Planck 2013 results. XV. CMB power spectra and likelihood

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; E Battaner; K Benabed; A Beno??t; A Benoit-L??vy; J-P Bernard; M Bersanelli; P Bielewicz; J Bobin; J J Bock; A Bonaldi; L Bonavera; J R Bond; J Borrill; F R Bouchet; F Boulanger; M Bridges; M Bucher; C Burigana; R C Butler; E Calabrese; J-F Cardoso; A Catalano; A Challinor; A Chamballu; H C Chiang; L-Y 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; J-M Delouis; F-X D??sert; C Dickinson; J M Diego; H Dole; S Donzelli; O Dor??; M Douspis; J Dunkley; X Dupac; G Efstathiou; F Elsner; T A En??lin; H K Eriksen; F Finelli; O Forni; M Frailis; A A Fraisse; E Franceschi; T C Gaier; S Galeotta; S Galli; K Ganga; M Giard; G Giardino; Y Giraud-H??raud; E Gjerl??w; J Gonz??lez-Nuevo; K M G??rski; S Gratton; A Gregorio; A Gruppuso; J E Gudmundsson; F K Hansen; D Hanson; D Harrison; G Helou; S Henrot-Versill??; C Hern??ndez-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; J Jewell; W C Jones; M Juvela; E Keih??nen; R Keskitalo; K Kiiveri; T S Kisner; R Kneissl; J Knoche; L Knox; M Kunz; H Kurki-Suonio; G Lagache; A L??hteenm??ki; J-M Lamarre; A Lasenby; M Lattanzi; R J Laureijs; C R Lawrence; M Le Jeune; S Leach; J P Leahy; R Leonardi; J Le??n-Tavares; J Lesgourgues; M Liguori; P B Lilje; M Linden-V??rnle; V Lindholm; M L??pez-Caniego; P M Lubin; J F Mac??as-P??rez; B Maffei; D Maino; N Mandolesi; D Marinucci; M Maris; D J Marshall; P G Martin; E Mart??nez-Gonz??lez; S Masi; M Massardi; S Matarrese; F Matthai; P Mazzotta; P R Meinhold; A Melchiorri; L Mendes; E Menegoni; A Mennella; M Migliaccio; M Millea; S Mitra; M-A Miville-Desch??nes; D Molinari; 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 N??rgaard-Nielsen; F Noviello; D Novikov; I Novikov; I J O'Dwyer; F Orieux; S Osborne; C A Oxborrow; F Paci; L Pagano; F Pajot; R Paladini; D Paoletti; B Partridge; F Pasian; G Patanchon; P Paykari; 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 Pr??zeau; S Prunet; J-L Puget; J P Rachen; A Rahlin; R Rebolo; M Reinecke; M Remazeilles; C Renault; S Ricciardi; T Riller; C Ringeval; I Ristorcelli; G Rocha; C Rosset; G Roudier; M Rowan-Robinson; J A Rubi??o-Mart??n; B Rusholme; M Sandri; L Sanselme; 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; 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; M T??rler; L Valenziano; J Valiviita; B Van Tent; J Varis; P Vielva; F Villa; N Vittorio; L A Wade; B D Wandelt; I K Wehus; M White; S D M White; D Yvon; A Zacchei; A Zonca; et al

