The Cosmic Microwave Background (CMB) radiation offers a unique window into the early Universe, facilitating precise examinations of fundamental cosmological theories. However, the quest for detecting B-modes in the CMB, predicted by theoretical models of inflation, faces substantial challenges in terms of calibration and foreground modeling. The COSMOCal (COsmic Survey of Millimeter wavelengths Objects for CMB experiments Calibration) project aims at enhancing the accuracy of the absolute calibration of the polarization angle $\psi$ of current and future CMB experiments. The concept includes the build of a very well known artificial source emitting in the frequency range [20-350] GHz that would act as an absolute calibrator for several polarization facilities on Earth. A feasibility study to place the artificial source in geostationary orbit, in the far field for all the telescopes on Earth, is ongoing. In the meanwhile ongoing hardware work is dedicated to build a prototype to test the technology, the precision and the stability of the polarization recovering in the 1 mm band (220-300 GHz). High-resolution experiments as the NIKA2 camera at the IRAM 30m telescope will be deployed for such use. Once carefully calibrated ($\Delta\psi$ < 0.1 degrees) it will be used to observe astrophysical sources such as the Crab nebula, which is the best candidate in the sky for the absolute calibration of CMB experiments.

The Cosmic Microwave Background (CMB) radiation offers a unique window into the early Universe, facilitating precise examinations of fundamental cosmological theories. However, the quest for detecting B-modes in the CMB, predicted by theoretical models of inflation, faces substantial challenges in terms of calibration and foreground modeling. The COSMOCal (COsmic Survey of Millimeter wavelengths Objects for CMB experiments Calibration) project aims at enhancing the accuracy of the absolute calibration of the polarization angle ψ of current and future CMB experiments. The concept includes the build of a very well known artificial source emitting in the frequency range [20-350] GHz that would act as an absolute calibrator for several polarization facilities on Earth. A feasibility study to place the artificial source in geostationary orbit, in the far field for all the telescopes on Earth, is ongoing. In the meanwhile ongoing hardware work is dedicated to build a prototype to test the technology, the precision and the stability of the polarization recovering in the 1 mm band (220-300 GHz). High-resolution experiments as the NIKA2 camera at the IRAM 30m telescope will be deployed for such use. Once carefully calibrated (Δψ < 0.1◦) it will be used to observe astrophysical sources such as the Crab nebula, which is the best candidate in the sky for the absolute calibration of CMB experiments.

The search for the primordial B-modes of the cosmic microwave background (CMB) relies on the separation from the brighter foreground dust signal. In this context, the characterisation of the spectral energy distribution (SED) of thermal dust in polarization has become a critical subject of study. We present a power-spectra analysis of Planck data, which improves on previous studies by using the newly released SRoll2 maps that correct residual data systematics, and by extending the analysis to regions near the Galactic plane. Our analysis focuses on the lowest multipoles between l=4 and 32, and three sky areas with sky fractions of fsky = 80 and the 353 GHz Q and U maps are used to compute residual maps at 100, 143 and 217 GHz, highlighting spatial variations of the dust polarization SED. Residuals are detected at the three frequencies for the three sky areas. We show that models based on total intensity data are underestimating by a significant factor the complexity of dust polarized CMB foreground. Our analysis emphasizes the need to include variations of polarization angles of the dust polarized CMB foreground. The frequency dependence of the EE and BB power spectra of the residual maps yields further insight. We find that the moments expansion to the first order of the modified black-body (MBB) spectrum provides a good fit to the EE power-spectra. This result suggests that the residuals could follow mainly from variations of dust MBB spectral parameters. However, this conclusion is challenged by cross-spectra showing that the residuals maps at the three frequencies are not fully correlated, and the fact that the BB power-spectra do not match the first order moment expansion of a MBB SED. This work sets new requirements for simulations of the dust polarized foreground and component separation methods (abridged)

