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Planck 2018 results. V. CMB power spectra and likelihoods

Planck Collaboration, N. Aghanim, Y. Akrami, 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. J. Bock, J. R. Bond, J. Borrill, F. R. Bouchet, F. Boulanger, M. Bucher, C. Burigana, R. C. Butler, E. Calabrese, J. -F. Cardoso, J. Carron, 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, R. Fernandez-Cobos, F. Finelli, M. Frailis, A. A. Fraisse, E. Franceschi, A. Frolov, S. Galeotta, S. Galli, K. Ganga, R. T. Génova-Santos, M. Gerbino, T. Ghosh, Y. Giraud-Héraud, 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, E. Keihänen, R. Keskitalo, K. Kiiveri, J. Kim, T. S. Kisner, N. Krachmalnicoff, M. Kunz, H. Kurki-Suonio, G. Lagache, J. -M. Lamarre, A. Lasenby, M. Lattanzi, C. R. Lawrence, M. Le Jeune, F. Levrier, A. Lewis, M. Liguori, P. B. Lilje, M. Lilley, V. Lindholm, M. López-Caniego, P. M. Lubin, Y. -Z. Ma, J. F. Macías-Pérez, G. Maggio, D. Maino, N. Mandolesi, A. Mangilli, A. Marcos-Caballero, M. Maris, P. G. Martin, E. Martínez-González, S. Matarrese, N. Mauri, J. D. McEwen, P. R. Meinhold, A. Melchiorri, A. Mennella, M. Migliaccio, M. Millea, M. -A. Miville-Deschênes, D. Molinari, A. Moneti, L. Montier, G. Morgante, A. Moss, P. Natoli, H. U. Nørgaard-Nielsen, L. Pagano, D. Paoletti, B. Partridge, G. Patanchon, H. V. Peiris, F. Perrotta, V. Pettorino, F. Piacentini, G. Polenta, J. -L. Puget, J. P. Rachen, M. Reinecke, M. Remazeilles, A. Renzi, G. Rocha, C. Rosset, G. Roudier, J. A. Rubiño-Martín, B. Ruiz-Granados, L. Salvati, M. Sandri, M. Savelainen, D. Scott, E. P. S. Shellard, C. Sirignano, G. Sirri, L. D. Spencer, 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

The paper introduces the Planck 2018 legacy CMB likelihoods, a robust, polarization-inclusive framework that fuses a low-ℓ Commander/SimAll pipeline with a high-ℓ Plik/CamSpec approach. By leveraging refined beam-leakage corrections, polarization-efficiency calibrations, and extensive end-to-end simulations, it achieves tighter constraints on τ and ΛCDM parameters while maintaining consistency across data splits, masks, and cross-spectra. The work provides a comprehensive validation suite and presents multiple high-ℓ implementations (Plik, CamSpec, Plik_lite) to test model robustness, establishing Planck 2018 as a foundational reference for current and future CMB analyses. Overall, polarization tomography from Planck 2018 strengthens the ΛCDM paradigm and demonstrates the value of meticulous systematic control in precision cosmology.

Abstract

This paper describes the 2018 Planck CMB likelihoods, following a hybrid approach similar to the 2015 one, with different approximations at low and high multipoles, and implementing several methodological and analysis refinements. With more realistic simulations, and better correction and modelling of systematics, we can now make full use of the High Frequency Instrument polarization data. The low-multipole 100x143 GHz EE cross-spectrum constrains the reionization optical-depth parameter $τ$ to better than 15% (in combination with with the other low- and high-$\ell$ likelihoods). We also update the 2015 baseline low-$\ell$ joint TEB likelihood based on the Low Frequency Instrument data, which provides a weaker $τ$ constraint. At high multipoles, a better model of the temperature-to-polarization leakage and corrections for the effective calibrations of the polarization channels (polarization efficiency or PE) allow us to fully use the polarization spectra, improving the constraints on the $Λ$CDM parameters by 20 to 30% compared to TT-only constraints. Tests on the modelling of the polarization demonstrate good consistency, with some residual modelling uncertainties, the accuracy of the PE modelling being the main limitation. Using our various tests, simulations, and comparison between different high-$\ell$ implementations, we estimate the consistency of the results to be better than the 0.5$σ$ level. Minor curiosities already present before (differences between $\ell$<800 and $\ell$>800 parameters or the preference for more smoothing of the $C_\ell$ peaks) are shown to be driven by the TT power spectrum and are not significantly modified by the inclusion of polarization. Overall, the legacy Planck CMB likelihoods provide a robust tool for constraining the cosmological model and represent a reference for future CMB observations. (Abridged)

