Planck 2013 results. XXII. Constraints on inflation
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Planck Collaboration
- Function : Author
P.A.R. Ade
- Function : Author
N. Aghanim
- Function : Author
C. Armitage-Caplan
- Function : Author
M. Arnaud
- Function : Author
M. Ashdown
- Function : Author
F. Atrio-Barandela
- Function : Author
J. Aumont
- Function : Author
- PersonId : 750370
- IdHAL : jonathan-aumont
- ORCID : 0000-0001-6279-0691
- IdRef : 121785653
C. Baccigalupi
- Function : Author
A. J. Banday
- Function : Author
- PersonId : 179497
- IdHAL : anthony-banday
- ORCID : 0000-0002-3358-0289
- IdRef : 073735302
R. B. Barreiro
- Function : Author
N. Bartolo
- Function : Author
E. Battaner
- Function : Author
K. Benabed
- Function : Author
A. Benoit-Levy
- Function : Author
J. -P. Bernard
- Function : Author
M. Bersanelli
- Function : Author
P. Bielewicz
- Function : Author
J. Bobin
- Function : Author
J. J. Bock
- Function : Author
A. Bonaldi
- Function : Author
J. R. Bond
- Function : Author
J. Borrill
- Function : Author
F. R. Bouchet
- Function : Author
- PersonId : 180816
- IdHAL : francois-r-bouchet
- ORCID : 0000-0002-8051-2924
- IdRef : 07733311X
M. Bridges
- Function : Author
C. Burigana
- Function : Author
R. C. Butler
- Function : Author
E. Calabrese
- Function : Author
J.-F. Cardoso
- Function : Author
- PersonId : 742037
- IdHAL : jean-francois-cardoso
- ORCID : 0000-0002-3388-6608
- IdRef : 035655216
A. Challinor
- Function : Author
A. Chamballu
- Function : Author
L. -y Chiang
- Function : Author
H. C. Chiang
- Function : Author
P. R. Christensen
- Function : Author
S. Church
- Function : Author
D. L. Clements
- Function : Author
S. Colombi
- Function : Author
L. P. L. Colombo
- Function : Author
F. Couchot
- Function : Author
- PersonId : 742631
- IdHAL : francois-couchot2
- ORCID : 0000-0002-7714-7700
- IdRef : 032240503
B. P. Crill
- Function : Author
A. Curto
- Function : Author
F. Cuttaia
- Function : Author
L. Danese
- Function : Author
R. D. Davies
- Function : Author
R. J. Davis
- Function : Author
P. de Bernardis
- Function : Author
A. de Rosa
- Function : Author
G. de Zotti
- Function : Author
J. -M. Delouis
- Function : Author
F. -X. Desert
- Function : Author
C. Dickinson
- Function : Author
J. M. Diego
- Function : Author
H. Dole
- Function : Author
S. Donzelli
- Function : Author
O. Dore
- Function : Author
M. Douspis
- Function : Author
J. Dunkley
- Function : Author
X. Dupac
- Function : Author
G. Efstathiou
- Function : Author
T. A. Ensslin
- Function : Author
H. K. Eriksen
- Function : Author
F. Finelli
- Function : Author
O. Forni
- Function : Author
- PersonId : 754595
- IdHAL : chloe-bourguignon
- ORCID : 0000-0002-4715-1725
M. Frailis
- Function : Author
E. Franceschi
- Function : Author
S. Galeotta
- Function : Author
M. Giard
- Function : Author
G. Giardino
- Function : Author
- PersonId : 756021
- IdRef : 034653848
J. Gonzalez-Nuevo
- Function : Author
K. M. Gorski
- Function : Author
Serge Gratton
- Function : Author
A. Gregorio
- Function : Author
A. Gruppuso
- Function : Author
J. Hamann
- Function : Author
F. K. Hansen
- Function : Author
D. Hanson
- Function : Author
D. Harrison
- Function : Author
- PersonId : 763313
- ORCID : 0000-0001-8635-4667
S. Henrot-Versille
- Function : Author
- PersonId : 740081
- IdHAL : sophie-henrot-versille
- ORCID : 0000-0003-1218-2991
- IdRef : 191080403
C. Hernandez-Monteagudo
- Function : Author
D. Herranz
- Function : Author
S. R. Hildebrandt
- Function : Author
E. Hivon
- Function : Author
M. Hobson
- Function : Author
- PersonId : 761656
- ORCID : 0000-0002-1915-7732
