Planck intermediate results: XVI. Profile likelihoods for cosmological parameters

P.A.R. Ade; N. Aghanim; M. Arnaud; M. Ashdown; J. Aumont; C. Baccigalupi; A.J. Banday; R.B. Barreiro; J.G. Bartlett; E. Battaner; K. Benabed; A. Benoit-Lévy; J.-P. Bernard; M. Bersanelli; P. Bielewicz; J. Bobin; A. Bonaldi; J.R. Bond; F.R. Bouchet; C. Burigana; J.-F. Cardoso; A. Catalano; A. Chamballu; H.C. Chiang; P.R. Christensen; D.L. Clements; S. Colombi; L.P.L. Colombo; F. Couchot; F. Cuttaia; L. Danese; R.D. Davies; R.J. Davis; P. de Bernardis; A. de Rosa; G. de Zotti; J. Delabrouille; C. Dickinson; J.M. Diego; H. Dole; S. Donzelli; O. Doré; M. Douspis; X. Dupac; T.A. Enßlin; H.K. Eriksen; F. Finelli; O. Forni; M. Frailis; E. Franceschi; S. Galeotta; S. Galli; K. Ganga; M. Giard; Y. Giraud-Héraud; J. González-Nuevo; K.M. Górski; A. Gregorio; A. Gruppuso; F.K. Hansen; 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; A.H. Jaffe; T.R. 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; C.R. Lawrence; R. Leonardi; A. Liddle; M. Liguori; P.B. Lilje; M. Linden-Vørnle; M. López-Caniego; P.M. Lubin; J.F. Macías-Pérez; B. Maffei; D. Maino; N. Mandolesi; M. Maris; P.G. Martin; E. Martínez-González; S. Masi; M. Massardi; S. Matarrese; P. Mazzotta; A. Melchiorri; L. Mendes; A. Mennella; M. Migliaccio; S. Mitra; M.-A. Miville-Deschênes; A. Moneti; L. Montier; G. Morgante; D. Munshi; J.A. Murphy; P. Naselsky; F. Nati; P. Natoli; F. Noviello; D. Novikov; I. Novikov; C.A. Oxborrow; L. Pagano; F. Pajot; D. Paoletti; F. Pasian; 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; J.-L. Puget; J.P. Rachen; R. Rebolo; M. Reinecke; M. Remazeilles; C. Renault; S. Ricciardi; T. Riller; I. Ristorcelli; G. Rocha; C. Rosset; G. Roudier; B. "Rouillé d'Orfeuil"; J.A. Rubiño-Martín; B. Rusholme; M. Sandri; M. Savelainen; G. Savini; L.D. Spencer; M. Spinelli; J.-L. Starck; F. Sureau; D. Sutton; A.-S. Suur-Uski; J.-F. Sygnet; J.A. Tauber; L. Terenzi; L. Toffolatti; M. Tomasi; M. Tristram; M. Tucci; G. Umana; L. Valenziano; J. Valiviita; B. Van Tent; P. Vielva; F. Villa; L.A. Wade; B.D. Wandelt; M. White; D. Yvon; A. Zacchei; A. Zonca

doi:10.1051/0004-6361/201323003

Planck intermediate results: XVI. Profile likelihoods for cosmological parameters