Planck 2018 results. V. CMB power spectra and likelihoods

TL;DR

The paper introduces the Planck 2018 legacy CMB likelihoods, a robust, polarization-inclusive framework that fuses a low-ℓ Commander/SimAll pipeline with a high-ℓ Plik/CamSpec approach. By leveraging refined beam-leakage corrections, polarization-efficiency calibrations, and extensive end-to-end simulations, it achieves tighter constraints on τ and ΛCDM parameters while maintaining consistency across data splits, masks, and cross-spectra. The work provides a comprehensive validation suite and presents multiple high-ℓ implementations (Plik, CamSpec, Plik_lite) to test model robustness, establishing Planck 2018 as a foundational reference for current and future CMB analyses. Overall, polarization tomography from Planck 2018 strengthens the ΛCDM paradigm and demonstrates the value of meticulous systematic control in precision cosmology.

Abstract

This paper describes the 2018 Planck CMB likelihoods, following a hybrid approach similar to the 2015 one, with different approximations at low and high multipoles, and implementing several methodological and analysis refinements. With more realistic simulations, and better correction and modelling of systematics, we can now make full use of the High Frequency Instrument polarization data. The low-multipole 100x143 GHz EE cross-spectrum constrains the reionization optical-depth parameter to better than 15% (in combination with with the other low- and high- likelihoods). We also update the 2015 baseline low- joint TEB likelihood based on the Low Frequency Instrument data, which provides a weaker constraint. At high multipoles, a better model of the temperature-to-polarization leakage and corrections for the effective calibrations of the polarization channels (polarization efficiency or PE) allow us to fully use the polarization spectra, improving the constraints on the CDM parameters by 20 to 30% compared to TT-only constraints. Tests on the modelling of the polarization demonstrate good consistency, with some residual modelling uncertainties, the accuracy of the PE modelling being the main limitation. Using our various tests, simulations, and comparison between different high- implementations, we estimate the consistency of the results to be better than the 0.5 level. Minor curiosities already present before (differences between <800 and >800 parameters or the preference for more smoothing of the peaks) are shown to be driven by the TT power spectrum and are not significantly modified by the inclusion of polarization. Overall, the legacy Planck CMB likelihoods provide a robust tool for constraining the cosmological model and represent a reference for future CMB observations. (Abridged)

Paper Structure

This paper contains 9 sections, 8 equations, 7 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Likelihood names:
  3. Citation conventions:
  4. Low multipoles
  5. TT low-$\ell$ likelihood
  6. Validation
  7. HFI-based low-$\ell$ likelihood
  8. Polarization low-resolution maps and cleaning procedure
  9. Summary description of Plik

Figures (7)

  • Figure 1: Top: Commander 2018 low-$\ell$ temperature map masked with the Commander 2018 mask. Middle and bottom: differences between the Commander 2018 map and the Commander 2015 map (middle) and the SMICA-dedicated low-$\ell$ map (bottom).
  • Figure 2: $TT$ angular power spectra ($D_\ell\equiv\ell(\ell+1)C_\ell/2\pi$) of the available low-$\ell$ component-separated maps: Commander 2018 (blue points); Commander 2015 (red points); SMICA 2018 (cyan points); and Commander 2015 and SMICA 2018 masked with the 2018 Commander mask (purple and green points, respectively).
  • Figure 3: Differences normalized to the sampling variance in the angular power spectrum with respect to the Commander 2015 one. The grey band is the $\pm3\sigma$ dispersion of 10000 MC angular power spectra differences calculated using either the Commander 2015 mask or the Commander 2018 mask.
  • Figure 4: Angular power spectrum of the low-$\ell$Commander maps compared to those of the other component-separated maps. Top: comparison performed with the component-separated maps of the 2018 release. Black points show the power spectrum of the 2018 low-$\ell$Commander map with the 2018 common mask from component separation. Bottom: comparison performed with the 2015 component-separated maps. Black points show the power spectrum of the 2015 low-$\ell$Commander map with the 2015 common mask from component separation. Blue and red points are, respectively, the power spectrum of the low-$\ell$Commander maps with the 2018 or 2015 native mask.
  • Figure 5: Average of the angular power spectrum differences between $\ell{=}2$ and $\ell_{\rm max}$ as a function of $\ell_{\rm max}$, expressed as a percentage. The differences are taken with respect to Commander 2015 results with its native mask. The dashed lines omit $\ell{=}5$.
  • ...and 2 more figures