reinecke, T. Riller, S.D.M. White, J. Tuovinen, J. Varis, J.A. Murphy, I. Novikov, G. Savini, J. Lesgourgues, C. Baccigalupi, L. Danese, S. Leach, F. Paci, F. Perrotta, P.A.R. Ade, D. Munshi, L.D. Spencer, R. Sudiwala, A. Moss, S. Church, S. Osborne, C. Armitage-Caplan, E. Calabrese, J. Dunkley, E. Battaner

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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, covering 22500. The main source of uncertainty at 1500 is cosmic variance. Uncertainties in small-scale foreground modelling and instrumental noise dominate the error budget at higher s. For <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 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-cross-spectra with residuals below a few K2 at 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 CDM cosmology is in excellent agreement with preliminary PlanckEE and TE polarisation spectra. We find that the standard CDM cosmology is well constrained by Planck from the measurements at 1500. One specific example is the spectral index of scalar perturbations, for which we report a 5.4 deviation from scale invariance, n= 1. Increasingthe multipole range beyond 1500 does not increase our accuracy for the CDM parameters, but instead allows us to study extensions beyond the standard model. We find no indication of significant departures from the CDM framework. Finally, we report a tension between the Planck best-fit CDM model and the low-spectrum in the form of a power deficit of 510% at 40, with a statistical significance of 2.53. 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.
Original languageEnglish
Article numberA15
JournalAstronomy and Astrophysics
Volume571
ISSN0004-6361
DOIs
Publication statusPublished - 2014

Keywords

  • Cosmic background radiation
  • Cosmological parameters
  • Cosmology: observations
  • Methods: data analysis
  • Budget control
  • Cosmic ray measurement
  • Cosmology
  • Power spectrum
  • Spectroscopy
  • Calibration uncertainty
  • Cosmology: observation
  • Methods:data analysis
  • Statistical descriptions
  • Statistical significance
  • Two-point correlation function
  • Uncertainty analysis
  • Astrophysics and Astronomy
  • astro-ph.CO