P.A.R. Ade, N. Aghanim, M. Arnaud, M. Ashdown, J. Aumont, C. Baccigalupi, A.J. Banday, R.B. Barreiro, J.G. Bartlett, E. Battaner, K. Benabed, A. Benoit-Lévy, J.-P. Bernard, M. Bersanelli, P. Bielewicz, J. Bobin, A. Bonaldi, J.R. Bond, F.R. Bouchet, C. BuriganaJ.-F. Cardoso, A. Catalano, A. Chamballu, H.C. Chiang, P.R. Christensen, D.L. Clements, S. Colombi, L.P.L. Colombo, F. Couchot, F. Cuttaia, L. Danese, R.D. Davies, R.J. Davis, P. de Bernardis, A. de Rosa, G. de Zotti, J. Delabrouille, C. Dickinson, J.M. Diego, H. Dole, S. Donzelli, O. Doré, M. Douspis, X. Dupac, T.A. Enßlin, H.K. Eriksen, F. Finelli, O. Forni, M. Frailis, E. Franceschi, S. Galeotta, S. Galli, K. Ganga, M. Giard, Y. Giraud-Héraud, J. González-Nuevo, K.M. Górski, A. Gregorio, A. Gruppuso, F.K. Hansen, 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, A.H. Jaffe, T.R. 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, C.R. Lawrence, R. Leonardi, A. Liddle, M. Liguori, P.B. Lilje, M. Linden-Vørnle, M. López-Caniego, P.M. Lubin, J.F. Macías-Pérez, B. Maffei, D. Maino, N. Mandolesi, M. Maris, P.G. Martin, E. Martínez-González, S. Masi, M. Massardi, S. Matarrese, P. Mazzotta, A. Melchiorri, L. Mendes, A. Mennella, M. Migliaccio, S. Mitra, M.-A. Miville-Deschênes, A. Moneti, L. Montier, G. Morgante, D. Munshi, J.A. Murphy, P. Naselsky, F. Nati, P. Natoli, F. Noviello, D. Novikov, I. Novikov, C.A. Oxborrow, L. Pagano, F. Pajot, D. Paoletti, F. Pasian, 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, J.-L. Puget, J.P. Rachen, R. Rebolo, M. Reinecke, M. Remazeilles, C. Renault, S. Ricciardi, T. Riller, I. Ristorcelli, G. Rocha, C. Rosset, G. Roudier, B. "Rouillé d'Orfeuil", J.A. Rubiño-Martín, B. Rusholme, M. Sandri, M. Savelainen, G. Savini, L.D. Spencer, M. Spinelli, J.-L. Starck, F. Sureau, D. Sutton, A.-S. Suur-Uski, J.-F. Sygnet, J.A. Tauber, L. Terenzi, L. Toffolatti, M. Tomasi, M. Tristram, M. Tucci, G. Umana, L. Valenziano, J. Valiviita, B. Van Tent, P. Vielva, F. Villa, L.A. Wade, B.D. Wandelt, M. White, D. Yvon, A. Zacchei, A. Zonca

University of Helsinki

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

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Abstract

We explore the 2013 Planck likelihood function with a high-precision multi-dimensional minimizer (Minuit). This allows a refinement of the ΛCDM best-fit solution with respect to previously-released results, and the construction of frequentist confidence intervals using profile likelihoods. The agreement with the cosmological results from the Bayesian framework is excellent, demonstrating the robustness of the Planck results to the statistical methodology. We investigate the inclusion of neutrino masses, where more significant differences may appear due to the non-Gaussian nature of the posterior mass distribution. By applying the Feldman-Cousins prescription, we again obtain results very similar to those of the Bayesian methodology. However, the profile-likelihood analysis of the cosmic microwave background (CMB) combination (Planck+WP+highL) reveals a minimum well within the unphysical negative-mass region. We show that inclusion of the Planck CMB-lensing information regularizes this issue, and provide a robust frequentist upper limit ∑ mν ≤ 0.26 eV (95% confidence) from the CMB+lensing+BAO data combination.

Original language	English
Article number	A54
Number of pages	10
Journal	Astronomy and Astrophysics
Volume	566
DOIs	https://doi.org/10.1051/0004-6361/201323003
Publication status	Published - 2014
MoE publication type	A1 Journal article-refereed

Keywords

cosmic background radiation
cosmology: observations
cosmology: theory
cosmological parameters
methods: statistical

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10.1051/0004-6361/201323003

Planck intermediate results. XVI. Profile likehoodsFinal published version, 352 KB

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School of Electrical Engineering
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Cite this

Ade, P. A. R., Aghanim, N., Arnaud, M., Ashdown, M., Aumont, J., Baccigalupi, C., Banday, A. J., Barreiro, R. B., Bartlett, J. G., Battaner, E., Benabed, K., Benoit-Lévy, A., Bernard, J.-P., Bersanelli, M., Bielewicz, P., Bobin, J., Bonaldi, A., Bond, J. R., Bouchet, F. R., ... Zonca, A. (2014). Planck intermediate results: XVI. Profile likelihoods for cosmological parameters. Astronomy and Astrophysics, 566, Article A54. https://doi.org/10.1051/0004-6361/201323003

