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1. Planck 2015 results XX. Constraints on inflation

Author

Ade, P. A. R., Aghanim, N., Arnaud, M., Arroja, F., Ashdown, M., Aumont, J., Baccigalupi, C., Ballardini, M., Banday, A. J., Barreiro, R. B., Bartolo, N., Battaner, E., Benabed, K., Benoit, A., Benoit-Levy, A., Bernard, J. -P., Bersanelli, M., Bielewicz, P., Bock, J. J., Bonaldi, A., Bonavera, L., Bondi, J. R., Borrillu, J., Bouchet, F. R., Boulanger, F., Bucher, M., Burigana, C., Butler, R. C., Calabrese, E., Cardoso, J. -F., Catalano, A., Challinor, A., Chamballu, A., Chary, R. -R., Chiang, H. C., Christensen, P. R., Churchl, S., Clements, D. L., Colombi, S., Colombo, L. P. L., Combet, C., Contreras, D., Couchot, F., Coulais, A., Crill, B. P., Curto, A., Cuttaia, F., Danese, L., Davies, R. D., Davis, R. J., de Bernardis, P., de Rosa, A., de Zotti, G., Delabrouillei, J., Desert, F. -X., Diego, J. M., Dole, H., Donzelli, S., Dore, O., Douspis, M., Ducout, A., Dupac, X., Efstathiou, G., Elsner, F., Ensslin, T. A., Eriksen, H. K., Fergusson, J., Finelli, F., Forni, O., Frailis, M., Fraisse, A. A., Franceschi, E., Frejsel, A., Frolov, A., Galeotta, S., Galli, S., Ganga, K., Gauthier, C., Giard, M., Giraud-Heraud, Y., Gjerlow, E., Gonzalez-Nuevo, J., Gorski, K. M., Gratton, S., Gregorio, A., Gruppuso, A., Gudmundsson, Jón E., Hamann, J., Handley, W., Hansen, F. K., Hanson, D., Harrison, D. L., Henrot-Versille, S., Hernandez-Monteagudo, C., Herranz, D., Hildebrandt, S. R., Hivon, E., Hobson, M., Holmes, W. A., Hornstrup, A., Hovest, W., Huang, Z., Huffenberger, K. M., Hurier, G., Jaffe, A. H., Jaffe, T. R., Jones, W. C., Juvela, M., Keihanen, E., Keskitalo, R., Kim, J., Kisner, T. S., Kneissl, R., Knoche, J., Kunz, M., Kurki-Suonio, H., Lagache, G., Lahteenmaki, A., Lamarre, J. -M., Lasenby, A., Lattanzi, M., Lawrence, C. R., Leonardi, R., Lesgourgues, J., Levrier, F., Lewis, A., Liguori, M., Lilje, P. B., Linden-Vornle, M., Lopez-Caniego, M., Lubin, P. M., Ma, Y. -Z., Macias-Perez, J. F., Maggio, G., Maino, D., Mandolesi, N., Mangilli, A., Maris, M., Martini, P. G., Martinez-Gonzalez, E., Masi, S., Matarrese, S., McGehee, P., Meinhold, P. R., Melchiorri, A., Mendes, L., Mennella, A., Migliaccio, M., Mitra, S., Miville-Deschenes, M. -A., Molinari, D., Moneti, A., Montier, L., Morgante, G., Mortlock, D., Moss, A., Munchmeyer, M., Munshi, D., Murphy, J. A., Naselsky, P., Nati, F., Natoli, P., Netterfield, C. B., Norgaard-Nielsen, H. U., Noviello, F., Novikov, D., Novikov, I., Oxborrow, C. A., Paci, F., Pagano, L., Pajot, F., Paladini, R., Pandolfi, S., Paoletti, D., Pasian, F., Patanchon, G., Pearson, T. J., Peiris, H. V., 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, G. W., Prezeau, G., Prunet, S., Puget, J. -L., Rachen, J. P., Reach, W. T., Rebolo, R., Reinecke, M., Remazeilles, M., Renault, C., Renzi, A., Ristorcelli, I., Rocha, G., Rosset, C., Rossetti, M., Roudier, G., Rowan-Robinson, M., Rubino-Martin, J. A., Rusholme, B., Sandri, M., Santos, D., Savelainen, M., Savini, G., Scott, D., Seiffert, M. D., Shellard, E. P. S., Shiraishi, M., Spencer, L. D., Stolyarov, V., Stompori, R., Sudiwala, R., Sunyaev, R., Sutton, D., Suur-Uski, A. -S., Sygnet, J. -F., Tauber, J. A., Terenzi, L., Toffolatti, L., Tomasi, M., Tristram, M., Trombetti, T., Tucci, M., Tuovinen, J., Valenziano, L., Valiviita, J., Van