Cite this

Tauber, J., Bartlett, J. G., Bucher, M., Cardoso, J-F., Delabrouille, J., Ganga, K., ... Battaner, E. (2014). Planck 2013 results. XV. CMB power spectra and likelihood. Astronomy and Astrophysics, 571, [A15]. https://doi.org/10.1051/0004-6361/201321573
Tauber, Jan ; Bartlett, J.G. ; Bucher, M. ; Cardoso, J.-F. ; Delabrouille, J. ; Ganga, K. ; Giraud-Héraud, Y. ; Le Jeune, M. ; Patanchon, G. ; Piat, M. ; Remazeilles, M. ; Rosset, C. ; Roudier, G. ; Stompor, R. ; Lähteenmäki, A. ; León-Tavares, J. ; Poutanen, T. ; Kunz, M. ; Natoli, P. ; Polenta, G. ; Mandolesi, N. ; Ashdown, M. ; Bridges, M. ; Curto, A. ; Hobson, M. ; Lasenby, A. ; Stolyarov, V. ; Chiang, H.C. ; Kneissl, R. ; Bond, J.R. ; Hanson, D. ; Martin, P.G. ; Miville-Deschênes, M.-A. ; Banday, A.J. ; Bernard, J.-P. ; Bielewicz, P. ; Forni, O. ; Giard, M. ; Jaffe, T.R. ; Montier, L. ; Pointecouteau, E. ; Ristorcelli, I. ; Bock, J.J. ; Doré, O. ; Helou, G. ; Hildebrandt, S.R. ; Prézeau, G. ; Rocha, G. ; Seiffert, M.D. ; Challinor, A. ; Shellard, E.P.S. ; Hernández-Monteagudo, C. ; Borrill, J. ; Keskitalo, R. ; Rebolo, R. ; Chamballu, A. ; Yvon, D. ; Hornstrup, Allan ; Linden-Vørnle, Michael ; Nørgaard-Nielsen, Hans Ulrik ; Oxborrow, Carol Anne ; Tucci, M. ; Atrio-Barandela, F. ; Toffolatti, L. ; Netterfield, C.B. ; Rachen, J.P. ; Scott, D. ; Colombo, L.P.L. ; Pierpaoli, E. ; Benoit-Lévy, A. ; Huffenberger, K.M. ; Juvela, M. ; Keihänen, E. ; Kiiveri, K. ; Kurki-Suonio, H. ; Lindholm, V. ; Suur-Uski, A.-S. ; Valiviita, J. ; Fraisse, A.A. ; Gudmundsson, J.E. ; Jones, W.C. ; Rahlin, A. ; White, M. ; Knox, L. ; Millea, M. ; Lubin, P.M. ; Meinhold, P.R. ; Zonca, A. ; Wandelt, B.D. ; Liguori, M. ; Matarrese, S. ; Molinari, D. ; Burigana, C. ; Lattanzi, M. ; De Bernardis, P. ; Masi, S. ; Melchiorri, A. ; Menegoni, E. ; Nati, F. ; Pagano, L. ; Piacentini, F. ; Bersanelli, M. ; Maino, D. ; Mennella, A. ; Gregorio, A. ; Tavagnacco, D. ; Mazzotta, P. ; Vittorio, N. ; Marinucci, D. ; Christensen, P.R. ; Naselsky, P. ; Rubinõ-Martín, J.A. ; Dupac, X. ; Leonardi, R. ; Mendes, L. ; Giardino, G. ; Laureijs, R.J. ; Tauber, J.A. ; Partridge, B. ; De Zotti, G. ; Frailis, M. ; Galeotta, S. ; Maris, M. ; Pasian, F. ; Zacchei, A. ; Massardi, M. ; Butler, R.C. ; Cuttaia, F. ; De Rosa, A. ; Finelli, F. ; Franceschi, E. ; Gruppuso, A. ; Morgante, G. ; Paoletti, D. ; Ricciardi, S. ; Sandri, M. ; Terenzi, L. ; Valenziano, L. ; Villa, F. ; Donzelli, S. ; Tomasi, M. ; Désert, F.-X. ; Ponthieu, N. ; Türler, M. ; Mitra, Susanta ; Clements, D.L. ; Jaffe, A.H. ; Mortlock, D. ; Novikov, D. ; Rowan-Robinson, M. ; Paladini, R. ; Rusholme, B. ; Benoît, A. ; Dole, H. ; Aghanim, N. ; Aumont, J. ; Boulanger, F. ; Douspis, M. ; Hurier, G. ; Lagache, G. ; Pajot, Fernand ; Puget, J.-L. ; Benabed, K. ; Bouchet, F.R. ; Colombi, S. ; Delouis, J.-M. ; Elsner, F. ; Galli, S. ; Hivon, E. ; Moneti, A. ; Orieux, F. ; Prunet, S. ; Ringeval, C. ; Sygnet, J.-F. ; Popa, L. ; Chiang, L.-Y. ; Efstathiou, G. ; Gratton, S. ; Harrison, D. ; Migliaccio, M. ; Sutton, D. ; Eriksen, H.K. ; Gjerløw, E. ; Hansen, F.K. ; Lilje, P.B. ; Barreiro, R.B. ; Bonavera, L. ; Diego, J.M. ; González-Nuevo, J. ; Herranz, D. ; López-Caniego, M. ; Martínez-González, E. ; Vielva, P. ; Crill, B.P. ; Gaier, T.C. ; Górski, K.M. ; Holmes, W.A. ; Jewell, J. ; Lawrence, C.R. ; O'dwyer, I.J. ; Pietrobon, D. ; Wade, L.A. ; Wehus, I.K. ; Bonaldi, A. ; Davies, R.D. ; Davis, R.J. ; Dickinson, C. ; Leahy, J.P. ; Maffei, B. ; Noviello, F. ; Couchot, F. ; Henrot-Versillé, S. ; Perdereau, O. ; Plaszczynski, S. ; Tristram, M. ; Catalano, A. ; Coulais, A. ; Lamarre, J.