@article{97a6b7aa0abc44778e27518847c35f73,

title = "Planck intermediate results: XVI. Profile likelihoods for cosmological parameters",

abstract = "We explore the 2013 Planck likelihood function with a high-precision multi-dimensional minimizer (Minuit). This allows a refinement of the ΛCDM best-fit solution with respect to previously-released results, and the construction of frequentist confidence intervals using profile likelihoods. The agreement with the cosmological results from the Bayesian framework is excellent, demonstrating the robustness of the Planck results to the statistical methodology. We investigate the inclusion of neutrino masses, where more significant differences may appear due to the non-Gaussian nature of the posterior mass distribution. By applying the Feldman-Cousins prescription, we again obtain results very similar to those of the Bayesian methodology. However, the profile-likelihood analysis of the cosmic microwave background (CMB) combination (Planck+WP+highL) reveals a minimum well within the unphysical negative-mass region. We show that inclusion of the Planck CMB-lensing information regularizes this issue, and provide a robust frequentist upper limit ∑ mν ≤ 0.26 eV (95% confidence) from the CMB+lensing+BAO data combination.",

keywords = "cosmic background radiation , cosmology: observations , cosmology: theory, cosmological parameters, methods: statistical",

author = "P.A.R. Ade and N. Aghanim and M. Arnaud and M. Ashdown and J. Aumont and C. Baccigalupi and A.J. Banday and R.B. Barreiro and J.G. Bartlett and E. Battaner and K. Benabed and A. Benoit-L{\'e}vy and J.-P. Bernard and M. Bersanelli and P. Bielewicz and J. Bobin and A. Bonaldi and J.R. Bond and F.R. Bouchet and C. Burigana and J.-F. Cardoso and A. Catalano and A. Chamballu and H.C. Chiang and P.R. Christensen and D.L. Clements and S. Colombi and L.P.L. Colombo and F. Couchot and F. Cuttaia and L. Danese and R.D. Davies and R.J. Davis and {de Bernardis}, P. and {de Rosa}, A. and {de Zotti}, G. and J. Delabrouille and C. Dickinson and J.M. Diego and H. Dole and S. Donzelli and O. Dor{\'e} and M. Douspis and X. Dupac and T.A. En{\ss}lin and H.K. Eriksen and F. Finelli and O. Forni and M. Frailis and E. Franceschi and S. Galeotta and S. Galli and K. Ganga and M. Giard and Y. Giraud-H{\'e}raud and J. Gonz{\'a}lez-Nuevo and K.M. G{\'o}rski and A. Gregorio and A. Gruppuso and F.K. Hansen and D.L. Harrison and S. Henrot-Versill{\'e} and C. Hern{\'a}ndez-Monteagudo and D. Herranz and S.R. Hildebrandt and E. Hivon and M. Hobson and W.A. Holmes and A. Hornstrup and W. Hovest and K.M. Huffenberger and A.H. Jaffe and T.R. Jaffe and W.C. Jones and M. Juvela and E. Keih{\"a}nen and R. Keskitalo and T.S. Kisner and R. Kneissl and J. Knoche and L. Knox and M. Kunz and H. Kurki-Suonio and G. Lagache and A. L{\"a}hteenm{\"a}ki and J.-M. Lamarre and A. Lasenby and C.R. Lawrence and R. Leonardi and A. Liddle and M. Liguori and P.B. Lilje and M. Linden-V{\o}rnle and M. L{\'o}pez-Caniego and P.M. Lubin and J.F. Mac{\'i}as-P{\'e}rez and B. Maffei and D. Maino and N. Mandolesi and M. Maris and P.G. Martin and E. Mart{\'i}nez-Gonz{\'a}lez and S. Masi and M. Massardi and S. Matarrese and P. Mazzotta and A. Melchiorri and L. Mendes and A. Mennella and M. Migliaccio and S. Mitra and M.-A. Miville-Desch{\^e}nes and A. Moneti and L. Montier and G. Morgante and D. Munshi and J.A. Murphy and P. Naselsky and F. Nati and P. Natoli and F. Noviello and D. Novikov and I. Novikov and C.A. Oxborrow and L. Pagano and F. Pajot and D. Paoletti and F. Pasian and O. Perdereau and L. Perotto and F. Perrotta and V. Pettorino and F. Piacentini and M. Piat and E. Pierpaoli and D. Pietrobon and S. Plaszczynski and E. Pointecouteau and G. Polenta and L. Popa and G.W. Pratt and J.-L. Puget and J.P. Rachen and R. Rebolo and M. Reinecke and M. Remazeilles and C. Renault and S. Ricciardi and T. Riller and I. Ristorcelli and G. Rocha and C. Rosset and G. Roudier and {{"}Rouill{\'e} d'Orfeuil{"}}, B. and J.A. Rubi{\~n}o-Mart{\'i}n and B. Rusholme and M. Sandri and M. Savelainen and G. Savini and L.D. Spencer and M. Spinelli and J.-L. Starck and F. Sureau and D. Sutton and A.-S. Suur-Uski and J.-F. Sygnet and J.A. Tauber and L. Terenzi and L. Toffolatti and M. Tomasi and M. Tristram and M. Tucci and G. Umana and L. Valenziano and J. Valiviita and {Van Tent}, B. and P. Vielva and F. Villa and L.A. Wade and B.D. Wandelt and M. White and D. Yvon and A. Zacchei and A. Zonca",