Tent, B., Vielva, P., Villa, F., Wade, L. A., Wandelt, B. D., Wehus, I. K., White, M., Yvon, D., Zacchei, A., Zibin, J. P., Zonca, A., Ade, P. A. R., Aghanim, N., Arnaud, M., Arroja, F., Ashdown, M., Aumont, J., Baccigalupi, C., Ballardini, M., Banday, A. J., Barreiro, R. B., Bartolo, N., Battaner, E., Benabed, K., Benoit, A., Benoit-Levy, A., Bernard, J. -P., Bersanelli, M., Bielewicz, P., Bock, J. J., Bonaldi, A., Bonavera, L., Bondi, J. R., Borrillu, J., Bouchet, F. R., Boulanger, F., Bucher, M., Burigana, C., Butler, R. C., Calabrese, E., Cardoso, J. -F., Catalano, A., Challinor, A., Chamballu, A., Chary, R. -R., Chiang, H. C., Christensen, P. R., Churchl, S., Clements, D. L., Colombi, S., Colombo, L. P. L., Combet, C., Contreras, D., Couchot, F., Coulais, A., Crill, B. P., Curto, A., Cuttaia, F., Danese, L., Davies, R. D., Davis, R. J., de Bernardis, P., de Rosa, A., de Zotti, G., Delabrouillei, J., Desert, F. -X., Diego, J. M., Dole, H., Donzelli, S., Dore, O., Douspis, M., Ducout, A., Dupac, X., Efstathiou, G., Elsner, F., Ensslin, T. A., Eriksen, H. K., Fergusson, J., Finelli, F., Forni, O., Frailis, M., Fraisse, A. A., Franceschi, E., Frejsel, A., Frolov, A., Galeotta, S., Galli, S., Ganga, K., Gauthier, C., Giard, M., Giraud-Heraud, Y., Gjerlow, E., Gonzalez-Nuevo, J., Gorski, K. M., Gratton, S., Gregorio, A., Gruppuso, A., Gudmundsson, Jón E., Hamann, J., Handley, W., Hansen, F. K., Hanson, D., Harrison, D. L., Henrot-Versille, S., Hernandez-Monteagudo, C., Herranz, D., Hildebrandt, S. R., Hivon, E., Hobson, M., Holmes, W. A., Hornstrup, A., Hovest, W., Huang, Z., Huffenberger, K. M., Hurier, G., Jaffe, A. H., Jaffe, T. R., Jones, W. C., Juvela, M., Keihanen, E., Keskitalo, R., Kim, J., Kisner, T. S., Kneissl, R., Knoche, J., Kunz, M., Kurki-Suonio, H., Lagache, G., Lahteenmaki, A., Lamarre, J. -M., Lasenby, A., Lattanzi, M., Lawrence, C. R., Leonardi, R., Lesgourgues, J., Levrier, F., Lewis, A., Liguori, M., Lilje, P. B., Linden-Vornle, M., Lopez-Caniego, M., Lubin, P. M., Ma, Y. -Z., Macias-Perez, J. F., Maggio, G., Maino, D., Mandolesi, N., Mangilli, A., Maris, M., Martini, P. G., Martinez-Gonzalez, E., Masi, S., Matarrese, S., McGehee, P., Meinhold, P. R., Melchiorri, A., Mendes, L., Mennella, A., Migliaccio, M., Mitra, S., Miville-Deschenes, M. -A., Molinari, D., Moneti, A., Montier, L., Morgante, G., Mortlock, D., Moss, A., Munchmeyer, M., Munshi, D., Murphy, J. A., Naselsky, P., Nati, F., Natoli, P., Netterfield, C. B., Norgaard-Nielsen, H. U., Noviello, F., Novikov, D., Novikov, I., Oxborrow, C. A., Paci, F., Pagano, L., Pajot, F., Paladini, R., Pandolfi, S., Paoletti, D., Pasian, F., Patanchon, G., Pearson, T. J., Peiris, H. V., 