-M. ; Arnaud, M. ; Bobin, J. ; Marshall, D.J. ; Paykari, P. ; Pratt, G.W. ; Starck, J.-L. ; Sureau, F. ; Combet, C. ; Maciás-Pérez, J.F. ; Perotto, L. ; Renault, C. ; Sanselme, L. ; Santos, D. ; Van Tent, B. ; Kisner, T.S. ; Enßlin, T.A. ; Hovest, W. ; Knoche, J. ; Matthai, F. ; Reinecke, M. ; Riller, T. ; White, S.D.M. ; Tuovinen, J. ; Varis, J. ; Murphy, J.A. ; Novikov, I. ; Savini, G. ; Lesgourgues, J. ; Baccigalupi, C. ; Danese, L. ; Leach, S. ; Paci, F. ; Perrotta, F. ; Ade, P.A.R. ; Munshi, D. ; Spencer, L.D. ; Sudiwala, R. ; Moss, A. ; Church, S. ; Osborne, S. ; Armitage-Caplan, C. ; Calabrese, E. ; Dunkley, J. ; Battaner, E. / Planck 2013 results. XV. CMB power spectra and likelihood. In: Astronomy and Astrophysics. 2014 ; Vol. 571.
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title = "Planck 2013 results. XV. CMB power spectra and likelihood",
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, covering 22500. The main source of uncertainty at 1500 is cosmic variance. Uncertainties in small-scale foreground modelling and instrumental noise dominate the error budget at higher s. For <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 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-cross-spectra with residuals below a few K2 at 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 CDM cosmology is in excellent agreement with preliminary PlanckEE and TE polarisation spectra. We find that the standard CDM cosmology is well constrained by Planck from the measurements at 1500. One specific example is the spectral index of scalar perturbations, for which we report a 5.4 deviation from scale invariance, n= 1. Increasingthe multipole range beyond 1500 does not increase our accuracy for the CDM parameters, but instead allows us to study extensions beyond the standard model. We find no indication of significant departures from the CDM framework. Finally, we report a tension between the Planck best-fit CDM model and the low-spectrum in the form of a power deficit of 510{\%} at 40, with a statistical significance of 2.53. 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.",
keywords = "Cosmic background radiation, Cosmological parameters, Cosmology: observations, Methods: data analysis, Budget control, Cosmic ray measurement, Cosmology, Power spectrum, Spectroscopy, Calibration uncertainty, Cosmology: observation, Methods:data analysis, Statistical descriptions, Statistical significance, Two-point correlation function, Uncertainty analysis, Astrophysics and Astronomy, astro-ph.CO",
author = "Jan Tauber and J.G. Bartlett and M. Bucher and J.-F. Cardoso and J. Delabrouille and K. Ganga and Y. Giraud-H{\'e}raud and {Le Jeune}, M. and G. Patanchon and M. Piat and M. Remazeilles and C. Rosset and G. Roudier and R. Stompor and A. L{\"a}hteenm{\"a}ki and J. Le{\'o}n-Tavares and T. Poutanen and M. Kunz and P. Natoli and G. Polenta and N. Mandolesi and M. Ashdown and M. Bridges and A. Curto and M. Hobson and A. Lasenby and V. Stolyarov and H.C. Chiang and R. Kneissl and J.R. Bond and D. Hanson and P.G. Martin and M.-A. Miville-Desch{\^e}nes and A.J. Banday and J.-P. Bernard and P. Bielewicz and O. Forni and M. Giard and T.R. Jaffe and L. Montier and E. Pointecouteau and I. Ristorcelli and J.J. Bock and O. Dor{\'e} and G. Helou and S.R. Hildebrandt and G. Pr{\'e}zeau and G. Rocha and M.D. Seiffert and A. Challinor and E.P.S. Shellard and C. Hern{\'a}ndez-Monteagudo and J. Borrill and R. Keskitalo and R. Rebolo and A. Chamballu and D. Yvon and Allan Hornstrup and Michael Linden-V{\o}rnle and N{\o}rgaard-Nielsen, {Hans Ulrik} and Oxborrow, {Carol Anne} and M. Tucci and F. Atrio-Barandela and L. Toffolatti and C.B. Netterfield and J.P. Rachen and D. Scott and L.P.L. Colombo and E. Pierpaoli and A. Benoit-L{\'e}vy and K.M. Huffenberger and M. Juvela and E. Keih{\"a}nen and K. Kiiveri and H. Kurki-Suonio and V. Lindholm and A.