year = "2014",

doi = "10.1051/0004-6361/201323003",

language = "English",

volume = "566",

journal = "Astronomy and Astrophysics",

issn = "0004-6361",

publisher = "EDP Sciences",

}

Ade, PAR, Aghanim, N, Arnaud, M, Ashdown, M, Aumont, J, Baccigalupi, C, Banday, AJ, Barreiro, RB, Bartlett, JG, Battaner, E, Benabed, K, Benoit-Lévy, A, Bernard, J-P, Bersanelli, M, Bielewicz, P, Bobin, J, Bonaldi, A, Bond, JR, Bouchet, FR, Burigana, C, Cardoso, J-F, Catalano, A, Chamballu, A, Chiang, HC, Christensen, PR, Clements, DL, Colombi, S, Colombo, LPL, Couchot, F, Cuttaia, F, Danese, L, Davies, RD, Davis, RJ, de Bernardis, P, de Rosa, A, de Zotti, G, Delabrouille, J, Dickinson, C, Diego, JM, Dole, H, Donzelli, S, Doré, O, Douspis, M, Dupac, X, Enßlin, TA, Eriksen, HK, Finelli, F, Forni, O, Frailis, M, Franceschi, E, Galeotta, S, Galli, S, Ganga, K, Giard, M, Giraud-Héraud, Y, González-Nuevo, J, Górski, KM, Gregorio, A, Gruppuso, A, Hansen, FK, Harrison, DL, Henrot-Versillé, S, Hernández-Monteagudo, C, Herranz, D, Hildebrandt, SR, Hivon, E, Hobson, M, Holmes, WA, Hornstrup, A, Hovest, W, Huffenberger, KM, Jaffe, AH, Jaffe, TR, Jones, WC, Juvela, M, Keihänen, E, Keskitalo, R, Kisner, TS, Kneissl, R, Knoche, J, Knox, L, Kunz, M, Kurki-Suonio, H, Lagache, G, Lähteenmäki, A, Lamarre, J-M, Lasenby, A, Lawrence, CR, Leonardi, R, Liddle, A, Liguori, M, Lilje, PB, Linden-Vørnle, M, López-Caniego, M, Lubin, PM, Macías-Pérez, JF, Maffei, B, Maino, D, Mandolesi, N, Maris, M, Martin, PG, Martínez-González, E, Masi, S, Massardi, M, Matarrese, S, Mazzotta, P, Melchiorri, A, Mendes, L, Mennella, A, Migliaccio, M, Mitra, S, Miville-Deschênes, M-A, Moneti, A, Montier, L, Morgante, G, Munshi, D, Murphy, JA, Naselsky, P, Nati, F, Natoli, P, Noviello, F, Novikov, D, Novikov, I, Oxborrow, CA, Pagano, L, Pajot, F, Paoletti, D, Pasian, F, Perdereau, O, Perotto, L, Perrotta, F, Pettorino, V, Piacentini, F, Piat, M, Pierpaoli, E, Pietrobon, D, Plaszczynski, S, Pointecouteau, E, Polenta, G, Popa, L, Pratt, GW, Puget, J-L, Rachen, JP, Rebolo, R, Reinecke, M, Remazeilles, M, Renault, C, Ricciardi, S, Riller, T, Ristorcelli, I, Rocha, G, Rosset, C, Roudier, G, "Rouillé d'Orfeuil", B, Rubiño-Martín, JA, Rusholme, B, Sandri, M, Savelainen, M, Savini, G, Spencer, LD, Spinelli, M, Starck, J-L, Sureau, F, Sutton, D, Suur-Uski, A-S, Sygnet, J-F, Tauber, JA, Terenzi, L, Toffolatti, L, Tomasi, M, Tristram, M, Tucci, M, Umana, G, Valenziano, L, Valiviita, J, Van Tent, B, Vielva, P, Villa, F, Wade, LA, Wandelt, BD, White, M, Yvon, D, Zacchei, A & Zonca, A 2014, 'Planck intermediate results: XVI. Profile likelihoods for cosmological parameters', Astronomy and Astrophysics, vol. 566, A54. https://doi.org/10.1051/0004-6361/201323003

