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

Planck Collaboration, Y. Akrami, F. Arroja, M. Ashdown, J. Aumont, C. Baccigalupi, M. Ballardini, A. J. Banday, R. B. Barreiro, N. Bartolo, S. Basak, K. Benabed, J. -P. Bernard, M. Bersanelli, P. Bielewicz, J. R. Bond, J. Borrill, F. R. Bouchet, M. Bucher, C. Burigana, R. C. Butler, E. Calabrese, J. -F. Cardoso, B. Casaponsa, A. Challinor, H. C. Chiang, L. P. L. Colombo, C. Combet, B. P. Crill, F. Cuttaia, P. de Bernardis, A. de Rosa, G. de Zotti, J. Delabrouille, J. -M. Delouis, E. Di Valentino, J. M. Diego, O. Doré, M. Douspis, A. Ducout, X. Dupac, S. Dusini, G. Efstathiou, F. Elsner, T. A. Enßlin, H. K. Eriksen, Y. Fantaye, J. Fergusson, R. Fernandez-Cobos, F. Finelli, M. Frailis, A. A. Fraisse, E. Franceschi, A. Frolov, S. Galeotta, K. Ganga, R. T. Génova-Santos, M. Gerbino, J. González-Nuevo, K. M. Górski, S. Gratton, A. Gruppuso, J. E. Gudmundsson, J. Hamann, W. Handley, F. K. Hansen, D. Herranz, E. Hivon, Z. Huang, A. H. Jaffe, W. C. Jones, G. Jung, E. Keihänen, R. Keskitalo, K. Kiiveri, J. Kim, N. Krachmalnicoff, M. Kunz, H. Kurki-Suonio, J. -M. Lamarre, A. Lasenby, M. Lattanzi, C. R. Lawrence, M. Le Jeune, F. Levrier, A. Lewis, M. Liguori, P. B. Lilje, V. Lindholm, M. López-Caniego, Y. -Z. Ma, J. F. Macías-Pérez, G. Maggio, D. Maino, N. Mandolesi, A. Marcos-Caballero, M. Maris, P. G. Martin, E. Martínez-González, S. Matarrese, N. Mauri, J. D. McEwen, P. D. Meerburg, P. R. Meinhold, A. Melchiorri, A. Mennella, M. Migliaccio, M. -A. Miville-Deschênes, D. Molinari, A. Moneti, L. Montier, G. Morgante, A. Moss, M. Münchmeyer, P. Natoli, F. Oppizzi, L. Pagano, D. Paoletti, B. Partridge, G. Patanchon, F. Perrotta, V. Pettorino, F. Piacentini, G. Polenta, J. -L. Puget, J. P. Rachen, B. Racine, M. Reinecke, M. Remazeilles, A. Renzi, G. Rocha, J. A. Rubiño-Martín, B. Ruiz-Granados, L. Salvati, M. Savelainen, D. Scott, E. P. S. Shellard, M. Shiraishi, C. Sirignano, G. Sirri, K. Smith, L. D. Spencer, L. Stanco, R. Sunyaev, A. -S. Suur-Uski, J. A. Tauber, D. Tavagnacco, M. Tenti, L. Toffolatti, M. Tomasi, T. Trombetti, J. Valiviita, B. Van Tent, P. Vielva, F. Villa, N. Vittorio, B. D. Wandelt, I. K. Wehus, A. Zacchei, A. Zonca

TL;DR

Planck 2018 PR3 delivers high-precision constraints on primordial non-Gaussianity by combining full-mission temperature and polarization data with multiple bispectrum estimators. The study systematically explores standard local, equilateral, and orthogonal shapes, runs extensive tests for robustness, and extends to a broad suite of NG models including running, oscillatory, isocurvature, and tensor NG, as well as trispectrum constraints. The results show no significant NG signals, providing tight bounds that strongly support the ΛCDM paradigm and standard single-field slow-roll inflation, while the detected lensing NG confirms the expected imprint of large-scale structure on the CMB. The paper translates these constraints into implications for a wide range of early-Universe models (DBI, EFT of inflation, curvaton, vector-field scenarios), and highlights the remaining pathways and target sensitivities for future experiments to reach f_NL ∼ 1 for decisive tests of multi-field and non-standard inflationary physics.

Abstract

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 modal bispectrum estimators, finding consistent values for the local, equilateral, and orthogonal bispectrum amplitudes. Our combined temperature and polarization analysis produces the following 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 the low-multipole (4 <= l < 40) polarization data, not included in our previous analysis, pass an extensive battery of tests, and are stable with respect to our 2015 measurements. Polarization bispectra display a significant improvement in robustness; they can now be used independently to set NG constraints. We consider a large number of additional cases, e.g. 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 detected with an improved significance compared to 2015, excluding the null hypothesis at 3.5 sigma. We present model-independent reconstructions and analyses of the CMB bispectrum. Our final constraint on the local trispectrum shape is g_NLl^local = (-5.8 +\-6.5) x 10^4 (68%CL, statistical), while constraints for other trispectra are also determined. We constrain the parameter space of different early-Universe scenarios, including general single-field models of inflation, multi-field and axion field parity-breaking models. Our results provide a high-precision test for structure-formation scenarios, in complete agreement with the basic picture of the LambdaCDM cosmology regarding the statistics of the initial conditions (abridged).