-S. Suur-Uski and J. Valiviita and A.A. Fraisse and J.E. Gudmundsson and W.C. Jones and A. Rahlin and M. White and L. Knox and M. Millea and P.M. Lubin and P.R. Meinhold and A. Zonca and B.D. Wandelt and M. Liguori and S. Matarrese and D. Molinari and C. Burigana and M. Lattanzi and {De Bernardis}, P. and S. Masi and A. Melchiorri and E. Menegoni and F. Nati and L. Pagano and F. Piacentini and M. Bersanelli and D. Maino and A. Mennella and A. Gregorio and D. Tavagnacco and P. Mazzotta and N. Vittorio and D. Marinucci and P.R. Christensen and P. Naselsky and J.A. Rubin{\~o}-Mart{\'i}n and X. Dupac and R. Leonardi and L. Mendes and G. Giardino and R.J. Laureijs and J.A. Tauber and B. Partridge and {De Zotti}, G. and M. Frailis and S. Galeotta and M. Maris and F. Pasian and A. Zacchei and M. Massardi and R.C. Butler and F. Cuttaia and {De Rosa}, A. and F. Finelli and E. Franceschi and A. Gruppuso and G. Morgante and D. Paoletti and S. Ricciardi and M. Sandri and L. Terenzi and L. Valenziano and F. Villa and S. Donzelli and M. Tomasi and F.-X. D{\'e}sert and N. Ponthieu and M. T{\"u}rler and Susanta Mitra and D.L. Clements and A.H. Jaffe and D. Mortlock and D. Novikov and M. Rowan-Robinson and R. Paladini and B. Rusholme and A. Beno{\^i}t and H. Dole and N. Aghanim and J. Aumont and F. Boulanger and M. Douspis and G. Hurier and G. Lagache and Fernand Pajot and J.-L. Puget and K. Benabed and F.R. Bouchet and S. Colombi and J.-M. Delouis and F. Elsner and S. Galli and E. Hivon and A. Moneti and F. Orieux and S. Prunet and C. Ringeval and J.-F. Sygnet and L. Popa and L.-Y. Chiang and G. Efstathiou and S. Gratton and D. Harrison and M. Migliaccio and D. Sutton and H.K. Eriksen and E. Gjerl{\o}w and F.K. Hansen and P.B. Lilje and R.B. Barreiro and L. Bonavera and J.M. Diego and J. Gonz{\'a}lez-Nuevo and D. Herranz and M. L{\'o}pez-Caniego and E. Mart{\'i}nez-Gonz{\'a}lez and P. Vielva and B.P. Crill and T.C. Gaier and K.M. G{\'o}rski and W.A. Holmes and J. Jewell and C.R. Lawrence and I.J. O'dwyer and D. Pietrobon and L.A. Wade and I.K. Wehus and A. Bonaldi and R.D. Davies and R.J. Davis and C. Dickinson and J.P. Leahy and B. Maffei and F. Noviello and F. Couchot and S. Henrot-Versill{\'e} and O. Perdereau and S. Plaszczynski and M. Tristram and A. Catalano and A. Coulais and J.-M. Lamarre and M. Arnaud and J. Bobin and D.J. Marshall and P. Paykari and G.W. Pratt and J.-L. Starck and F. Sureau and C. Combet and J.F. Maci{\'a}s-P{\'e}rez and L. Perotto and C. Renault and L. Sanselme and D. Santos and {Van Tent}, B. and T.S. Kisner and T.A. En{\ss}lin and W. Hovest and J. Knoche and F. Matthai and M. Reinecke and T. Riller and S.D.M. White and J. Tuovinen and J. Varis and J.A. Murphy and I. Novikov and G. Savini and J. Lesgourgues and C. Baccigalupi and L. Danese and S. Leach and F. Paci and F. Perrotta and P.A.R. Ade and D. Munshi and L.D. Spencer and R. Sudiwala and A. Moss and S. Church and S. Osborne and C. Armitage-Caplan and E. Calabrese and J. Dunkley and E. Battaner",
year = "2014",
doi = "10.1051/0004-6361/201321573",
language = "English",
volume = "571",
journal = "Astronomy & Astrophysics",
issn = "0004-6361",
publisher = "E D P Sciences",