W. A. Holmes
- Function : Author
A. Hornstrup
- Function : Author
W. Hovest
- Function : Author
K. M. Huffenberger
- Function : Author
T. R. Jaffe
- Function : Author
A. H. Jaffe
- Function : Author
W. C. Jones
- Function : Author
M. Juvela
- Function : Author
E. Keihaanen
- Function : Author
R. Keskitalo
- Function : Author
T. S. Kisner
- Function : Author
R. Kneissl
- Function : Author
J. Knoche
- Function : Author
L. Knox
- Function : Author
M. Kunz
- Function : Author
H. Kurki-Suonio
- Function : Author
Guilaine Lagache
- Function : Author
- PersonId : 21058
- IdHAL : guilaine-lagache
A. Lahteenmaki
- Function : Author
A. Lasenby
- Function : Author
R. J. Laureijs
- Function : Author
C. R. Lawrence
- Function : Author
S. Leach
- Function : Author
J. P. Leahy
- Function : Author
R. Leonardi
- Function : Author
J. Lesgourgues
- Function : Author
M. Liguori
- Function : Author
P. B. Lilje
- Function : Author
M. Linden-Vernle
- Function : Author
M. Lopez-Caniego
- Function : Author
P. M. Lubin
- Function : Author
B. Maffei
- Function : Author
D. Maino
- Function : Author
N. Mandolesi
- Function : Author
M. Maris
- Function : Author
D. J. Marshall
- Function : Author
P. G. Martin
- Function : Author
E. Martinez-Gonzalez
- Function : Author
S. Masi
- Function : Author
S. Matarrese
- Function : Author
F. Matthai
- Function : Author
P. Mazzotta
- Function : Author
P. R. Meinhold
- Function : Author
A. Melchiorri
- Function : Author
L. Mendes
- Function : Author
A. Mennella
- Function : Author
M. Migliaccio
- Function : Author
Subhabrata Mitra
- Function : Author
M. -A. Miville-Deschenes
- Function : Author
- PersonId : 741816
- IdHAL : marc-antoine-miville-deschenes
- ORCID : 0000-0002-7351-6062
- IdRef : 078115361
A. Moneti
- Function : Author
L. Montier
- Function : Author
G. Morgante
- Function : Author
D. Mortlock
- Function : Author
A. Moss
- Function : Author
D. Munshi
- Function : Author
P. Naselsky
- Function : Author
F. Nati
- Function : Author
- PersonId : 754354
- IdHAL : sughosh-deshpande
P. Natoli
- Function : Author
C. B. Netterfield
- Function : Author
H. U. Norgaard-Nielsen
- Function : Author
F. Noviello
- Function : Author
D. Novikov
- Function : Author
I. Novikov
- Function : Author
I. J. O'Dwyer
- Function : Author
S. Osborne
- Function : Author
C. A. Oxborrow
- Function : Author
F. Paci
- Function : Author
L. Pagano
- Function : Author
F. Pajot
- Function : Author
- PersonId : 742082
- IdHAL : francois-pajot
- IdRef : 13140718X
R. Paladini
- Function : Author
- PersonId : 754744
- IdHAL : maud-haffner
- ORCID : 0000-0002-5056-9831
S. Pandolfi
- Function : Author
D. Paoletti
- Function : Author
B. Partridge
- Function : Author
F. Pasian
- Function : Author
H. V. Peiris
- Function : Author
L. Perotto
- Function : Author
- PersonId : 742116
- IdHAL : lperotto
- ORCID : 0000-0001-6937-5052
- IdRef : 118429221
F. Perrotta
- Function : Author
F. Piacentini
- Function : Author
E. Pierpaoli
- Function : Author
D. Pietrobon
- Function : Author
Stéphane Plaszczynski
- Function : Author
- PersonId : 9483
- IdHAL : stephane-plaszczynski
- ORCID : 0000-0002-1278-109X
- IdRef : 156370042
E. Pointecouteau
- Function : Author
- PersonId : 738693
- IdHAL : etienne-pointecouteau
- ORCID : 0000-0001-8488-3645
- IdRef : 080631878
G. Polenta
- Function : Author
N. Ponthieu
- Function : Author
L. Popa
- Function : Author
T. Poutanen
- Function : Author
G. W. Pratt
- Function : Author
G. Prezeau
- Function : Author
S. Prunet
- Function : Author
- PersonId : 739461
- IdHAL : simon-prunet
- ORCID : 0000-0002-1755-4582
- IdRef : 151240094
J. -L. Puget
- Function : Author