The polarized thermal emission from diffuse Galactic dust is the main foreground present in measurements of the polarization of the cosmic microwave background (CMB) at frequencies above 100 GHz. In this paper we exploit the uniqueness of the Planck HFI polarization data from 100 to 353 GHz to measure the polarized dust angular power spectra CEE ` and C BB ` over the multipole range 40 < ` < 600 well away from the Galactic plane. These measurements will bring new insights into interstellar dust physics and allow a precise determination of the level of contamination for CMB polarization experiments. Despite the non-Gaussian and anisotropic nature of Galactic dust, we show that general statistical properties of the emission can be characterized accurately over large fractions of the sky using angular power spectra. The polarization power spectra of the dust are well described by power laws in multipole, C` ∝ `, with exponents αEE,BB = −2.42± 0.02. The amplitudes of the polarization power spectra vary with the average brightness in a way similar to the intensity power spectra. The frequency dependence of the dust polarization spectra is consistent with modified blackbody emission with βd = 1.59 and Td = 19.6 K down to the lowest Planck HFI frequencies. We find a systematic difference between the amplitudes of the Galactic Band E-modes, CBB ` /C EE ` = 0.5. We verify that these general properties are preserved towards high Galactic latitudes with low dust column densities. We show that even in the faintest dust-emitting regions there are no “clean” windows in the sky where primordial CMB B-mode polarization measurements could be made without subtraction of foreground emission. Finally, we investigate the level of dust polarization in the specific field recently targeted by the BICEP2 experiment. Extrapolation of the Planck 353 GHz data to 150 GHz gives a dust powerDBB ` ≡ `(`+ 1)CBB ` /(2π) of 1.32× 10−2 μKCMB over the multipole range of the primordial recombination bump (40 < ` < 120); the statistical uncertainty is ±0.29 × 10−2 μKCMB and there is an additional uncertainty (+0.28,−0.24) × 10−2 μKCMB from the extrapolation. This level is the same magnitude as reported by BICEP2 over this ` range, which highlights the need for assessment of the polarized dust signal even in the cleanest windows of the sky.

The cosmic microwave background (CMB) anisotropies are difficult to measure at large angular scales. In this paper, we present a new analysis of the Planck High Frequency Instrument data that brings the cosmological part and its major foreground signal close to the detector noise. The solar dipole signal induced by the motion of the Solar System with respect to the CMB is a very efficient tool for calibrating a detector or cross-calibrating sets of detectors with high accuracy. In this work, the solar dipole signal is used to extract corrections of the frequency map offsets, reducing uncertainties significantly. The solar dipole parameters are refined together with the improvement of the high-frequency foregrounds and the CMB large-scale cosmological anisotropies. The stability of the solar dipole parameters is a powerful way to control Galactic foreground removal in the component separation process. We use this stability to build a model of the spatial variations in spectral energy distribution of the interstellar dust emission. Knowledge of these variations will help future CMB analyses of intensity and polarization used to measure faint signals related to the optical reionization depth and the tensor-to-scalar ratio of the primordial anisotropies. The results of this work are: improved solar dipole parameters, a new interstellar dust model, and a large-scale intensity map of cosmological anisotropies.