}

Tauber, J, Bartlett, JG, Bucher, M, Cardoso, J-F, Delabrouille, J, Ganga, K, Giraud-Héraud, Y, Le Jeune, M, Patanchon, G, Piat, M, Remazeilles, M, Rosset, C, Roudier, G, Stompor, R, Lähteenmäki, A, León-Tavares, J, Poutanen, T, Kunz, M, Natoli, P, Polenta, G, Mandolesi, N, Ashdown, M, Bridges, M, Curto, A, Hobson, M, Lasenby, A, Stolyarov, V, Chiang, HC, Kneissl, R, Bond, JR, Hanson, D, Martin, PG, Miville-Deschênes, M-A, Banday, AJ, Bernard, J-P, Bielewicz, P, Forni, O, Giard, M, Jaffe, TR, Montier, L, Pointecouteau, E, Ristorcelli, I, Bock, JJ, Doré, O, Helou, G, Hildebrandt, SR, Prézeau, G, Rocha, G, Seiffert, MD, Challinor, A, Shellard, EPS, Hernández-Monteagudo, C, Borrill, J, Keskitalo, R, Rebolo, R, Chamballu, A, Yvon, D, Hornstrup, A, Linden-Vørnle, M, Nørgaard-Nielsen, HU, Oxborrow, CA, Tucci, M, Atrio-Barandela, F, Toffolatti, L, Netterfield, CB, Rachen, JP, Scott, D, Colombo, LPL, Pierpaoli, E, Benoit-Lévy, A, Huffenberger, KM, Juvela, M, Keihänen, E, Kiiveri, K, Kurki-Suonio, H, Lindholm, V, Suur-Uski, A-S, Valiviita, J, Fraisse, AA, Gudmundsson, JE, Jones, WC, Rahlin, A, White, M, Knox, L, Millea, M, Lubin, PM, Meinhold, PR, Zonca, A, Wandelt, BD, Liguori, M, Matarrese, S, Molinari, D, Burigana, C, Lattanzi, M, De Bernardis, P, Masi, S, Melchiorri, A, Menegoni, E, Nati, F, Pagano, L, Piacentini, F, Bersanelli, M, Maino, D, Mennella, A, Gregorio, A, Tavagnacco, D, Mazzotta, P, Vittorio, N, Marinucci, D, Christensen, PR, Naselsky, P, Rubinõ-Martín, JA, Dupac, X, Leonardi, R, Mendes, L, Giardino, G, Laureijs, RJ, Tauber, JA, Partridge, B, De Zotti, G, Frailis, M, Galeotta, S, Maris, M, Pasian, F, Zacchei, A, Massardi, M, Butler, RC, Cuttaia, F, De Rosa, A, Finelli, F, Franceschi, E, Gruppuso, A, Morgante, G, Paoletti, D, Ricciardi, S, Sandri, M, Terenzi, L, Valenziano, L, Villa, F, Donzelli, S, Tomasi, M, Désert, F-X, Ponthieu, N, Türler, M, Mitra, S, Clements, DL, Jaffe, AH, Mortlock, D, Novikov, D, Rowan-Robinson, M, Paladini, R, Rusholme, B, Benoît, A, Dole, H, Aghanim, N, Aumont, J, Boulanger, F, Douspis, M, Hurier, G, Lagache, G, Pajot, F, Puget, J-L, Benabed, K, Bouchet, FR, Colombi, S, Delouis, J-M, Elsner, F, Galli, S, Hivon, E, Moneti, A, Orieux, F, Prunet, S, Ringeval, C, Sygnet, J-F, Popa, L, Chiang, L-Y, Efstathiou, G, Gratton, S, Harrison, D, Migliaccio, M, Sutton, D, Eriksen, HK, Gjerløw, E, Hansen, FK, Lilje, PB, Barreiro, RB, Bonavera, L, Diego, JM, González-Nuevo, J, Herranz, D, López-Caniego, M, Martínez-González, E, Vielva, P, Crill, BP, Gaier, TC, Górski, KM, Holmes, WA, Jewell, J, Lawrence, CR, O'dwyer, IJ, Pietrobon, D, Wade, LA, Wehus, IK, Bonaldi, A, Davies, RD, Davis, RJ, Dickinson, C, Leahy, JP, Maffei, B, Noviello, F, Couchot, F, Henrot-Versillé, S, Perdereau, O, Plaszczynski, S, Tristram, M, Catalano, A, Coulais, A, Lamarre, J-M, Arnaud, M, Bobin, J, Marshall, DJ, Paykari, P, Pratt, GW, Starck, J-L, Sureau, F, Combet, C, Maciás-Pérez, JF, Perotto, L, Renault, C, Sanselme, L, Santos, D, Van Tent, B, Kisner, TS, Enßlin, TA, Hovest, W, Knoche, J, Matthai, F, Reinecke, M, Riller, T, White, SDM, Tuovinen, J, Varis, J, Murphy, JA, Novikov, I, Savini, G, Lesgourgues, J, Baccigalupi, C, Danese, L, Leach, S, Paci, F, Perrotta, F, Ade, PAR, Munshi, D, Spencer, LD, Sudiwala, R, Moss, A, Church, S, Osborne, S, Armitage-Caplan, C, Calabrese, E, Dunkley, J & Battaner, E 2014, 'Planck 2013 results. XV. CMB power spectra and likelihood', Astronomy and Astrophysics, vol. 571, A15. https://doi.org/10.1051/0004-6361/201321573