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, G. W., Prezeau, G., Prunet, S., Puget, J. -L., Rachen, J. P., Reach, W. T., Rebolo, R., Reinecke, M., Remazeilles, M., Renault, C., Renzi, A., Ristorcelli, I., Rocha, G., Rosset, C., Rossetti, M., Roudier, G., Rowan-Robinson, M., Rubino-Martin, J. A., Rusholme, B., Sandri, M., Santos, D., Savelainen, M., Savini, G., Scott, D., Seiffert, M. D., Shellard, E. P. S., Shiraishi, M., Spencer, L. D., Stolyarov, V., Stompori, R., Sudiwala, R., Sunyaev, R., Sutton, D., Suur-Uski, A. -S., Sygnet, J. -F., Tauber, J. A., Terenzi, L., Toffolatti, L., Tomasi, M., Tristram, M., Trombetti, T., Tucci, M., Tuovinen, J., Valenziano, L., Valiviita, J., Van Tent, B., Vielva, P., Villa, F., Wade, L. A., Wandelt, B. D., Wehus, I. K., White, M., Yvon, D., Zacchei, A., Zibin, J. P., and Zonca, A.

Abstract

We present the implications for cosmic inflation of the Planck measurements of the cosmic microwave background (CMB) anisotropies in both temperature and polarization based on the full Planck survey, which includes more than twice the integration time of the nominal survey used for the 2013 release papers. The Planck full mission temperature data and a first release of polarization data on large angular scales measure the spectral index of curvature perturbations to be n(s) = 0.968 +/- 0.006 and tightly constrain its scale dependence to dn(s)/dln k = -0.003 +/- 0.007 when combined with the Planck lensing likelihood. When the Planck high-l polarization data are included, the results are consistent and uncertainties are further reduced. The upper bound on the tensor-to-scalar ratio is r(0).(002) < 0.11 (95% CL). This upper limit is consistent with the B-mode polarization constraint r < 0.12 (95% CL) obtained from a joint analysis of the BICEP2/Keck Array and Planck data. These results imply that V(phi) proportional to phi(2) and natural inflation are now disfavoured compared to models predicting a smaller tensor-to-scalar ratio, such as R-2 inflation. We search for several physically motivated deviations from a simple power-law spectrum of curvature perturbations, including those motivated by a reconstruction of the inflaton potential not relying on the slow-roll approximation. We find that such models are not preferred, either according to a Bayesian model comparison or according to a frequentist simulation-based analysis. Three independent methods reconstructing the primordial power spectrum consistently recover a featureless and smooth P-R (k) over the range of scales 0.008 Mpc(-1) less than or similar to k less than or similar to 0.1 Mpc(-1). At large scales, each method finds deviations from a power law, connected to a deficit at multipoles l approximate to 20-40 in the temperature power spectrum, but at an uncompelling statistical significance owing to the

Published
2016
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2. Planck 2015 results. XX. Constraints on inflation

Author