J. P. Rachen
- Function : Author
R. Rebolo
- Function : Author
M. Reinecke
- Function : Author
S. Ricciardi
- Function : Author
T. Riller
- Function : Author
I. Ristorcelli
- Function : Author
G. Rocha
- Function : Author
M. Rowan-Robinson
- Function : Author
J. A. Rubino-Martin
- Function : Author
B. Rusholme
- Function : Author
M. Sandri
- Function : Author
M. Savelainen
- Function : Author
G. Savini
- Function : Author
D. Scott
- Function : Author
M. D. Seiffert
- Function : Author
E. P. S. Shellard
- Function : Author
L. D. Spencer
- Function : Author
Jean-Luc Starck
- Function : Author
- PersonId : 850921
V. Stolyarov
- Function : Author
- PersonId : 758585
- ORCID : 0000-0001-6059-6270
Radek Stompor
- Function : Author
- PersonId : 821080
- ORCID : 0000-0002-5217-8367
R. Sudiwala
- Function : Author
R. Sunyaev
- Function : Author
F. Sureau
- Function : Author
D. Sutton
- Function : Author
A. -S. Suur-Uski
- Function : Author
J. -F. Sygnet
- Function : Author
J. A. Tauber
- Function : Author
D. Tavagnacco
- Function : Author
L. Terenzi
- Function : Author
L. Toffolatti
- Function : Author
M. Tomasi
- Function : Author
M. Tristram
- Function : Author
- PersonId : 9484
- IdHAL : matthieu-tristram
- ORCID : 0000-0001-7276-8324
- IdRef : 098039229
J. Tuovinen
- Function : Author
L. Valenziano
- Function : Author
J. Valiviita
- Function : Author
B. van Tent
- Function : Author
J. Varis
- Function : Author
P. Vielva
- Function : Author
Francesca Villa
- Function : Author
N. Vittorio
- Function : Author
L. A. Wade
- Function : Author
B. D. Wandelt
- Function : Author
M. White
- Function : Author
A. Wilkinson
- Function : Author
D. Yvon
- Function : Author
A. Zacchei
- Function : Author
A. Zonca
- Function : Author
Abstract
We analyse the implications of the Planck data for cosmic inflation. The Planck nominal mission temperature anisotropy measurements, combined with the WMAP large-angle polarization, constrain the scalar spectral index to n_s = 0.960 pm 0.0073, ruling out exact scale invariance at over 5 sigma. Planck establishes an upper bound on the tensor-to-scalar ratio at r < 0.11 (95% CL). Planck data shrink the space of allowed standard inflationary models, preferring potentials with V'' < 0. Exponential potential models, the simplest hybrid inflationary models, and monomial potential models of degree n > 2 do not provide a good fit to the data. Planck does not find any statistically significant running of the scalar spectral index, obtaining d n_s/d ln k = -0.0134 pm 0.0090. Several analyses dropping the slow-roll approximation are carried out, including detailed model comparison and inflationary potential reconstruction. We investigate whether the primordial power spectrum contains any features. A penalized likelihood approach suggests a feature near the smallest scales probed by Planck at an estimated significance of ~3 sigma after correction for the look elsewhere effect. Models with a parameterized oscillatory feature can improve the fit chi^2 by ~ 10; however, Bayesian evidence does not prefer these models. We constrain several single-field inflation models with generalized Lagrangians by combining power spectrum data with bounds on f_NL measured by Planck. The fractional primordial contribution of CDM isocurvature modes in the curvaton and axion scenarios has upper bounds of 0.25% or 3.9% (95% CL), respectively. In models with arbitrarily correlated CDM or neutrino isocurvature modes, an anticorrelation can improve chi^2 by ~4 due to a moderate tension between l < 40 and higher multipoles. Nonetheless, the data are consistent with adiabatic initial conditions.