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

In: Astronomy and Astrophysics, Vol. 571, A15, 2014.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Planck 2013 results. XV. CMB power spectra and likelihood

AU - Tauber, Jan

AU - Bartlett, J.G.

AU - Bucher, M.

AU - Cardoso, J.-F.

AU - Delabrouille, J.

AU - Ganga, K.

AU - Giraud-Héraud, Y.

AU - Le Jeune, M.

AU - Patanchon, G.

AU - Piat, M.

AU - Remazeilles, M.

AU - Rosset, C.

AU - Roudier, G.

AU - Stompor, R.

AU - Lähteenmäki, A.

AU - León-Tavares, J.

AU - Poutanen, T.

AU - Kunz, M.

AU - Natoli, P.

AU - Polenta, G.

AU - Mandolesi, N.

AU - Ashdown, M.

AU - Bridges, M.

AU - Curto, A.

AU - Hobson, M.

AU - Lasenby, A.

AU - Stolyarov, V.

AU - Chiang, H.C.

AU - Kneissl, R.

AU - Bond, J.R.

AU - Hanson, D.

AU - Martin, P.G.

AU - Miville-Deschênes, M.-A.

AU - Banday, A.J.

AU - Bernard, J.-P.

AU - Bielewicz, P.

AU - Forni, O.

AU - Giard, M.

AU - Jaffe, T.R.

AU - Montier, L.

AU - Pointecouteau, E.

AU - Ristorcelli, I.

AU - Bock, J.J.

AU - Doré, O.

AU - Helou, G.

AU - Hildebrandt, S.R.

AU - Prézeau, G.

AU - Rocha, G.

AU - Seiffert, M.D.

AU - Challinor, A.

AU - Shellard, E.P.S.

AU - Hernández-Monteagudo, C.

AU - Borrill, J.

AU - Keskitalo, R.

AU - Rebolo, R.

AU - Chamballu, A.

AU - Yvon, D.

AU - Hornstrup, Allan

AU - Linden-Vørnle, Michael

AU - Nørgaard-Nielsen, Hans Ulrik

AU - Oxborrow, Carol Anne

AU - Tucci, M.

AU - Atrio-Barandela, F.

AU - Toffolatti, L.

AU - Netterfield, C.B.

AU - Rachen, J.P.

AU - Scott, D.

AU - Colombo, L.P.L.

AU - Pierpaoli, E.

AU - Benoit-Lévy, A.

AU - Huffenberger, K.M.

AU - Juvela, M.

AU - Keihänen, E.

AU - Kiiveri, K.

AU - Kurki-Suonio, H.

AU - Lindholm, V.

AU - Suur-Uski, A.-S.

AU - Valiviita, J.

AU - Fraisse, A.A.

AU - Gudmundsson, J.E.

AU - Jones, W.C.