Ade, Par, Aghanim, N, Arnaud, M, Arroja, F, Ashdown, M, Aumont, J, Baccigalupi, C, Ballardini, M, B, A. J., A, Barreiro, Rb, Bartolo, N, Battaner, E, Benabed, K, Benoit, A, Benoit-Levy, A, Bernard, J, Bersanelli, M, Bielewicz, P, Bock, Jj, Bonaldi, A, Bonavera, L, Bondi, Jr, Borrillu, J, Bouchet, Fr, Boulanger, F, Bucher, M, Burigana, C, Butler, Rc, Calabrese, E, Cardoso, J, Catalano, A, Challinor, A, Chamballu, A, Chary, R, Chiang, Hc, Christensen, Pr, Churchl, S, Clements, Dl, Colombi, S, Colombo, Lpl, Combet, C, Contreras, D, 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, Delabrouillei, J, Desert, F, Diego, Jm, Dole, H, Donzelli, S, Dore, O, Douspis, M, Ducout, A, Dupac, X, Efstathiou, G, Elsner, F, Ensslin, Ta, Eriksen, Hk, Fergusson, J, Finelli, F, Forni, O, Frailis, M, Fraisse, Aa, Franceschi, E, Frejsel, A, Frolov, A, Galeotta, S, Galli, S, Ganga, K, Gauthier, C, Giard, M, Giraud-Heraud, Y, Gjerlow, E, Gonzalez-Nuevo, J, Gorski, Km, Gratton, S, Gregorio, A, Gruppuso, A, Gudmundsson, Je, Hamann, J, H, Ley, W, Hansen, Fk, Hanson, D, Harrison, Dl, Henrot-Versille, S, Hern, ez-Monteagudo, C, Herranz, D, Hildebr, S. R., T, Hivon, E, Hobson, M, Holmes, Wa, Hornstrup, A, Hovest, W, Huang, Z, Huffenberger, Km, Hurier, G, Jaffe, Ah, Jaffe, Tr, Jones, Wc, Juvela, M, Keihanen, E, Keskitalo, R, Kim, J, Kisner, Ts, Kneissl, R, Knoche, J, Kunz, M, Kurki-Suonio, H, Lagache, G, Lahteenmaki, A, Lamarre, J, Lasenby, A, Lattanzi, M, Lawrence, Cr, Leonardi, R, Lesgourgues, J, Levrier, F, Lewis, A, Liguori, M, Lilje, Pb, Linden-Vornle, M, Lopez-Caniego, M, Lubin, Pm, Y. -Z., M, Macias-Perez, Jf, Maggio, G, Maino, D, M, Olesi, N, Mangilli, A, Maris, M, Martini, Pg, Martinez-Gonzalez, E, Masi, S, Matarrese, S, Mcgehee, P, Meinhold, Pr, Melchiorri, A, Mendes, L, Mennella, A, Migliaccio, M, Mitra, S, Miville-Deschenes, M, Molinari, D, Moneti, A, Montier, L, Morgante, G, Mortlock, D, Moss, A, Munchmeyer, M, Munshi, D, Murphy, Ja, Naselsky, P, Nati, F, Natoli, P, Netterfield, Cb, Norgaard-Nielsen, Hu, Noviello, F, Novikov, D, Novikov, I, Oxborrow, Ca, Paci, F, Pagano, L, Pajot, F, Paladini, R, P, Olfi, S, Paoletti, D, Pasian, F, Patanchon, G, Pearson, Tj, Peiris, Hv, 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, Prezeau, G, Prunet, S, Puget, J, Rachen, Jp, Reach, Wt, Rebolo, R, Reinecke, M, Remazeilles, M, Renault, C, Renzi, A, Ristorcelli, I, Rocha, G, Rosset, C, Rossetti, M, Roudier, G, Rowan-Robinson, M, Rubino-Martin, Ja, Rusholme, B, S, Ri, M, Santos, D, Savelainen, M, Savini, G, Scott, D, Seiffert, Md, Shellard, Eps, Shiraishi, M, Spencer, Ld, Stolyarov, V, Stompori, R, Sudiwala, R, Sunyaev, R, Sutton, D, Suur-Uski, A, Sygnet, J, Tauber, Ja, Terenzi, L, Toffolatti, L, Tomasi, M, Tristram, M, Trombetti, T, Tucci, M, Tuovinen, J, Valenziano, L, Valiviita, J, Van Tent, B, Vielva, P, Villa, F, Wade, La, W, Elt, Bd, Wehus, Ik, White, M, Yvon, D, Zacchei, A, Zibin, Jp, Zonca, A, Planck, C, Ade, P.A.R., Aghanim, N., Arnaud, M., Arroja, F., Ashdown, M., Aumont, J., Baccigalupi, C., Ballardini, M., Banday, A.J., Barreiro, R.B., Bartolo, N., Battaner, E., Benabed, K., Benoît, A., Benoit-Lévy, A., Bernard, J.-P., Bersanelli, M., Bielewicz, P., Bock, J.J., Bonaldi, A., Bonavera, L., Bond, J.R., Borrill, J., Bouchet, F.R., Boulanger, F., Bucher, M., Burigana, C., Butler, R.C., Calabrese, E., Cardoso, J.-F., Catalano, A., Challinor, A., Chamballu, A., Chary, R.