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Planck 2018 results. IX. Constraints on primordial non-Gaussianity

Akrami, Y. and Crill, B. P. and Doré, O. and Rocha, G. and Górski, K. M. and Lawrence, C. R. (2020) Planck 2018 results. IX. Constraints on primordial non-Gaussianity. Astronomy and Astrophysics, 641 . Art. No. A9. ISSN 0004-6361.

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We analyse the Planck full-mission cosmic microwave background (CMB) temperature and E-mode polarization maps to obtain constraints on primordial non-Gaussianity (NG). We compare estimates obtained from separable template-fitting, binned, and optimal modal bispectrum estimators, finding consistent values for the local, equilateral, and orthogonal bispectrum amplitudes. Our combined temperature and polarization analysis produces the following final results: f_(NL)^(local) = −0.9 ± 5.1; f_(NL)^(equil) = −26 ± 47; and f_(NL)^(ortho) = −38 ± 24 (68% CL, statistical). These results include low-multipole (4 ≤ ℓ <  40) polarization data that are not included in our previous analysis. The results also pass an extensive battery of tests (with additional tests regarding foreground residuals compared to 2015), and they are stable with respect to our 2015 measurements (with small fluctuations, at the level of a fraction of a standard deviation, which is consistent with changes in data processing). Polarization-only bispectra display a significant improvement in robustness; they can now be used independently to set primordial NG constraints with a sensitivity comparable to WMAP temperature-based results and they give excellent agreement. In addition to the analysis of the standard local, equilateral, and orthogonal bispectrum shapes, we consider a large number of additional cases, such as scale-dependent feature and resonance bispectra, isocurvature primordial NG, and parity-breaking models, where we also place tight constraints but do not detect any signal. The non-primordial lensing bispectrum is, however, detected with an improved significance compared to 2015, excluding the null hypothesis at 3.5σ. Beyond estimates of individual shape amplitudes, we also present model-independent reconstructions and analyses of the Planck CMB bispectrum. Our final constraint on the local primordial trispectrum shape is g_(NL)^(local) = (−5.8 ± 6.5) × 10⁴ (68% CL, statistical), while constraints for other trispectrum shapes are also determined. Exploiting the tight limits on various bispectrum and trispectrum shapes, we constrain the parameter space of different early-Universe scenarios that generate primordial NG, including general single-field models of inflation, multi-field models (e.g. curvaton models), models of inflation with axion fields producing parity-violation bispectra in the tensor sector, and inflationary models involving vector-like fields with directionally-dependent bispectra. Our results provide a high-precision test for structure-formation scenarios, showing complete agreement with the basic picture of the ΛCDM cosmology regarding the statistics of the initial conditions, with cosmic structures arising from adiabatic, passive, Gaussian, and primordial seed perturbations.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Akrami, Y.0000-0002-2407-7956
Crill, B. P.0000-0002-4650-8518
Doré, O.0000-0002-5009-7563
Rocha, G.0000-0002-4150-8076
Additional Information:© 2020 ESO. Article published by EDP Sciences. Received 15 May 2019; Accepted 5 November 2019; Published online 11 September 2020. 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); and 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 Some of the results in this paper have been derived using the HEALPix package. We also acknowledge the use of CAMB. Part of this work was undertaken on the STFC COSMOS@DiRAC HPC Facility at the University of Cambridge, funded by UK BIS NEI grants. We gratefully acknowledge the IN2P3 Computer Center ( for providing a significant amount of the computing resources and services needed for the analysis. 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 U.S. Department of Energy under Contract No. DE-AC02-05CH11231. Some computations were performed on the GPC and Niagara cluster at the SciNet HPC Consortium; SciNet is funded by the Canada Foundation for Innovation under the auspices of Compute Canada, the Government of Ontario, and the University of Toronto.
Funding AgencyGrant Number
European Space Agency (ESA)UNSPECIFIED
Centre National d'Études Spatiales (CNES)UNSPECIFIED
Centre National de la Recherche Scientifique (CNRS)UNSPECIFIED
Institut national des sciences de l'Univers (INSU)UNSPECIFIED
Institut National de Physique Nucléaire et de Physique des Particules (IN2P3)UNSPECIFIED
Agenzia Spaziale Italiana (ASI)UNSPECIFIED
Consiglio Nazionale delle Ricerche (CNR)UNSPECIFIED
Istituto Nazionale di Astrofisica (INAF)UNSPECIFIED
Department of Energy (DOE)DE-AC02-05CH11231
Science and Technology Facilities Council (STFC)UNSPECIFIED
United Kingdom Space Agency (UKSA)UNSPECIFIED
Consejo Superior de Investigaciones Científicas (CSIC)UNSPECIFIED
Ministerio de Economía, Industria y Competitividad (MINECO)UNSPECIFIED
Junta de AndalucíaUNSPECIFIED
Red Española de Supercomputación (RES)UNSPECIFIED
Ministry of Employment and the Economy (Finland)UNSPECIFIED
Academy of FinlandUNSPECIFIED
Finnish IT Center for Science (CSC)UNSPECIFIED
Deutsches Zentrum für Luft- und Raumfahrt (DLR)UNSPECIFIED
Max Planck SocietyUNSPECIFIED
Canadian Space Agency (CSA)UNSPECIFIED
State Secretariat for Education and Research (Switzerland)UNSPECIFIED
Swiss Space Office (SSO)UNSPECIFIED
Research Council of NorwayUNSPECIFIED
Science Foundation, IrelandUNSPECIFIED
Fundação para a Ciência e a Tecnologia (FCT)UNSPECIFIED
Ministério da Ciência, Tecnologia e Ensino Superior (MCTES)UNSPECIFIED
European Research Council (ERC)UNSPECIFIED
Partnership for Advanced Computing in Europe (PRACE)UNSPECIFIED
Subject Keywords:cosmic background radiation – cosmology: observations – cosmology: theory – early Universe – inflation – methods: data analysis
Record Number:CaltechAUTHORS:20190930-132041388
Persistent URL:
Official Citation:Planck 2018 results - IX. Constraints on primordial non-Gaussianity. Planck Collaboration, Y. Akrami, et. al., A&A, 641 (2020) A9; DOI:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:98948
Deposited By: Tony Diaz
Deposited On:30 Sep 2019 20:37
Last Modified:11 Sep 2020 20:38

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