doi:10.1051/0004-6361/201321573

Planck 2013 results. XV. CMB power spectra and likelihood

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, E Battaner, K Benabed, A Beno??t, A Benoit-L??vy, J-P Bernard, M Bersanelli, P Bielewicz, J BobinJ J Bock, A Bonaldi, L Bonavera, J R Bond, J Borrill, F R Bouchet, F Boulanger, M Bridges, M Bucher, C Burigana, R C Butler, E Calabrese, J-F Cardoso, A Catalano, A Challinor, A Chamballu, H C Chiang, L-Y 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, J-M Delouis, F-X D??sert, C Dickinson, J M Diego, H Dole, S Donzelli, O Dor??, M Douspis, J Dunkley, X Dupac, G Efstathiou, F Elsner, T A En??lin, H K Eriksen, F Finelli, O Forni, M Frailis, A A Fraisse, E Franceschi, T C Gaier, S Galeotta, S Galli, K Ganga, M Giard, G Giardino, Y Giraud-H??raud, E Gjerl??w, J Gonz??lez-Nuevo, K M G??rski, S Gratton, A Gregorio, A Gruppuso, J E Gudmundsson, F K Hansen, D Hanson, D Harrison, G Helou, S Henrot-Versill??, C Hern??ndez-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, J Jewell, W C Jones, M Juvela, E Keih??nen, R Keskitalo, K Kiiveri, T S Kisner, R Kneissl, J Knoche, L Knox, M Kunz, H Kurki-Suonio, G Lagache, A L??hteenm??ki, J-M Lamarre, A Lasenby, M Lattanzi, R J Laureijs, C R Lawrence, M Le Jeune, S Leach, J P Leahy, R Leonardi, J Le??n-Tavares, J Lesgourgues, M Liguori, P B Lilje, M Linden-V??rnle, V Lindholm, M L??pez-Caniego, P M Lubin, J F Mac??as-P??rez, B Maffei, D Maino, N Mandolesi, D Marinucci, M Maris, D J Marshall, P G Martin, E Mart??nez-Gonz??lez, S Masi, M Massardi, S Matarrese, F Matthai, P Mazzotta, P R Meinhold, A Melchiorri, L Mendes, E Menegoni, A Mennella, M Migliaccio, M Millea, S Mitra, M-A Miville-Desch??nes, D Molinari, 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 N??rgaard-Nielsen, F Noviello, D Novikov, I Novikov, I J O'Dwyer, F Orieux, S Osborne, C A Oxborrow, F Paci, L Pagano, F Pajot, R Paladini, D Paoletti, B Partridge, F Pasian, G Patanchon, P Paykari, 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 Pr??zeau, S Prunet, J-L Puget, J P Rachen, A Rahlin, R Rebolo, M Reinecke, M Remazeilles, C Renault, S Ricciardi, T Riller, C Ringeval, I Ristorcelli, G Rocha, C Rosset, G Roudier, M Rowan-Robinson, J A Rubi??o-Mart??n, B Rusholme, M Sandri, L Sanselme, 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, 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, M T??rler, L Valenziano, J Valiviita, B Van Tent, J Varis, P Vielva, F Villa, N Vittorio, L A Wade, B D Wandelt, I K Wehus, M White, S D M White, D Yvon, A Zacchei, A Zonca, et al

Research output: Contribution to journal › Article › peer-review

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 {\textless}= l{\textless}= 2500. The main source of uncertainty at l ??? 1500 is cosmic variance. Uncertainties in small-scale foreground modelling andinstrumental noise dominate the error budget at higher ls. For l {\textless} 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 {\textgreater}= 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 withresiduals below a few {muK}2 at l ??? 1000, inagreement 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 {LambdaCDM} cosmology is in excellent agreement with preliminary {PlanckEE} and {TE} polarisation spectra. We find that the standard {LambdaCDM} 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 5.4sigma deviation from scale invariance,ns = 1. Increasing the multipole range beyond l {\textasciitilde}=1500 does not increase our accuracy for the {LambdaCDM} parameters, but instead allows us to study extensions beyond the standard model. We find no indication of significant departures from the {LambdaCDM} framework. Finally, we report a tension between the Planck best-fit {LambdaCDM} model and the low-l spectrum in the form of a power deficit of 5-10\% at l ??? 40, with a statistical significance of 2.5-3sigma.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 language	English
Journal	Astronomy and Astrophysics
Volume	571
DOIs	https://doi.org/10.1051/0004-6361/201321573
Publication status	Published - Nov 2014