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

TL;DR

Planck 2018 PR3 delivers high-precision constraints on primordial non-Gaussianity by combining full-mission temperature and polarization data with multiple bispectrum estimators. The study systematically explores standard local, equilateral, and orthogonal shapes, runs extensive tests for robustness, and extends to a broad suite of NG models including running, oscillatory, isocurvature, and tensor NG, as well as trispectrum constraints. The results show no significant NG signals, providing tight bounds that strongly support the ΛCDM paradigm and standard single-field slow-roll inflation, while the detected lensing NG confirms the expected imprint of large-scale structure on the CMB. The paper translates these constraints into implications for a wide range of early-Universe models (DBI, EFT of inflation, curvaton, vector-field scenarios), and highlights the remaining pathways and target sensitivities for future experiments to reach f_NL ∼ 1 for decisive tests of multi-field and non-standard inflationary physics.

Abstract

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 modal bispectrum estimators, finding consistent values for the local, equilateral, and orthogonal bispectrum amplitudes. Our combined temperature and polarization analysis produces the following 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 the low-multipole (4 <= l < 40) polarization data, not included in our previous analysis, pass an extensive battery of tests, and are stable with respect to our 2015 measurements. Polarization bispectra display a significant improvement in robustness; they can now be used independently to set NG constraints. We consider a large number of additional cases, e.g. 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 detected with an improved significance compared to 2015, excluding the null hypothesis at 3.5 sigma. We present model-independent reconstructions and analyses of the CMB bispectrum. Our final constraint on the local trispectrum shape is g_NLl^local = (-5.8 +\-6.5) x 10^4 (68%CL, statistical), while constraints for other trispectra are also determined. We constrain the parameter space of different early-Universe scenarios, including general single-field models of inflation, multi-field and axion field parity-breaking models. Our results provide a high-precision test for structure-formation scenarios, in complete agreement with the basic picture of the LambdaCDM cosmology regarding the statistics of the initial conditions (abridged).

Paper Structure

This paper contains 69 sections, 97 equations, 20 figures, 24 tables.

Table of Contents

  1. Introduction
  2. Models
  3. General single-field models of inflation
  4. Multi-field models
  5. Isocurvature non-Gaussianity
  6. Running non-Gaussianity
  7. Local-type scale-dependent bispectrum
  8. Equilateral type scale-dependent bispectrum
  9. Oscillatory bispectrum models
  10. Resonance and axion monodromy
  11. Scale-dependent oscillatory features
  12. Non-Gaussianity from excited initial states
  13. Directional-dependent NG
  14. Parity-violating tensor non-Gaussianity motivated by pseudo-scalars
  15. Estimators and data analysis procedures
  16. ...and 54 more sections

Figures (20)

  • Figure 1: Weights of each polarization configuration going into the total value of $f_\textrm{NL}$ for, from left to right, local, equilateral, and orthogonal shapes. Note that since we impose $\ell_1 \leq \ell_2 \leq \ell_3$, there is a difference between, e.g., TEE (smallest $\ell$ is temperature) and EET (largest $\ell$ is temperature).
  • Figure 2: Weights of each polarization configuration going into the total value of the a,ii mixed $f_\textrm{NL}$ parameter for, from left to right, CDM, neutrino-density, and neutrino-velocity isocurvature, in addition to the adiabatic mode. Note that since we impose $\ell_1 \leq \ell_2 \leq \ell_3$, there is a difference between, e.g., TEE (where the smallest $\ell$ is temperature) and EET (where the largest $\ell$ is temperature).
  • Figure 3: PDF of the running parameter $n_{\rm NG}$ for the one-field local model. Top: SMICA map. Bottom: Commander map. Blue squares give the marginalized posterior assuming a constant prior, green circles are the posterior assuming a Jeffreys prior, and red triangles are the profiled Likelihood.
  • Figure 4: PDF of the running parameter $n_{\rm NG}$ for the two-field local model. Top: SMICA map. Bottom: Commander map. Blue squares give the marginalized posterior assuming a constant prior, green circles are the posterior assuming a Jeffreys prior, and red triangles are the profiled Likelihood.
  • Figure 5: PDF of the running parameter $n_{\rm NG}$ for the geometric mean equilateral parametrization. Top: SMICA map. Bottom: Commander map. Blue squares give the marginalized posterior assuming a constant prior, green circles are the posterior assuming a Jeffreys prior, and red triangles are the profiled Likelihood.
  • ...and 15 more figures