Planck Collaboration: N. Aghanim54, Y. Akrami15,57,59, M. Ashdown65,5, J. Aumont95, C. Baccigalupi78, M. Ballardini21,41, A. J. Banday95,8, R. B. Barreiro61, N. Bartolo29,62, S. Basak85, R. Battye64, K. Benabed55,90, J.-P. Bernard95,8, M. Bersanelli32,45, P. Bielewicz75,78, J. J. Bock63,10, J. R. Bond7, J. Borrill12,93, F. R. Bouchet55,90, F. Boulanger89,54,55, M. Bucher2,6, C. Burigana44,30,47, R. C. Butler41, E. Calabrese82, J.-F. Cardoso55,90, J. Carron23, A. Challinor58,65,11, H. C. Chiang25,6, J. Chluba64, L. P. L. Colombo32, C. Combet68, D. Contreras20, B. P. Crill63,10, F. Cuttaia41, P. de Bernardis31, G. de Zotti42, J. Delabrouille2, J.-M. Delouis67, E. Di Valentino64, J. M. Diego61, O. Doré63,10, M. Douspis54, A. Ducout66, X. Dupac35, S. Dusini62, G. Efstathiou65,58 , F. Elsner72, T. A. Enßlin72, H. K. Eriksen59, Y. Fantaye3,19, M. Farhang76, J. Fergusson11, R. Fernandez-Cobos61, F. Finelli41,47, F. Forastieri30,48, M. Frailis43, A. A. Fraisse25, E. Franceschi41, A. Frolov87, S. Galeotta43, S. Galli55,90 , K. Ganga2, R. T. Génova-Santos60,16, M. Gerbino38, T. Ghosh81,9, J. González-Nuevo17, K. M. Górski63,97, S. Gratton65,58, A. Gruppuso41,47, J. E. Gudmundsson94,25, J. Hamann86, W. Handley65,5, F. K. Hansen59, D. Herranz61, S. R. Hildebrandt63,10, E. Hivon55,90, Z. Huang83, A. H. Jaffe53, W. C. Jones25, A. Karakci59, E. Keihänen24, R. Keskitalo12, K. Kiiveri24,40, J. Kim72, T. S. Kisner70, L. Knox27, N. Krachmalnicoff78, M. Kunz14,54,3, H. Kurki-Suonio24,40, G. Lagache4, J.-M. Lamarre89, A. Lasenby5,65, M. Lattanzi48,30, C. R. Lawrence63, M. Le Jeune2, P. Lemos58,65, J. Lesgourgues 56, F. Levrier89, A. Lewis23 , M. Liguori29,62, P. B. Lilje59, M. Lilley55,90, V. Lindholm24,40, M. López-Caniego35, P. M. Lubin28, Y.-Z. Ma77,80,74, J. F. Macías-Pérez68, G. Maggio43, D. Maino32,45,49, N. Mandolesi41,30, A. Mangilli8, A. Marcos-Caballero61, M. Maris43, P. G. Martin7, M. Martinelli96, E. Martínez-González61, S. Matarrese29,62,37, N. Mauri47, J. D. McEwen73, P. R. Meinhold28, A. Melchiorri31,50, A. Mennella32,45, M. Migliaccio34,51, M. Millea27,88,55, S. Mitra52,63, M.-A. Miville-Deschênes1,54, D. Molinari30,41,48, L. Montier95,8, G. Morgante41, A. Moss84, P. Natoli30,92,48, H. U. Nørgaard-Nielsen13, L. Pagano30,48,54, D. Paoletti41,47, B. Partridge39, G. Patanchon2, H. V. Peiris22, F. Perrotta78, V. Pettorino1, F. Piacentini31, L. Polastri30,48, G. Polenta92, J.-L. Puget54,55, J. P. Rachen18, M. Reinecke72, M. Remazeilles64, A. Renzi 62, G. Rocha63,10, C. Rosset2, G. Roudier2,89,63, J. A Rubiño-Martín60,16, B. Ruiz-Granados60,16, L. Salvati54, M. Sandri41, M. Savelainen24,40,71, D. Scott20, E. P. S. Shellard11, C. Sirignano29,62, G. Sirri47, L. D. Spencer82, R. Sunyaev72,91, A.-S. Suur-Uski24,40, J. A. Tauber36, D. Tavagnacco43,33, M. Tenti46, L. Toffolatti17,41, M. Tomasi32,45, T. Trombetti44,48, L. Valenziano41, J. Valiviita24,40, B. Van Tent69, L. Vibert54,55, P. Vielva61, F. Villa41, N. Vittorio34, B.D. Wandelt55,90, I. K. Wehus59, M. White26, S. D. M. White72, A. Zacchei43, and A. Zonca79

