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arxiv: 1907.12875 · v2 · pith:O44MIPIVnew · submitted 2019-07-30 · 🌌 astro-ph.CO

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
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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. Dor\'e M. Douspis A. Ducout X. Dupac S. Dusini G. Efstathiou F. Elsner T. A. En{\ss}lin 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. G\'enova-Santos M. Gerbino T. Ghosh Y. Giraud-H\'eraud J. Gonz\'alez-Nuevo K. M. G\'orski 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. Keih\"anen 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. L\'opez-Caniego P. M. Lubin Y.-Z. Ma J. F. Mac\'ias-P\'erez G. Maggio D. Maino N. Mandolesi A. Mangilli A. Marcos-Caballero M. Maris P. G. Martin E. Mart\'inez-Gonz\'alez S. Matarrese N. Mauri J. D. McEwen P. R. Meinhold A. Melchiorri A. Mennella M. Migliaccio M. Millea M.-A. Miville-Desch\^enes D. Molinari A. Moneti L. Montier G. Morgante A. Moss P. Natoli H. U. N{\o}rgaard-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. Rubi\~no-Mart\'in 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
This is my paper

Pith reviewed 2026-05-15 21:53 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords CMB power spectraPlanck likelihoodspolarizationreionization optical depthLambdaCDM parameterssystematics correctionscosmological constraints
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The pith

Refined corrections let Planck 2018 use full polarization data and tighten LambdaCDM constraints by 20-30 percent.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper updates the Planck CMB likelihoods with a hybrid low- and high-multipole construction and several analysis refinements. Better modelling of temperature-to-polarization leakage and polarization efficiency now permits full use of the High Frequency Instrument polarization spectra. Low-multipole EE data improves the reionization optical depth constraint while high-multipole polarization tightens LambdaCDM parameters relative to temperature-only analyses. Internal consistency tests place any residual differences below the 0.5 sigma level, making the likelihoods a standard reference.

Core claim

The 2018 Planck CMB likelihoods, constructed with improved simulations and explicit corrections for leakage and polarization efficiency, enable complete incorporation of polarization spectra. This yields 20-30 percent stronger constraints on LambdaCDM parameters at high multipoles and a tighter bound on the reionization optical depth from the low-multipole 100x143 GHz EE cross-spectrum, with overall consistency verified to better than 0.5 sigma across implementations.

What carries the argument

Hybrid low- and high-multipole likelihood with explicit temperature-to-polarization leakage modelling and polarization efficiency corrections.

If this is right

  • The low-multipole EE cross-spectrum constrains the reionization optical depth to better than 15 percent when combined with other likelihoods.
  • High-multipole polarization data improves LambdaCDM parameter precision by 20 to 30 percent over temperature-only constraints.
  • Minor differences between ell ranges below and above 800 remain driven by the temperature spectrum and are unchanged by polarization.
  • The likelihoods provide a consistent reference for future CMB observations and cosmological model tests.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Next-generation CMB surveys can treat these likelihoods as a baseline for cross-validation of new polarization measurements.
  • Greater reliance on E-mode data for parameter estimation will become standard once polarization efficiency calibration improves further.
  • Any proposed extension to LambdaCDM should be checked against both the full TEB and TT-only versions to confirm that polarization does not introduce new tensions.

Load-bearing premise

Residual uncertainties after polarization efficiency modelling and leakage corrections remain small enough that they do not shift cosmological parameters by more than the stated consistency level.

What would settle it

An independent high-multipole analysis or new simulation revealing parameter shifts larger than 0.5 sigma between polarization-inclusive and TT-only results would falsify the claimed robustness.

read the original 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 $\tau$ 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 $\tau$ 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 $\Lambda$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$\sigma$ 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)

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The paper presents the Planck 2018 CMB power spectra and likelihoods via a hybrid low- and high-multipole approach, incorporating refined simulations, improved corrections for temperature-to-polarization leakage, and polarization efficiency (PE) modelling. It enables full use of HFI polarization data, yielding 20–30% tighter ΛCDM constraints than TT-only, a τ constraint better than 15%, and internal consistency better than 0.5σ across implementations, while identifying residual PE modelling uncertainties as the dominant limitation. The likelihoods are positioned as the legacy Planck reference for cosmology.

Significance. If the central claims hold, this delivers the definitive Planck 2018 likelihoods that tighten cosmological parameter constraints by 20–30% through polarization inclusion and provide a benchmark reference for future CMB experiments. The extensive simulation-based consistency tests and cross-implementation comparisons add substantial value for model testing and parameter estimation.

major comments (1)
  1. [Abstract] Abstract (high-ℓ likelihood description): the paper identifies PE modelling accuracy as the main remaining limitation with residual uncertainties after T-to-P leakage and channel calibration corrections, yet does not show an explicit marginalization, covariance inflation, or propagation of these uncertainties into the final high-ℓ likelihood covariance; this is load-bearing for the claim that consistency remains better than 0.5σ and that the 20–30% improvement is robust.
minor comments (1)
  1. Ensure that all simulation and cross-check figures are accompanied by quantitative metrics (e.g., Δχ² or parameter shifts) rather than qualitative statements alone.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive assessment and constructive comment on our manuscript. We address the major comment point by point below.

read point-by-point responses
  1. Referee: [Abstract] Abstract (high-ℓ likelihood description): the paper identifies PE modelling accuracy as the main remaining limitation with residual uncertainties after T-to-P leakage and channel calibration corrections, yet does not show an explicit marginalization, covariance inflation, or propagation of these uncertainties into the final high-ℓ likelihood covariance; this is load-bearing for the claim that consistency remains better than 0.5σ and that the 20–30% improvement is robust.

    Authors: We agree that the abstract does not explicitly describe marginalization or covariance inflation for residual PE uncertainties. In the manuscript, these uncertainties are instead bounded through extensive end-to-end simulations and direct comparisons between independent high-ℓ implementations (Plik and CamSpec). The tests confirm that residual effects on ΛCDM parameters remain below 0.5σ with no evidence of coherent bias, thereby supporting the robustness of the 20–30% improvement from polarization. We do not inflate the covariance because the simulations indicate the residuals act as additional scatter rather than systematic shifts. We will revise the abstract and relevant sections to clarify this simulation-based validation approach. revision: yes

Circularity Check

0 steps flagged

No significant circularity in likelihood construction from data

full rationale

The paper constructs the 2018 Planck CMB likelihoods directly from time-ordered observational data and external simulations, applying corrections for temperature-to-polarization leakage and polarization efficiency modeling at high multipoles while using a hybrid low/high-ℓ approach. No equations reduce reported constraints or consistency tests (e.g., <0.5σ level) to quantities defined by the fit itself, and no load-bearing steps rely on self-citations or ansatzes that collapse the derivation to its inputs. The central results remain independent of the fitted cosmological parameters.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The analysis rests on standard CMB assumptions (Gaussian fluctuations, known foregrounds) and prior Planck instrument characterizations without introducing new free parameters or entities beyond calibration factors already present in earlier releases.

free parameters (1)
  • polarization efficiency factors
    Channel-specific calibration corrections applied to polarization spectra; values are determined from the data and simulations described in the analysis.
axioms (1)
  • domain assumption Gaussianity of CMB fluctuations and known foreground spectral behavior
    Implicit in the construction of the likelihood functions at both low and high multipoles.

pith-pipeline@v0.9.0 · 6648 in / 1281 out tokens · 50370 ms · 2026-05-15T21:53:13.209166+00:00 · methodology

discussion (0)

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