Keywords

cosmic background radiation
cosmological parameters
cosmology: observations
methods: data analysis

Access to Document

10.1051/0004-6361/201321573

http://adsabs.harvard.edu/abs/2014A%26A...571A..15P

Cite this

Collaboration, P., Ade, P. A. R., Aghanim, N., Armitage-Caplan, C., Arnaud, M., Ashdown, M., Atrio-Barandela, F., Aumont, J., Baccigalupi, C., Banday, A. J., Barreiro, R. B., Bartlett, J. G., Battaner, E., Benabed, K., Beno??t, A., Benoit-L??vy, A., Bernard, J.-P., Bersanelli, M., Bielewicz, P., ... al, E. (2014). Planck 2013 results. XV. CMB power spectra and likelihood. Astronomy and Astrophysics, 571. https://doi.org/10.1051/0004-6361/201321573

@article{ec943e7a1bbe4f98b02d204d6bdf49e1,

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, l, covering 2 {\textless}= l{\textless}= 2500. The main source of uncertainty at l ??? 1500 is cosmic variance. Uncertainties in small-scale foreground modelling andinstrumental noise dominate the error budget at higher ls. For l {\textless} 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 {\textgreater}= 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 withresiduals below a few {muK}2 at l ??? 1000, inagreement 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 {LambdaCDM} cosmology is in excellent agreement with preliminary {PlanckEE} and {TE} polarisation spectra. We find that the standard {LambdaCDM} 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 5.4sigma deviation from scale invariance,ns = 1. Increasing the multipole range beyond l {\textasciitilde}=1500 does not increase our accuracy for the {LambdaCDM} parameters, but instead allows us to study extensions beyond the standard model. We find no indication of significant departures from the {LambdaCDM} framework. Finally, we report a tension between the Planck best-fit {LambdaCDM} model and the low-l spectrum in the form of a power deficit of 5-10\% at l ??? 40, with a statistical significance of 2.5-3sigma.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",