Observations of the submillimetre emission from Galactic dust, in both total intensity I and polarization, have received tremendous interest thanks to the Planck full-sky maps. In this paper we make use of such full-sky maps of dust polarized emission produced from the third public release of Planck data. As the basis for expanding on astrophysical studies of the polarized thermal emission from Galactic dust, we present full-sky maps of the dust polarization fraction p, polarization angle psi, and dispersion function of polarization angles ?. The joint distribution (one-point statistics) of p and N-H confirms that the mean and maximum polarization fractions decrease with increasing N-H. The uncertainty on the maximum observed polarization fraction, (max) = 22.0(-1.4)(+3.5) p max = 22 . 0 - 1.4 + 3.5 % at 353 GHz and 80 ' resolution, is dominated by the uncertainty on the Galactic emission zero level in total intensity, in particular towards diffuse lines of sight at high Galactic latitudes. Furthermore, the inverse behaviour between p and ? found earlier is seen to be present at high latitudes. This follows the ?proportional to p(-1) relationship expected from models of the polarized sky (including numerical simulations of magnetohydrodynamical turbulence) that include effects from only the topology of the turbulent magnetic field, but otherwise have uniform alignment and dust properties. Thus, the statistical properties of p, psi, and ? for the most part reflect the structure of the Galactic magnetic field. Nevertheless, we search for potential signatures of varying grain alignment and dust properties. First, we analyse the product map ?xp, looking for residual trends. While the polarization fraction p decreases by a factor of 3-4 between N-H=10(20) cm(-2) and N-H=2x10(22) cm(-2), out of the Galactic plane, this product ?xp only decreases by about 25%. Because ? is independent of the grain alignment efficiency, this demonstrates that the systematic decrease in p with N-H is determined mostly by the magnetic-field structure and not by a drop in grain alignment. This systematic trend is observed both in the diffuse interstellar medium (ISM) and in molecular clouds of the Gould Belt. Second, we look for a dependence of polarization properties on the dust temperature, as we would expect from the radiative alignment torque (RAT) theory. We find no systematic trend of ?xp with the dust temperature T-d, whether in the diffuse ISM or in the molecular clouds of the Gould Belt. In the diffuse ISM, lines of sight with high polarization fraction p and low polarization angle dispersion ? tend, on the contrary, to have colder dust than lines of sight with low p and high ?. We also compare the Planck thermal dust polarization with starlight polarization data in the visible at high Galactic latitudes. The agreement in polarization angles is remarkable, and is consistent with what we expect from the noise and the observed dispersion of polarization angles in the visible on the scale of the Planck beam. The two polarization emission-to-extinction ratios, R-P/p and R-S/V, which primarily characterize dust optical properties, have only a weak dependence on the column density, and converge towards the values previously determined for translucent lines of sight. We also determine an upper limit for the polarization fraction in extinction, p(V)/E(B-V), of 13% at high Galactic latitude, compatible with the polarization fraction p approximate to 20% observed at 353 GHz. Taken together, these results provide strong constraints for models of Galactic dust in diffuse gas.

The European Space Agency's Planck satellite, which was dedicated to studying the early Universe and its subsequent evolution, was launched on 14 May 2009. It scanned the microwave and submillimetre sky continuously between 12 August 2009 and 23 October 2013, producing deep, high-resolution, all-sky maps in nine frequency bands from 30 to 857 GHz. This paper presents the cosmological legacy of Planck, which currently provides our strongest constraints on the parameters of the standard cosmological model and some of the tightest limits available on deviations from that model. The 6-parameter Lambda CDM model continues to provide an excellent fit to the cosmic microwave background data at high and low redshift, describing the cosmological information in over a billion map pixels with just six parameters. With 18 peaks in the temperature and polarization angular power spectra constrained well, Planck measures five of the six parameters to better than 1% (simultaneously), with the best-determined parameter (theta (*)) now known to 0.03%. We describe the multi-component sky as seen by Planck, the success of the Lambda CDM model, and the connection to lower-redshift probes of structure formation. We also give a comprehensive summary of the major changes introduced in this 2018 release. The Planck data, alone and in combination with other probes, provide stringent constraints on our models of the early Universe and the large-scale structure within which all astrophysical objects form and evolve. We discuss some lessons learned from the Planck mission, and highlight areas ripe for further experimental advances.