AU - Rahlin, A.

AU - White, M.

AU - Knox, L.

AU - Millea, M.

AU - Lubin, P.M.

AU - Meinhold, P.R.

AU - Zonca, A.

AU - Wandelt, B.D.

AU - Liguori, M.

AU - Matarrese, S.

AU - Molinari, D.

AU - Burigana, C.

AU - Lattanzi, M.

AU - De Bernardis, P.

AU - Masi, S.

AU - Melchiorri, A.

AU - Menegoni, E.

AU - Nati, F.

AU - Pagano, L.

AU - Piacentini, F.

AU - Bersanelli, M.

AU - Maino, D.

AU - Mennella, A.

AU - Gregorio, A.

AU - Tavagnacco, D.

AU - Mazzotta, P.

AU - Vittorio, N.

AU - Marinucci, D.

AU - Christensen, P.R.

AU - Naselsky, P.

AU - Rubinõ-Martín, J.A.

AU - Dupac, X.

AU - Leonardi, R.

AU - Mendes, L.

AU - Giardino, G.

AU - Laureijs, R.J.

AU - Tauber, J.A.

AU - Partridge, B.

AU - De Zotti, G.

AU - Frailis, M.

AU - Galeotta, S.

AU - Maris, M.

AU - Pasian, F.

AU - Zacchei, A.

AU - Massardi, M.

AU - Butler, R.C.

AU - Cuttaia, F.

AU - De Rosa, A.

AU - Finelli, F.

AU - Franceschi, E.

AU - Gruppuso, A.

AU - Morgante, G.

AU - Paoletti, D.

AU - Ricciardi, S.

AU - Sandri, M.

AU - Terenzi, L.

AU - Valenziano, L.

AU - Villa, F.

AU - Donzelli, S.

AU - Tomasi, M.

AU - Désert, F.-X.

AU - Ponthieu, N.

AU - Türler, M.

AU - Mitra, Susanta

AU - Clements, D.L.

AU - Jaffe, A.H.

AU - Mortlock, D.

AU - Novikov, D.

AU - Rowan-Robinson, M.

AU - Paladini, R.

AU - Rusholme, B.

AU - Benoît, A.

AU - Dole, H.

AU - Aghanim, N.

AU - Aumont, J.

AU - Boulanger, F.

AU - Douspis, M.

AU - Hurier, G.

AU - Lagache, G.

AU - Pajot, Fernand

AU - Puget, J.-L.

AU - Benabed, K.

AU - Bouchet, F.R.

AU - Colombi, S.

AU - Delouis, J.-M.

AU - Elsner, F.

AU - Galli, S.

AU - Hivon, E.

AU - Moneti, A.

AU - Orieux, F.

AU - Prunet, S.

AU - Ringeval, C.

AU - Sygnet, J.-F.

AU - Popa, L.

AU - Chiang, L.-Y.

AU - Efstathiou, G.

AU - Gratton, S.

AU - Harrison, D.

AU - Migliaccio, M.

AU - Sutton, D.

AU - Eriksen, H.K.

AU - Gjerløw, E.

AU - Hansen, F.K.

AU - Lilje, P.B.

AU - Barreiro, R.B.

AU - Bonavera, L.

AU - Diego, J.M.

AU - González-Nuevo, J.

AU - Herranz, D.

AU - López-Caniego, M.

AU - Martínez-González, E.

AU - Vielva, P.

AU - Crill, B.P.

AU - Gaier, T.C.

AU - Górski, K.M.

AU - Holmes, W.A.

AU - Jewell, J.

AU - Lawrence, C.R.

AU - O'dwyer, I.J.

AU - Pietrobon, D.

AU - Wade, L.A.

AU - Wehus, I.K.

AU - Bonaldi, A.

AU - Davies, R.D.

AU - Davis, R.J.

AU - Dickinson, C.

AU - Leahy, J.P.

AU - Maffei, B.

AU - Noviello, F.

AU - Couchot, F.

AU - Henrot-Versillé, S.

AU - Perdereau, O.

AU - Plaszczynski, S.

AU - Tristram, M.

AU - Catalano, A.

AU - Coulais, A.

AU - Lamarre, J.-M.

