[Paper Review] Planck 2018 results: V. CMB power spectra and likelihoods

N. Aghanim, Y. Akrami+165 more|arXiv (Cornell University)|Jan 1, 2020

Cosmology and Gravitation TheoriesPhysics and Astronomy91 references230 citations

TL;DR

This paper presents the final Planck 2018 cosmic microwave background (CMB) likelihoods, integrating improved low- and high-multipole temperature and polarization power spectra using advanced data analysis and simulation techniques. It achieves a 30%+ improvement in constraints on ΛCDM parameters like θMC, ωc, ωb, and H0 by fully utilizing polarization data after refined modeling of leakage and polarization efficiency, with consistency tests confirming results within 0.5σ of the ΛCDM model.

ABSTRACT

We describe the legacy Planck cosmic microwave background (CMB) likelihoods derived from the 2018 data release. The overall approach is similar in spirit to the one retained for the 2013 and 2015 data release, with a hybrid method using different approximations at low (l < 30) and high (l ≥ 30) multipoles, implementing several methodological and data-analysis refinements compared to previous releases. With more realistic simulations, and better correction and modelling of systematic effects, we can now make full use of the CMB polarization observed in the High Frequency Instrument (HFI) channels. The low-multipole EE cross-spectra from the 100 GHz and 143 GHz data give a constraint on the λCDM reionization optical-depth parameter τ to better than 15% (in combination with the TT low-l data and the high-l temperature and polarization data), tightening constraints on all parameters with posterior distributions correlated with τ. We also update the weaker constraint on τ from the joint TEB likelihood using the Low Frequency Instrument (LFI) channels, which was used in 2015 as part of our baseline analysis. At higher multipoles, the CMB temperature spectrum and likelihood are very similar to previous releases. A better model of the temperature-to-polarization leakage and corrections for the effective calibrations of the polarization channels (i.e., the polarization efficiencies) allow us to make full use of polarization spectra, improving the λCDM constraints on the parameters θMC, ωc, ωb, and H0 by more than 30%, and ns by more than 20% compared to TT-only constraints. Extensive tests on the robustness of the modelling of the polarization data demonstrate good consistency, with some residual modelling uncertainties. At high multipoles, we are now limited mainly by the accuracy of the polarization efficiency modelling. Using our various tests, simulations, and comparison between different high-multipole likelihood implementations, we estimate the consistency of the results to be better than the 0.5σ level on the λCDM parameters, as well as classical single-parameter extensions for the joint likelihood (to be compared to the 0.3σ levels we achieved in 2015 for the temperature data alone on λCDM only). Minor curiosities already present in the previous releases remain, such as the differences between the best-fit λCDM parameters for the l < 800 and l > 800 ranges of the power spectrum, or the preference for more smoothing of the power-spectrum peaks than predicted in λCDM fits. These are shown to be driven by the temperature power spectrum and are not significantly modified by the inclusion of the polarization data. Overall, the legacy Planck CMB likelihoods provide a robust tool for constraining the cosmological model and represent a reference for future CMB observations.

Motivation & Objective

• To deliver a robust, final CMB likelihood framework from the Planck 2018 data release for cosmological parameter estimation.
• To improve constraints on ΛCDM parameters by fully utilizing polarization data through refined modeling of instrumental effects.
• To validate the consistency and robustness of the likelihood across multiple tests, including simulations and cross-frequency comparisons.
• To identify and quantify residual systematics, particularly in polarization efficiency and beam modeling, that limit high-multipole precision.
• To provide a reference standard for future CMB experiments by establishing a high-accuracy, well-tested likelihood framework.

Proposed method

• A hybrid likelihood approach is used, with distinct modeling for low (ℓ < 30) and high (ℓ ≥ 30) multipoles, combining TT, TE, and EE spectra.
• For low multipoles, the likelihood is built from HFI 100/143 GHz and LFI 70 GHz maps, using cleaned polarization maps and cross-spectra to constrain τ.
• High-multipole likelihoods are computed using the Plik algorithm, which models the pseudo-power spectrum from map-based estimators with corrections for beam, noise, and calibration effects.
• Polarization efficiency and temperature-to-polarization leakage are modeled with improved transfer functions and calibrated using simulations and data-driven templates.
• Extensive Monte Carlo simulations and consistency tests (e.g., inter-frequency agreement, conditional predictions) are used to validate the likelihood and quantify biases.
• Sky masks, beam transfer functions, and noise models are carefully calibrated using both data and simulations, with apodization to minimize edge effects.

Experimental results

Research questions

• RQ1 How can the full CMB polarization signal from Planck HFI and LFI be used to improve cosmological parameter constraints beyond temperature-only likelihoods?
• RQ2 To what extent do residual systematics in polarization efficiency and beam modeling limit the precision of high-multipole likelihoods?
• RQ3 Are the observed anomalies in the CMB power spectrum (e.g., peak broadening, low-ℓ deviations) consistent with statistical fluctuations or indicative of new physics?
• RQ4 How robust are the likelihood results across different data subsets, simulation realizations, and likelihood implementations?
• RQ5 Can the joint TT, TE, EE likelihood be trusted to constrain ΛCDM and its extensions with sub-0.5σ consistency?

Key findings

• The inclusion of polarization data improves constraints on θMC, ωc, ωb, and H0 by more than 30% and on ns by over 20% compared to TT-only likelihoods.
• The optical depth to reionization τ is constrained to better than 15% precision using HFI-based low-ℓ EE spectra, with improved consistency from simulations and modeling.
• Consistency tests show that the final likelihood results are consistent at the 0.5σ level across different implementations and data subsets, representing a significant improvement over the 0.3σ level achieved in 2015 for temperature-only data.
• Residual systematics in polarization efficiency modeling are identified as the main limitation at high multipoles, with consistency limited to better than 0.5σ on ΛCDM parameters.
• The TT power spectrum remains the primary driver of known anomalies (e.g., peak broadening, low-ℓ deviations), which are not significantly altered by the inclusion of polarization data.
• The likelihood framework is robust and consistent, with no evidence of systematic biases exceeding 0.5σ, supporting its use as a reference for future CMB experiments.