We present a final description of the data-processing pipeline for the Planck, Low Frequency Instrument (LFI), implemented for the 2018 data release. Several improvements have been made with respect to the previous release, especially in the calibration process and in the correction of instrumental features such as the effects of nonlinearity in the response of the analogue-to-digital converters. We provide a brief pedagogical introduction to the complete pipeline, as well as a detailed description of the important changes implemented. Self-consistency of the pipeline is demonstrated using dedicated simulations and null tests. We present the final version of the LFI full sky maps at 30, 44, and 70 GHz, both in temperature and polarization, together with a refined estimate of the Solar dipole and a final assessment of the main LFI instrumental parameters.

We present full-sky maps of the cosmic microwave background (CMB) and polarized synchrotron and thermal dust emission, derived from the third set of Planck frequency maps. These products have significantly lower contamination from instrumental systematic effects than previous versions. The methodologies used to derive these maps follow those described in earlier papers, adopting four methods (Commander, NILC, SEVEM, and SMICA) to extract the CMB component, as well as three methods (Commander, GNILC, and SMICA) to extract astrophysical components. Our revised CMB temperature maps agree with corresponding products in the Planck 2015 delivery, whereas the polarization maps exhibit significantly lower large-scale power, reflecting the improved data processing described in companion papers; however, the noise properties of the resulting data products are complicated, and the best available end-to-end simulations exhibit relative biases with respect to the data at the few percent level. Using these maps, we are for the first time able to fit the spectral index of thermal dust independently over 3 degree regions. We derive a conservative estimate of the mean spectral index of polarized thermal dust emission of beta_d = 1.55 +/- 0.05, where the uncertainty marginalizes both over all known systematic uncertainties and different estimation techniques. For polarized synchrotron emission, we find a mean spectral index of beta_s = -3.1 +/- 0.1, consistent with previously reported measurements. We note that the current data processing does not allow for construction of unbiased single-bolometer maps, and this limits our ability to extract CO emission and correlated components. The foreground results for intensity derived in this paper therefore do not supersede corresponding Planck 2015 products. For polarization the new results supersede the corresponding 2015 products in all respects.

We report on the implications for cosmic inflation of the 2018 release of the Planck cosmic microwave background (CMB) anisotropy measurements. The results are fully consistent with those reported using the data from the two previous Planck cosmological releases, but have smaller uncertainties thanks to improvements in the characterization of polarization at low and high multipoles. Planck temperature, polarization, and lensing data determine the spectral index of scalar perturbations to be n(s)=0.9649 +/- 0.0042 at 68% CL. We find no evidence for a scale dependence of n(s), either as a running or as a running of the running. The Universe is found to be consistent with spatial flatness with a precision of 0.4% at 95% CL by combining Planck with a compilation of baryon acoustic oscillation data. The Planck 95% CL upper limit on the tensor-to-scalar ratio, r(0.002)< 0.10, is further tightened by combining with the BICEP2/Keck Array BK15 data to obtain r(0.002)< 0.056. In the framework of standard single-field inflationary models with Einstein gravity, these results imply that: (a) the predictions of slow-roll models with a concave potential, V ''(phi) < 0, are increasingly favoured by the data; and (b) based on two different methods for reconstructing the inflaton potential, we find no evidence for dynamics beyond slow roll. Three different methods for the non-parametric reconstruction of the primordial power spectrum consistently confirm a pure power law in the range of comoving scales 0.005 Mpc(-1)less than or similar to k less than or similar to 0.2 Mpc(-1). A complementary analysis also finds no evidence for theoretically motivated parameterized features in the Planck power spectra. For the case of oscillatory features that are logarithmic or linear in k, this result is further strengthened by a new combined analysis including the Planck bispectrum data. The new Planck polarization data provide a stringent test of the adiabaticity of the initial conditions for the cosmological fluctuations. In correlated, mixed adiabatic and isocurvature models, the non-adiabatic contribution to the observed CMB temperature variance is constrained to 1.3%, 1.7%, and 1.7% at 95% CL for cold dark matter, neutrino density, and neutrino velocity, respectively. Planck power spectra plus lensing set constraints on the amplitude of compensated cold dark matter-baryon isocurvature perturbations that are consistent with current complementary measurements. The polarization data also provide improved constraints on inflationary models that predict a small statistically anisotropic quadupolar modulation of the primordial fluctuations. However, the polarization data do not support physical models for a scale-dependent dipolar modulation. All these findings support the key predictions of the standard single-field inflationary models, which will be further tested by future cosmological observations.