author = "Planck Collaboration and Ade, {P A R} and N Aghanim and C Armitage-Caplan and M Arnaud and M Ashdown and F Atrio-Barandela and J Aumont and C Baccigalupi and Banday, {A J} and Barreiro, {R B} and Bartlett, {J G} and E Battaner and K Benabed and A Beno??t and A Benoit-L??vy and J-P Bernard and M Bersanelli and P Bielewicz and J Bobin and Bock, {J J} and A Bonaldi and L Bonavera and Bond, {J R} and J Borrill and Bouchet, {F R} and F Boulanger and M Bridges and M Bucher and C Burigana and Butler, {R C} and E Calabrese and J-F Cardoso and A Catalano and A Challinor and A Chamballu and Chiang, {H C} and L-Y Chiang and Christensen, {P R} and S Church and Clements, {D L} and S Colombi and Colombo, {L P L} and C Combet and F Couchot and A Coulais and Crill, {B P} and A Curto and F Cuttaia and L Danese and Davies, {R D} and Davis, {R J} and {de Bernardis}, P and {de Rosa}, A and {de Zotti}, G and J Delabrouille and J-M Delouis and F-X D??sert and C Dickinson and Diego, {J M} and H Dole and S Donzelli and O Dor?? and M Douspis and J Dunkley and X Dupac and G Efstathiou and F Elsner and En??lin, {T A} and Eriksen, {H K} and F Finelli and O Forni and M Frailis and Fraisse, {A A} and E Franceschi and Gaier, {T C} and S Galeotta and S Galli and K Ganga and M Giard and G Giardino and Y Giraud-H??raud and E Gjerl??w and J Gonz??lez-Nuevo and G??rski, {K M} and S Gratton and A Gregorio and A Gruppuso and Gudmundsson, {J E} and Hansen, {F K} and D Hanson and D Harrison and G Helou and S Henrot-Versill?? and C Hern??ndez-Monteagudo and D Herranz and Hildebrandt, {S R} and E Hivon and M Hobson and Holmes, {W A} and A Hornstrup and W Hovest and Huffenberger, {K M} and G Hurier and Jaffe, {A H} and Jaffe, {T R} and J Jewell and Jones, {W C} and M Juvela and E Keih??nen and R Keskitalo and K Kiiveri and Kisner, {T S} and R Kneissl and J Knoche and L Knox and M Kunz and H Kurki-Suonio and G Lagache and A L??hteenm??ki and J-M Lamarre and A Lasenby and M Lattanzi and Laureijs, {R J} and Lawrence, {C R} and {Le Jeune}, M and S Leach and Leahy, {J P} and R Leonardi and J Le??n-Tavares and J Lesgourgues and M Liguori and Lilje, {P B} and M Linden-V??rnle and V Lindholm and M L??pez-Caniego and Lubin, {P M} and Mac??as-P??rez, {J F} and B Maffei and D Maino and N Mandolesi and D Marinucci and M Maris and Marshall, {D J} and Martin, {P G} and E Mart??nez-Gonz??lez and S Masi and M Massardi and S Matarrese and F Matthai and P Mazzotta and Meinhold, {P R} and A Melchiorri and L Mendes and E Menegoni and A Mennella and M Migliaccio and M Millea and S Mitra and M-A Miville-Desch??nes and D Molinari and A Moneti and L Montier and G Morgante and D Mortlock and A Moss and D Munshi and Murphy, {J A} and P Naselsky and F Nati and P Natoli and Netterfield, {C B} and N??rgaard-Nielsen, {H U} and F Noviello and D Novikov and I Novikov and O'Dwyer, {I J} and F Orieux and S Osborne and Oxborrow, {C A} and F Paci and L Pagano and F Pajot and R Paladini and D Paoletti and B Partridge and F Pasian and G Patanchon and P Paykari and O Perdereau and L Perotto and F Perrotta and F Piacentini and M Piat and E Pierpaoli and D Pietrobon and S Plaszczynski and E Pointecouteau and G Polenta and N Ponthieu and L Popa and T Poutanen and Pratt, {G W} and G Pr??zeau and S Prunet and J-L Puget and Rachen, {J P} and A Rahlin and R Rebolo and M Reinecke and M Remazeilles and C Renault and S Ricciardi and T Riller and C Ringeval and I Ristorcelli and G Rocha and C Rosset and G Roudier and M Rowan-Robinson and Rubi??o-Mart??n, {J A} and B Rusholme and M Sandri and L Sanselme and D Santos and G Savini and D Scott and Seiffert, {M D} and Shellard, {E P S} and Spencer, {L D} and J-L Starck and V Stolyarov and R Stompor and R Sudiwala and F Sureau and D Sutton and A-S Suur-Uski and J-F Sygnet and Tauber, {J A} and D Tavagnacco and L Terenzi and L Toffolatti and M Tomasi and M Tristram and M Tucci and J Tuovinen and M T??rler and L Valenziano and J Valiviita and {Van Tent}, B and J Varis and P Vielva and F Villa and N Vittorio and Wade, {L A} and Wandelt, {B D} and Wehus, {I K} and M White and White, {S D M} and D Yvon and A Zacchei and A Zonca and et al",