TY - JOUR

T1 - Planck intermediate results

T2 - XVI. Profile likelihoods for cosmological parameters

AU - Ade, P.A.R.

AU - Aghanim, N.

AU - Arnaud, M.

AU - Ashdown, M.

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 - Benoit-Lévy, A.

AU - Bernard, J.-P.

AU - Bersanelli, M.

AU - Bielewicz, P.

AU - Bobin, J.

AU - Bonaldi, A.

AU - Bond, J.R.

AU - Bouchet, F.R.

AU - Burigana, C.

AU - Cardoso, J.-F.

AU - Catalano, A.

AU - Chamballu, A.

AU - Chiang, H.C.

AU - Christensen, P.R.

AU - Clements, D.L.

AU - Colombi, S.

AU - Colombo, L.P.L.

AU - Couchot, F.

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 - Dickinson, C.

AU - Diego, J.M.

AU - Dole, H.

AU - Donzelli, S.

AU - Doré, O.

AU - Douspis, M.

AU - Dupac, X.

AU - Enßlin, T.A.

AU - Eriksen, H.K.

AU - Finelli, F.

AU - Forni, O.

AU - Frailis, M.

AU - Franceschi, E.

AU - Galeotta, S.

AU - Galli, S.

AU - Ganga, K.

AU - Giard, M.

AU - Giraud-Héraud, Y.

AU - González-Nuevo, J.

AU - Górski, K.M.

AU - Gregorio, A.

AU - Gruppuso, A.

AU - Hansen, F.K.

AU - Harrison, D.L.

AU - Henrot-Versillé, S.

AU - Hernández-Monteagudo, C.

AU - Herranz, D.

AU - Hildebrandt, S.R.

AU - Hivon, E.

AU - Hobson, M.

AU - Holmes, W.A.

AU - Hornstrup, A.

AU - Hovest, W.

AU - Huffenberger, K.M.

AU - Jaffe, A.H.

AU - Jaffe, T.R.

AU - Jones, W.C.

AU - Juvela, M.

AU - Keihänen, E.

AU - Keskitalo, R.

AU - Kisner, T.S.

AU - Kneissl, R.

AU - Knoche, J.

AU - Knox, L.

AU - Kunz, M.

AU - Kurki-Suonio, H.

AU - Lagache, G.

AU - Lähteenmäki, A.

AU - Lamarre, J.-M.

AU - Lasenby, A.

AU - Lawrence, C.R.

AU - Leonardi, R.

AU - Liddle, A.

AU - Liguori, M.

AU - Lilje, P.B.

AU - Linden-Vørnle, M.

AU - López-Caniego, M.

AU - Lubin, P.M.

AU - Macías-Pérez, J.F.

AU - Maffei, B.

AU - Maino, D.

AU - Mandolesi, N.

AU - Maris, M.

AU - Martin, P.G.

AU - Martínez-González, E.

AU - Masi, S.

AU - Massardi, M.

AU - Matarrese, S.

AU - Mazzotta, P.

AU - Melchiorri, A.

AU - Mendes, L.

AU - Mennella, A.

AU - Migliaccio, M.

AU - Mitra, S.

AU - Miville-Deschênes, M.-A.

AU - Moneti, A.

AU - Montier, L.

AU - Morgante, G.

AU - Munshi, D.

AU - Murphy, J.A.

AU - Naselsky, P.

AU - Nati, F.

AU - Natoli, P.

AU - Noviello, F.

AU - Novikov, D.

AU - Novikov, I.

AU - Oxborrow, C.A.