We describe an extension of the most recent version of the Planck Catalogue of Compact Sources (PCCS2), produced using a new multi-band Bayesian Extraction and Estimation Package (BeeP). BeeP assumes that the compact sources present in PCCS2 at 857 GHz have a dust-like spectral energy distribution (SED), which leads to emission at both lower and higher frequencies, and adjusts the parameters of the source and its SED to fit the emission observed in Planck's three highest frequency channels at 353, 545, and 857 GHz, as well as the IRIS map at 3000 GHz. In order to reduce confusion regarding diffuse cirrus emission, BeeP's data model includes a description of the background emission surrounding each source, and it adjusts the confidence in the source parameter extraction based on the statistical properties of the spatial distribution of the background emission. BeeP produces the following three new sets of parameters for each source: (a) fits to a modified blackbody (MBB) thermal emission model of the source; (b) SED-independent source flux densities at each frequency considered; and (c) fits to an MBB model of the background in which the source is embedded. BeeP also calculates, for each source, a reliability parameter, which takes into account confusion due to the surrounding cirrus. This parameter can be used to extract sub-samples of high-frequency sources with statistically well-understood properties. We define a high-reliability subset (BeeP/base), containing 26 083 sources (54.1% of the total PCCS2 catalogue), the majority of which have no information on reliability in the PCCS2. We describe the characteristics of this specific high-quality subset of PCCS2 and its validation against other data sets, specifically for: the sub-sample of PCCS2 located in low-cirrus areas; the Planck Catalogue of Galactic Cold Clumps; the Herschel GAMA15-field catalogue; and the temperature- and spectral-index-reconstructed dust maps obtained with Planck's Generalized Needlet Internal Linear Combination method. The results of the BeeP extension of PCCS2, which are made publicly available via the Planck Legacy Archive, will enable the study of the thermal properties of well-defined samples of compact Galactic and extragalactic dusty sources.

Analysis of the Planck 2018 data set indicates that the statistical properties of the cosmic microwave background (CMB) temperature anisotropies are in excellent agreement with previous studies using the 2013 and 2015 data releases. In particular, they are consistent with the Gaussian predictions of the Lambda CDM cosmological model, yet also confirm the presence of several so-called "anomalies" on large angular scales. The novelty of the current study, however, lies in being a first attempt at a comprehensive analysis of the statistics of the polarization signal over all angular scales, using either maps of the Stokes parameters, Q and U, or the E-mode signal derived from these using a new methodology (which we describe in an appendix). Although remarkable progress has been made in reducing the systematic effects that contaminated the 2015 polarization maps on large angular scales, it is still the case that residual systematics (and our ability to simulate them) can limit some tests of non-Gaussianity and isotropy. However, a detailed set of null tests applied to the maps indicates that these issues do not dominate the analysis on intermediate and large angular scales (i.e., l less than or similar to 400). In this regime, no unambiguous detections of cosmological non-Gaussianity, or of anomalies corresponding to those seen in temperature, are claimed. Notably, the stacking of CMB polarization signals centred on the positions of temperature hot and cold spots exhibits excellent agreement with the Lambda CDM cosmological model, and also gives a clear indication of how Planck provides state-of-the-art measurements of CMB temperature and polarization on degree scales.