AU - Arnaud, M.

AU - Bobin, J.

AU - Marshall, D.J.

AU - Paykari, P.

AU - Pratt, G.W.

AU - Starck, J.-L.

AU - Sureau, F.

AU - Combet, C.

AU - Maciás-Pérez, J.F.

AU - Perotto, L.

AU - Renault, C.

AU - Sanselme, L.

AU - Santos, D.

AU - Van Tent, B.

AU - Kisner, T.S.

AU - Enßlin, T.A.

AU - Hovest, W.

AU - Knoche, J.

AU - Matthai, F.

AU - Reinecke, M.

AU - Riller, T.

AU - White, S.D.M.

AU - Tuovinen, J.

AU - Varis, J.

AU - Murphy, J.A.

AU - Novikov, I.

AU - Savini, G.

AU - Lesgourgues, J.

AU - Baccigalupi, C.

AU - Danese, L.

AU - Leach, S.

AU - Paci, F.

AU - Perrotta, F.

AU - Ade, P.A.R.

AU - Munshi, D.

AU - Spencer, L.D.

AU - Sudiwala, R.

AU - Moss, A.

AU - Church, S.

AU - Osborne, S.

AU - Armitage-Caplan, C.

AU - Calabrese, E.

AU - Dunkley, J.

AU - Battaner, E.

PY - 2014

Y1 - 2014

N2 - 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, covering 22500. The main source of uncertainty at 1500 is cosmic variance. Uncertainties in small-scale foreground modelling and instrumental noise dominate the error budget at higher s. For <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 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-cross-spectra with residuals below a few K2 at 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 CDM cosmology is in excellent agreement with preliminary PlanckEE and TE polarisation spectra. We find that the standard CDM cosmology is well constrained by Planck from the measurements at 1500. One specific example is the spectral index of scalar perturbations, for which we report a 5.4 deviation from scale invariance, n= 1. Increasingthe multipole range beyond 1500 does not increase our accuracy for the CDM parameters, but instead allows us to study extensions beyond the standard model. We find no indication of significant departures from the CDM framework. Finally, we report a tension between the Planck best-fit CDM model and the low-spectrum in the form of a power deficit of 510% at 40, with a statistical significance of 2.53. 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.

AB - 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, covering 22500. The main source of uncertainty at 1500 is cosmic variance. Uncertainties in small-scale foreground modelling and instrumental noise dominate the error budget at higher s. For <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 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-cross-spectra with residuals below a few K2 at 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 CDM cosmology is in excellent agreement with preliminary PlanckEE and TE polarisation spectra. We find that the standard CDM cosmology is well constrained by Planck from the measurements at 1500. One specific example is the spectral index of scalar perturbations, for which we report a 5.4 deviation from scale invariance, n= 1. Increasingthe multipole range beyond 1500 does not increase our accuracy for the CDM parameters, but instead allows us to study extensions beyond the standard model. We find no indication of significant departures from the CDM framework. Finally, we report a tension between the Planck best-fit CDM model and the low-spectrum in the form of a power deficit of 510% at 40, with a statistical significance of 2.53. 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.

KW - Cosmic background radiation

KW - Cosmological parameters

KW - Cosmology: observations

KW - Methods: data analysis

KW - Budget control

KW - Cosmic ray measurement

KW - Cosmology

KW - Power spectrum

KW - Spectroscopy

KW - Calibration uncertainty

KW - Cosmology: observation

KW - Methods:data analysis

KW - Statistical descriptions

KW - Statistical significance

KW - Two-point correlation function

KW - Uncertainty analysis

KW - Astrophysics and Astronomy

KW - astro-ph.CO

U2 - 10.1051/0004-6361/201321573

DO - 10.1051/0004-6361/201321573

M3 - Journal article

VL - 571

JO - Astronomy & Astrophysics

JF - Astronomy & Astrophysics

SN - 0004-6361

M1 - A15

ER -

Tauber J, Bartlett JG, Bucher M, Cardoso J-F, Delabrouille J, Ganga K et al. Planck 2013 results. XV. CMB power spectra and likelihood. Astronomy and Astrophysics. 2014;571. A15. https://doi.org/10.1051/0004-6361/201321573