AU - Pagano, L.

AU - Pajot, F.

AU - Paoletti, D.

AU - Pasian, F.

AU - Perdereau, O.

AU - Perotto, L.

AU - Perrotta, F.

AU - Pettorino, V.

AU - Piacentini, F.

AU - Piat, M.

AU - Pierpaoli, E.

AU - Pietrobon, D.

AU - Plaszczynski, S.

AU - Pointecouteau, E.

AU - Polenta, G.

AU - Popa, L.

AU - Pratt, G.W.

AU - Puget, J.-L.

AU - Rachen, J.P.

AU - Rebolo, R.

AU - Reinecke, M.

AU - Remazeilles, M.

AU - Renault, C.

AU - Ricciardi, S.

AU - Riller, T.

AU - Ristorcelli, I.

AU - Rocha, G.

AU - Rosset, C.

AU - Roudier, G.

AU - "Rouillé d'Orfeuil", B.

AU - Rubiño-Martín, J.A.

AU - Rusholme, B.

AU - Sandri, M.

AU - Savelainen, M.

AU - Savini, G.

AU - Spencer, L.D.

AU - Spinelli, M.

AU - Starck, J.-L.

AU - Sureau, F.

AU - Sutton, D.

AU - Suur-Uski, A.-S.

AU - Sygnet, J.-F.

AU - Tauber, J.A.

AU - Terenzi, L.

AU - Toffolatti, L.

AU - Tomasi, M.

AU - Tristram, M.

AU - Tucci, M.

AU - Umana, G.

AU - Valenziano, L.

AU - Valiviita, J.

AU - Van Tent, B.

AU - Vielva, P.

AU - Villa, F.

AU - Wade, L.A.

AU - Wandelt, B.D.

AU - White, M.

AU - Yvon, D.

AU - Zacchei, A.

AU - Zonca, A.

PY - 2014

Y1 - 2014

N2 - We explore the 2013 Planck likelihood function with a high-precision multi-dimensional minimizer (Minuit). This allows a refinement of the ΛCDM best-fit solution with respect to previously-released results, and the construction of frequentist confidence intervals using profile likelihoods. The agreement with the cosmological results from the Bayesian framework is excellent, demonstrating the robustness of the Planck results to the statistical methodology. We investigate the inclusion of neutrino masses, where more significant differences may appear due to the non-Gaussian nature of the posterior mass distribution. By applying the Feldman-Cousins prescription, we again obtain results very similar to those of the Bayesian methodology. However, the profile-likelihood analysis of the cosmic microwave background (CMB) combination (Planck+WP+highL) reveals a minimum well within the unphysical negative-mass region. We show that inclusion of the Planck CMB-lensing information regularizes this issue, and provide a robust frequentist upper limit ∑ mν ≤ 0.26 eV (95% confidence) from the CMB+lensing+BAO data combination.

AB - We explore the 2013 Planck likelihood function with a high-precision multi-dimensional minimizer (Minuit). This allows a refinement of the ΛCDM best-fit solution with respect to previously-released results, and the construction of frequentist confidence intervals using profile likelihoods. The agreement with the cosmological results from the Bayesian framework is excellent, demonstrating the robustness of the Planck results to the statistical methodology. We investigate the inclusion of neutrino masses, where more significant differences may appear due to the non-Gaussian nature of the posterior mass distribution. By applying the Feldman-Cousins prescription, we again obtain results very similar to those of the Bayesian methodology. However, the profile-likelihood analysis of the cosmic microwave background (CMB) combination (Planck+WP+highL) reveals a minimum well within the unphysical negative-mass region. We show that inclusion of the Planck CMB-lensing information regularizes this issue, and provide a robust frequentist upper limit ∑ mν ≤ 0.26 eV (95% confidence) from the CMB+lensing+BAO data combination.

KW - cosmic background radiation

KW - cosmology: observations

KW - cosmology: theory

KW - cosmological parameters

KW - methods: statistical

U2 - 10.1051/0004-6361/201323003

DO - 10.1051/0004-6361/201323003

M3 - Article

SN - 0004-6361

VL - 566

JO - Astronomy and Astrophysics

JF - Astronomy and Astrophysics

M1 - A54

ER -

Planck intermediate results: XVI. Profile likelihoods for cosmological parameters

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Metsähovi Radio Observatory

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