We present an estimation of the reionization optical depth tau from an improved analysis of data from the High Frequency Instrument (HFI) on board the Planck satellite. By using an improved version of the HFI map-making code, we greatly reduce the residual large-scale contamination a ffecting the data, characterised in, but not fully removed from, the Planck 2018 legacy release. This brings the dipole distortion systematic e ffect, contaminating the very low multipoles, below the noise level. On large-scale polarization-only data, we measure tau = 0.0566(-0).(+0)(0062).(0053) at 68% C.L., reducing the Planck 2018 legacy release uncertainty by similar to 40%. Within the Lambda CDM model, in combination with the Planck large-scale temperature likelihood, and the high-l temperature and polarization likelihood, we measure tau = 0.059 +/- 0.006 at 68% C.L., which corresponds to a mid-point reionization redshift of z(re) = 8.14 +/- 0.61 at 68% C.L. This estimation of the reionization optical depth with 10% accuracy is the strongest constraint to date.

The study of polarized dust emission has become entwined with the analysis of the cosmic microwave background (CMB) polarization. We use new Planck maps to characterize Galactic dust emission as a foreground to the CMB polarization. We present Planck EE, BB, and TE power spectra of dust polarization at 353 GHz for six nested sky regions covering from 24 to 71 % of the sky. We present power-law fits to the angular power spectra, yielding evidence for statistically significant variations of the exponents over sky regions and a difference between the values for the EE and BB spectra. The TE correlation and E/B power asymmetry extend to low multipoles that were not included in earlier Planck polarization papers. We also report evidence for a positive TB dust signal. Combining data from Planck and WMAP, we determine the amplitudes and spectral energy distributions (SEDs) of polarized foregrounds, including the correlation between dust and synchrotron polarized emission, for the six sky regions as a function of multipole. This quantifies the challenge of the component separation procedure required for detecting the reionization and recombination peaks of primordial CMB B modes. The SED of polarized dust emission is fit well by a single-temperature modified blackbody emission law from 353 GHz to below 70 GHz. For a dust temperature of 19.6 K, the mean spectral index for dust polarization is $\beta_{\rm d}^{P} = 1.53\pm0.02 $. By fitting multi-frequency cross-spectra, we examine the correlation of the dust polarization maps across frequency. We find no evidence for decorrelation. If the Planck limit for the largest sky region applies to the smaller sky regions observed by sub-orbital experiments, then decorrelation might not be a problem for CMB experiments aiming at a primordial B-mode detection limit on the tensor-to-scalar ratio $r\simeq0.01$ at the recombination peak.