-R., Chiang, H.C., Christensen, P.R., Church, S., Clements, D.L., Colombi, S., Colombo, L.P.L., Combet, C., Contreras, D., Couchot, F., Coulais, A., Crill, B.P., Curto, A., Cuttaia, F., Danese, L., Davies, R.D., Davis, R.J., De Bernardis, P., De Rosa, A., De Zotti, G., Delabrouille, J., Désert, F.-X., Diego, J.M., Dole, H., Donzelli, S., Doré, O., Douspis, M., Ducout, A., Dupac, X., Efstathiou, G., Elsner, F., Enßlin, T.A., Eriksen, H.K., Fergusson, J., Finelli, F., Forni, O., Frailis, M., Fraisse, A.A., Franceschi, E., Frejsel, A., Frolov, A., Galeotta, S., Galli, S., Ganga, K., Gauthier, C., Giard, M., Giraud-Héraud, Y., Gjerløw, E., González-Nuevo, J., Górski, K.M., Gratton, S., Gregorio, A., Gruppuso, A., Gudmundsson, J.E., Hamann, J., Handley, W., Hansen, F.K., Hanson, D., Harrison, D.L., Henrot-Versillé, S., Hernández-Monteagudo, C., Herranz, D., Hildebrandt, S.R., Hivon, E., Hobson, M., Holmes, W.A., Hornstrup, A., Hovest, W., Huang, Z., Huffenberger, K.M., Hurier, G., Jaffe, A.H., Jaffe, T.R., Jones, W.C., Juvela, M., Keihänen, E., Keskitalo, R., Kim, J., Kisner, T.S., Kneissl, R., Knoche, J., Kunz, M., Kurki-Suonio, H., Lagache, G., Lähteenmäki, A., Lamarre, J.-M., Lasenby, A., Lattanzi, M., Lawrence, C.R., Leonardi, R., Lesgourgues, J., Levrier, F., Lewis, A., Liguori, M., Lilje, P.B., Linden-Vørnle, M., López-Caniego, M., Lubin, P.M., Ma, Y.-Z., Maciás-Pérez, J.F., Maggio, G., Maino, D., Mandolesi, N., Mangilli, A., Maris, M., Martin, P.G., Martínez-González, E., Masi, S., Matarrese, S., Mcgehee, P., Meinhold, P.R., Melchiorri, A., Mendes, L., Mennella, A., Migliaccio, M., Mitra, S., Miville-Deschênes, M.-A., Molinari, D., Moneti, A., Montier, L., Morgante, G., Mortlock, D., Moss, A., Münchmeyer, M., Munshi, D., Murphy, J.A., Naselsky, P., Nati, F., Natoli, P., Netterfield, C.B., Nørgaard-Nielsen, H.U., Noviello, F., Novikov, D., Novikov, I., Oxborrow, C.A., Paci, F., Pagano, L., Pajot, F., Paladini, R., Pandolfi, S., Paoletti, D., Pasian, F., Patanchon, G., Pearson, T.J., Peiris, H.V., 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, G.W., Prézeau, G., Prunet, S., Puget, J.-L., Rachen, J.P., Reach, W.T., Rebolo, R., Reinecke, M., Remazeilles, M., Renault, C., Renzi, A., Ristorcelli, I., Rocha, G., Rosset, C., Rossetti, M., Roudier, G., Rowan-Robinson, M., Rubinõ-Martín, J.A., Rusholme, B., Sandri, M., Santos, D., Savelainen, M., Savini, G., Scott, D., Seiffert, M.D., Shellard, E.P.S., Shiraishi, M., Spencer, L.D., Stolyarov, V., Stompor, R., Sudiwala, R., Sunyaev, R., Sutton, D., Suur-Uski, A.-S., Sygnet, J.-F., Tauber, J.A., Terenzi, L., Toffolatti, L., Tomasi, M., Tristram, M., Trombetti, T., Tucci, M., Tuovinen, J., Valenziano, L., Valiviita, J., Van Tent, B., Vielva, P., Villa, F., Wade, L.A., Wandelt, B.D., Wehus, I.K., White, M., Yvon, D., Zacchei, A., Zibin, J.P., Zonca, A., Ade, P, Aghanim, N, Arnaud, M, Arroja, F, Ashdown, M, Aumont, J, Baccigalupi, C, Ballardini, M, Banday, A, Barreiro, R, Bartolo, N, Battaner, E, Benabed, K, Benoît, A, Benoit