year = "2014",

month = nov,

doi = "10.1051/0004-6361/201321573",

language = "English",

volume = "571",

journal = "Astronomy and Astrophysics",

issn = "1432-0746",

publisher = "EDP Sciences",

}

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

TY - JOUR

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

AU - Collaboration, Planck

AU - Ade, P A R

AU - Aghanim, N

AU - Armitage-Caplan, C

AU - Arnaud, M

AU - Ashdown, M

AU - Atrio-Barandela, F

AU - Aumont, J

AU - Baccigalupi, C

AU - Banday, A J

AU - Barreiro, R B

AU - Bartlett, J G

AU - Battaner, E

AU - Benabed, K

AU - Beno??t, A

AU - Benoit-L??vy, A

AU - Bernard, J-P

AU - Bersanelli, M

AU - Bielewicz, P

AU - Bobin, J

AU - Bock, J J

AU - Bonaldi, A

AU - Bonavera, L

AU - Bond, J R

AU - Borrill, J

AU - Bouchet, F R

AU - Boulanger, F

AU - Bridges, M

AU - Bucher, M

AU - Burigana, C

AU - Butler, R C

AU - Calabrese, E

AU - Cardoso, J-F

AU - Catalano, A

AU - Challinor, A

AU - Chamballu, A

AU - Chiang, H C

AU - Chiang, L-Y

AU - Christensen, P R

AU - Church, S

AU - Clements, D L

AU - Colombi, S

AU - Colombo, L P L

AU - Combet, C

AU - Couchot, F

AU - Coulais, A

AU - Crill, B P

AU - Curto, A

AU - Cuttaia, F

AU - Danese, L

AU - Davies, R D

AU - Davis, R J

AU - de Bernardis, P

AU - de Rosa, A

AU - de Zotti, G

AU - Delabrouille, J

AU - Delouis, J-M

AU - D??sert, F-X

AU - Dickinson, C

AU - Diego, J M

AU - Dole, H

AU - Donzelli, S

AU - Dor??, O

AU - Douspis, M

AU - Dunkley, J

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PY - 2014/11

Y1 - 2014/11

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, l, covering 2 {\textless}= l{\textless}= 2500. The main source of uncertainty at l ??? 1500 is cosmic variance. Uncertainties in small-scale foreground modelling andinstrumental noise dominate the error budget at higher ls. For l {\textless} 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 {\textgreater}= 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 withresiduals below a few {muK}2 at l ??? 1000, inagreement 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 {LambdaCDM} cosmology is in excellent agreement with preliminary {PlanckEE} and {TE} polarisation spectra. We find that the standard {LambdaCDM} 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 5.4sigma deviation from scale invariance,ns = 1. Increasing the multipole range beyond l {\textasciitilde}=1500 does not increase our accuracy for the {LambdaCDM} parameters, but instead allows us to study extensions beyond the standard model. We find no indication of significant departures from the {LambdaCDM} framework. Finally, we report a tension between the Planck best-fit {LambdaCDM} model and the low-l spectrum in the form of a power deficit of 5-10\% at l ??? 40, with a statistical significance of 2.5-3sigma.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, l, covering 2 {\textless}= l{\textless}= 2500. The main source of uncertainty at l ??? 1500 is cosmic variance. Uncertainties in small-scale foreground modelling andinstrumental noise dominate the error budget at higher ls. For l {\textless} 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 {\textgreater}= 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 withresiduals below a few {muK}2 at l ??? 1000, inagreement 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 {LambdaCDM} cosmology is in excellent agreement with preliminary {PlanckEE} and {TE} polarisation spectra. We find that the standard {LambdaCDM} 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 5.4sigma deviation from scale invariance,ns = 1. Increasing the multipole range beyond l {\textasciitilde}=1500 does not increase our accuracy for the {LambdaCDM} parameters, but instead allows us to study extensions beyond the standard model. We find no indication of significant departures from the {LambdaCDM} framework. Finally, we report a tension between the Planck best-fit {LambdaCDM} model and the low-l spectrum in the form of a power deficit of 5-10\% at l ??? 40, with a statistical significance of 2.5-3sigma.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

U2 - 10.1051/0004-6361/201321573

DO - 10.1051/0004-6361/201321573

M3 - Article

SN - 1432-0746

SN - 2329-1265

VL - 571

JO - Astronomy and Astrophysics

JF - Astronomy and Astrophysics

ER -

Planck 2013 results. XV. CMB power spectra and likelihood

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