We present cosmological parameter results from the final full-mission Planck measurements of the cosmic microwave background (CMB) anisotropies, combining information from the temperature and polarization maps and the lensing reconstruction. Compared to the 2015 results, improved measurements of large-scale polarization allow the reionization optical depth to be measured with higher precision, leading to significant gains in the precision of other correlated parameters. Improved modelling of the small-scale polarization leads to more robust constraints on many parameters, with residual modelling uncertainties estimated to affect them only at the 0.5 sigma level. We find good consistency with the standard spatially-flat 6-parameter Lambda CDM cosmology having a power-law spectrum of adiabatic scalar perturbations (denoted "base Lambda CDM" in this paper), from polarization, temperature, and lensing, separately and in combination. A combined analysis gives dark matter density Omega (c)h(2)=0.120 +/- 0.001, baryon density Omega (b)h(2)=0.0224 +/- 0.0001, scalar spectral index n(s)=0.965 +/- 0.004, and optical depth tau =0.054 +/- 0.007 (in this abstract we quote 68% confidence regions on measured parameters and 95% on upper limits). The angular acoustic scale is measured to 0.03% precision, with 100 theta (*)=1.0411 +/- 0.0003. These results are only weakly dependent on the cosmological model and remain stable, with somewhat increased errors, in many commonly considered extensions. Assuming the base-Lambda CDM cosmology, the inferred (model-dependent) late-Universe parameters are: Hubble constant H-0=(67.4 +/- 0.5) km s(-1) Mpc(-1); matter density parameter Omega (m)=0.315 +/- 0.007; and matter fluctuation amplitude sigma (8)=0.811 +/- 0.006. We find no compelling evidence for extensions to the base-Lambda CDM model. Combining with baryon acoustic oscillation (BAO) measurements (and considering single-parameter extensions) we constrain the effective extra relativistic degrees of freedom to be N-eff=2.99 +/- 0.17, in agreement with the Standard Model prediction N-eff=3.046, and find that the neutrino mass is tightly constrained to Sigma m(nu)< 0.12 eV. The CMB spectra continue to prefer higher lensing amplitudes than predicted in base CDM at over 2 sigma, which pulls some parameters that affect the lensing amplitude away from the Lambda CDM model; however, this is not supported by the lensing reconstruction or (in models that also change the background geometry) BAO data. The joint constraint with BAO measurements on spatial curvature is consistent with a flat universe, Omega (K)=0.001 +/- 0.002. Also combining with Type Ia supernovae (SNe), the dark-energy equation of state parameter is measured to be w(0)=-1.03 +/- 0.03, consistent with a cosmological constant. We find no evidence for deviations from a purely power-law primordial spectrum, and combining with data from BAO, BICEP2, and Keck Array data, we place a limit on the tensor-to-scalar ratio r(0.002)< 0.06. Standard big-bang nucleosynthesis predictions for the helium and deuterium abundances for the base-CDM cosmology are in excellent agreement with observations. The Planck base-Lambda CDM results are in good agreement with BAO, SNe, and some galaxy lensing observations, but in slight tension with the Dark Energy Survey's combined-probe results including galaxy clustering (which prefers lower fluctuation amplitudes or matter density parameters), and in significant, 3.6 sigma, tension with local measurements of the Hubble constant (which prefer a higher value). Simple model extensions that can partially resolve these tensions are not favoured by the Planck data.

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).

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)

This paper presents the High Frequency Instrument (HFI) data processing procedures for the Planck 2018 release. Major improvements in mapmaking have been achieved since the previous Planck 2015 release, many of which were used and described already in an intermediate paper dedicated to the Planck polarized data at low multipoles. These improvements enabled the first significant measurement of the reionization optical depth parameter using Planck-HFI data. This paper presents an extensive analysis of systematic effects, including the use of end-to-end simulations to facilitate their removal and characterize the residuals. The polarized data, which presented a number of known problems in the 2015 Planck release, are very significantly improved, especially the leakage from intensity to polarization. Calibration, based on the cosmic microwave background (CMB) dipole, is now extremely accurate and in the frequency range 100-353 GHz reduces intensity-to-polarization leakage caused by calibration mismatch. The Solar dipole direction has been determined in the three lowest HFI frequency channels to within one arc minute, and its amplitude has an absolute uncertainty smaller than 0.35 mu K, an accuracy of order 10(-4). This is a major legacy from the Planck HFI for future CMB experiments. The removal of bandpass leakage has been improved for the main high-frequency foregrounds by extracting the bandpass-mismatch coefficients for each detector as part of the mapmaking process; these values in turn improve the intensity maps. This is a major change in the philosophy of "frequency maps", which are now computed from single detector data, all adjusted to the same average bandpass response for the main foregrounds. End-to-end simulations have been shown to reproduce very well the relative gain calibration of detectors, as well as drifts within a frequency induced by the residuals of the main systematic effect (analogue-to-digital convertor non-linearity residuals). Using these simulations, we have been able to measure and correct the small frequency calibration bias induced by this systematic effect at the 10(-4) level. There is no detectable sign of a residual calibration bias between the first and second acoustic peaks in the CMB channels, at the 10(-3) level.