Lévy, A, Bernard, J, Bersanelli, M, Bielewicz, P, Bock, J, Bonaldi, A, Bonavera, L, Bond, J, Borrill, J, Bouchet, F, Boulanger, F, Bucher, M, Burigana, C, Butler, R, Calabrese, E, Cardoso, J, Catalano, A, Challinor, A, Chamballu, A, Chary, R, Chiang, H, Christensen, P, Church, S, Clements, D, Colombi, S, Colombo, L, Combet, C, Contreras, D, Couchot, F, Coulais, A, Crill, B, Curto, A, Cuttaia, F, Danese, L, Davies, R, Davis, R, DE BERNARDIS, P, De Rosa, A, De Zotti, G, Delabrouille, J, Désert, F, Diego, J, Dole, H, Donzelli, S, Doré, O, Douspis, M, Ducout, A, Dupac, X, Efstathiou, G, Elsner, F, Enßlin, T, Eriksen, H, Fergusson, J, Finelli, F, Forni, O, Frailis, M, Fraisse, A, Franceschi, E, Frejsel, A, Frolov, A, Galeotta, S, Galli, S, Ganga, K, Gauthier, C, Giard, M, Giraud Héraud, Y, Gjerløw, E, González Nuevo, J, Górski, K, Gratton, S, Gregorio, A, Gruppuso, A, Gudmundsson, J, Hamann, J, Handley, W, Hansen, F, Hanson, D, Harrison, D, Henrot Versillé, S, Hernández Monteagudo, C, Herranz, D, Hildebrandt, S, Hivon, E, Hobson, M, Holmes, W, Hornstrup, A, Hovest, W, Huang, Z, Huffenberger, K, Hurier, G, Jaffe, A, Jaffe, T, Jones, W, Juvela, M, Keihänen, E, Keskitalo, R, Kim, J, Kisner, T, Kneissl, R, Knoche, J, Kunz, M, Kurki Suonio, H, Lagache, G, Lähteenmäki, A, Lamarre, J, Lasenby, A, Lattanzi, M, Lawrence, C, Leonardi, R, Lesgourgues, J, Levrier, F, Lewis, A, Liguori, M, Lilje, P, Linden Vørnle, M, López Caniego, M, Lubin, P, Ma, Y, Maciás Pérez, J, Maggio, G, Maino, D, Mandolesi, N, Mangilli, A, Maris, M, Martin, P, Martínez González, E, Masi, S, Matarrese, S, Mcgehee, P, Meinhold, P, Melchiorri, A, Mendes, L, Mennella, A, Migliaccio, M, Mitra, S, Miville Deschênes, M, Molinari, D, Moneti, A, Montier, L, Morgante, G, Mortlock, D, Moss, A, Münchmeyer, M, Munshi, D, Murphy, J, Naselsky, P, Nati, F, Natoli, P, Netterfield, C, Nørgaard Nielsen, H, Noviello, F, Novikov, D, Novikov, I, Oxborrow, C, Paci, F, Pagano, L, Pajot, F, Paladini, R, Pandolfi, S, Paoletti, D, Pasian, F, Patanchon, G, Pearson, T, Peiris, H, 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, G, Prézeau, G, Prunet, S, Puget, J, Rachen, J, Reach, W, Rebolo, R, Reinecke, M, Remazeilles, M, Renault, C, Renzi, A, Ristorcelli, I, Rocha, G, Rosset, C, Rossetti, M, Roudier, G, Rowan Robinson, M, Rubinõ Martín, J, Rusholme, B, Sandri, M, Santos, D, Savelainen, M, Savini, G, Scott, D, Seiffert, M, Shellard, E, Shiraishi, M, Spencer, L, Stolyarov, V, Stompor, R, Sudiwala, R, Sunyaev, R, Sutton, D, Suur Uski, A, Sygnet, J, Tauber, J, Terenzi, L, Toffolatti, L, Tomasi, M, Tristram, M, Trombetti, T, Tucci, M, Tuovinen, J, Valenziano, L, Valiviita, J, Van Tent, B, Vielva, P, Villa, F, Wade, L, Wandelt, B, Wehus, I, White, M, Yvon, D, Zacchei, A, Zibin, J, Zonca, A, Hélium : du fondamental aux applications (HELFA), Institut Néel (NEEL), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Laboratoire de l'Accélérateur Linéaire (LAL), Centre National de la Recherche Scientifique (CNRS)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Université Paris-Sud - Paris 11 (UP11), Institut d'astrophysique spatiale (IAS), Université Paris-Sud - Paris 11 (UP11)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Physique Subatomique et de Cosmologie (LPSC), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), PLANCK, Hélium : du fondamental aux applications (NEEL - HELFA), AstroParticule et Cosmologie (APC (UMR_7164)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Université Paris-Sud - Paris 11 (UP11)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Physique Théorique d'Orsay [Orsay] (LPT), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), Ade, P. A. R., Banday, A. J., Barreiro, R. B., Benoit Lévy, A., Bernard, J. P., Bock, J. J., Bond, J. R., Bouchet, F. R., Butler, R. C., Cardoso, J. F., Chary, R. R., Chiang, H. C., Christensen, P. R., Clements, D. L., Colombo, L. P. L., Crill, B. P., Davies, R. D., Davis, R. J., Désert, F. X., Diego, J. M., Donzelli, Simona, Enßlin, T. A., Eriksen, H. K., Fraisse, A. A., Giraud Héraud, Y., González Nuevo, J., Górski, K. M., Gregorio, Anna, Gudmundsson, J. E., Hansen, F. K., Harrison, D. L., Henrot Versillé, S., Hernández Monteagudo, C., Hildebrandt, S. R., Holmes, W. A., Huffenberger, K. M., Jaffe, A. H., Jaffe, T. R., Jones, W. C., Kisner, T. S., Kurki Suonio, H., Lamarre, J. M., Lawrence, C. R., Lilje, P. B., Linden Vørnle, M., López Caniego, M., Lubin, P. M., Ma, Y. Z., Maciás Pérez, J. F., Martin, P. G., Martínez González, E., Meinhold, P. R., Miville Deschênes, M. A., Murphy, J. A., Netterfield, C. B., Nørgaard Nielsen, H. U., Oxborrow, C. A., Pearson, T. J., Peiris, H. V., Pratt, G. W., Puget, J. L., Rachen, J. P., Reach, W. T., Rowan Robinson, M., Rubinõ Martín, J. A., Seiffert, M. D., Shellard, E. P. S., Spencer, L. D., Suur Uski, A. S., Sygnet, J. F., Tauber, J. A., Wade, L. A., Wandelt, B. D., Wehus, I. K., Zibin, J. P., and Science and Technology Facilities Council (STFC)

Subjects
Inflation, [SDU.ASTR.CO]Sciences of the Universe [physics]/Astrophysics [astro-ph]/Cosmology and Extra-Galactic Astrophysics [astro-ph.CO], Astronomy, Astrophysics, Cosmic background radiation, 01 natural sciences, Early Universe, 010303 astronomy & astrophysics, GeneralLiterature_REFERENCE(e.g.,dictionaries,encyclopedias,glossaries), media_common, QB, Physics, Planck temperature, Physical Sciences, astro-ph.CO, symbols, Astrophysics - Cosmology and Nongalactic Astrophysics, Cosmology and Nongalactic Astrophysics (astro-ph.CO), media_common.quotation_subject, NATURAL INFLATION, FOS: Physical sciences, Astrophysics::Cosmology and Extragalactic Astrophysics, Astronomy & Astrophysics, NO, symbols.namesake, Theoretical physics, Settore FIS/05 - Astronomia e Astrofisica, theory [Cosmology], LARGE-SCALE STRUCTURE, 0103 physical sciences, Planck, Cosmology: theory, Astronomy and Astrophysics, Space and Planetary Science, Science & Technology, 010308 nuclear & particles physics, COSMOLOGICAL PERTURBATIONS, Astronomy and Astrophysic, 0201 Astronomical And Space Sciences, TENSOR PERTURBATIONS, 13. Climate action, PROBE WMAP OBSERVATIONS, PRE-BIG-BANG, 2-FIELD INFLATION, MICROWAVE BACKGROUND POLARIZATION, BARYON ACOUSTIC-OSCILLATIONS, EXPANDING UNIVERSE, cosmic background radiation, cosmology: theory, early Universe, inflation
Abstract

The Planck Collaboration acknowledges the support of: ESA; CNES and CNRS/INSU-IN2P3-INP (France); ASI, CNR, and INAF (Italy); NASA and DoE (USA); STFC and UKSA (UK); CSIC, MINECO, JA, and RES (Spain); Tekes, AoF, and CSC (Finland); DLR and MPG (Germany); CSA (Canada); DTU Space (Denmark); SER/SSO (Switzerland); RCN (Norway); SFI (Ireland); FCT/MCTES (Portugal); ERC and PRACE (EU). A description of the Planck Collaboration and a list of its members, indicating which technical or scientific activities they have been involved in, can be found at http://www.cosmos.esa.int/web/planck/ planck-collaboration. This research used resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the US Department of Energy under Contract No. DE-AC02-05CH11231. Part of this work was undertaken at the STFC DiRAC HPC Facilities at the University of Cambridge, funded by UK BIS National E-infrastructure capital grants. We gratefully acknowledge the IN2P3 Computer Center (http://cc.in2p3.fr) for providing a significant amount of the computing resources and services needed for this work., We present the implications for cosmic inflation of the Planck measurements of the cosmic microwave background (CMB) anisotropies in both temperature and polarization based on the full Planck survey, which includes more than twice the integration time of the nominal survey used for the 2013 release papers. The Planck full mission temperature data and a first release of polarization data on large angular scales measure the spectral index of curvature perturbations to be ns = 0.968 ± 0.006 and tightly constrain its scale dependence to dns/dln k = −0.003 ± 0.007 when combined with the Planck lensing likelihood. When the Planck high-` polarization data are included, the results are consistent and uncertainties are further reduced. The upper bound on the tensor-to-scalar ratio is r0.002 < 0.11 (95% CL). This upper limit is consistent with the B-mode polarization constraint r < 0.12 (95% CL) obtained from a joint analysis of the BICEP2/Keck Array and Planck data. These results imply that V(φ) ∝ φ 2 and natural inflation are now disfavoured compared to models predicting a smaller tensor-to-scalar ratio, such as R 2 inflation. We search for several physically motivated deviations from a simple power-law spectrum of curvature perturbations, including those motivated by a reconstruction of the inflaton potential not relying on the slow-roll approximation. We find that such models are not preferred, either according to a Bayesian model comparison or according to a frequentist simulation-based analysis. Three independent methods reconstructing the primordial power spectrum consistently recover a featureless and smooth PR(k) over the range of scales 0.008 Mpc−1, Planck (http://www.esa.int/Planck) is a project of the European Space Agency (ESA) with instruments provided by two scientific consortia funded by ESA member states and led by Principal Investigators from France and Italy, telescope reflectors provided through a collaboration between ESA and a scientific consortium led and funded by Denmark, and additional contributions from NASA (USA).

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