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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.

The largest temperature anisotropy in the cosmic microwave background (CMB) is the dipole, which has been measured with increasing accuracy for more than three decades, particularly with the Planck satellite. The simplest interpretation of the dipole is that it is due to our motion with respect to the rest frame of the CMB. Since current CMB experiments infer temperature anisotropies from angular intensity variations, the dipole modulates the temperature anisotropies with the same frequency dependence as the thermal Sunyaev-Zeldovich (tSZ) effect. We present the first, and significant, detection of this signal in the tSZ maps and find that it is consistent with direct measurements of the CMB dipole, as expected. The signal contributes power in the tSZ maps, which is modulated in a quadrupolar pattern, and we estimate its contribution to the tSZ bispectrum, noting that it contributes negligible noise to the bispectrum at relevant scales.

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.

The largest temperature anisotropy in the cosmic microwave background (CMB) is the dipole, which has been measured with increasing accuracy for more than three decades, particularly with the Planck satellite. The simplest interpretation of the dipole is that it is due to our motion with respect to the rest frame of the CMB. Since current CMB experiments infer temperature anisotropies from angular intensity variations, the dipole modulates the temperature anisotropies with the same frequency dependence as the thermal Sunyaev-Zeldovich (tSZ) effect. We present the first, and significant, detection of this signal in the tSZ maps and find that it is consistent with direct measurements of the CMB dipole, as expected. The signal contributes power in the tSZ maps, which is modulated in a quadrupolar pattern, and we estimate its contribution to the tSZ bispectrum, noting that it contributes negligible noise to the bispectrum at relevant scales.

We present the NPIPE processing pipeline, which produces calibrated frequency maps in temperature and polarization from data from the Planck Low Frequency Instrument (LFI) and High Frequency Instrument (HFI) using high-performance computers. NPIPE represents a natural evolution of previous Planck analysis efforts, and combines some of the most powerful features of the separate LFI and HFI analysis pipelines. For example, following the LFI 2018 processing procedure, NPIPE uses foreground polarization priors during the calibration stage in order to break scanning-induced degeneracies. Similarly, NPIPE employs the HFI 2018 time-domain processing methodology to correct for bandpass mismatch at all frequencies. In addition, NPIPE introduces several improvements, including, but not limited to: inclusion of the 8% of data collected during repointing manoeuvres; smoothing of the LFI reference load data streams; in-flight estimation of detector polarization parameters; and construction of maximally independent detector-set split maps. For component-separation purposes, important improvements include: maps that retain the CMB Solar dipole, allowing for high-precision relative calibration in higher-level analyses; well-defined single-detector maps, allowing for robust CO extraction; and HFI temperature maps between 217 and 857 GHz that are binned into 0′.9 pixels (Nside = 4096), ensuring that the full angular information in the data is represented in the maps even at the highest Planck resolutions. The net effect of these improvements is lower levels of noise and systematics in both frequency and component maps at essentially all angular scales, as well as notably improved internal consistency between the various frequency channels. Based on the NPIPE maps, we present the first estimate of the Solar dipole determined through component separation across all nine Planck frequencies. The amplitude is (3366.6 ± 2.7) μK, consistent with, albeit slightly higher than, earlier estimates. From the large-scale polarization data, we derive an updated estimate of the optical depth of reionization of τ = 0.051 ± 0.006, which appears robust with respect to data and sky cuts. There are 600 complete signal, noise and systematics simulations of the full-frequency and detector-set maps. As a Planck first, these simulations include full time-domain processing of the beam-convolved CMB anisotropies. The release of NPIPE maps and simulations is accompanied with a complete suite of raw and processed time-ordered data and the software, scripts, auxiliary data, and parameter files needed to improve further on the analysis and to run matching simulations.

We present the NPIPE processing pipeline, which produces calibrated frequency maps in temperature and polarization from data from the Planck Low Frequency Instrument (LFI) and High Frequency Instrument (HFI) using high-performance computers. NPIPE represents a natural evolution of previous Planck analysis efforts, and combines some of the most powerful features of the separate LFI and HFI analysis pipelines. For example, following the LFI 2018 processing procedure, NPIPE uses foreground polarization priors during the calibration stage in order to break scanning-induced degeneracies. Similarly, NPIPE employs the HFI 2018 time-domain processing methodology to correct for bandpass mismatch at all frequencies. In addition, NPIPE introduces several improvements, including, but not limited to: inclusion of the 8% of data collected during repointing manoeuvres; smoothing of the LFI reference load data streams; in-flight estimation of detector polarization parameters; and construction of maximally independent detector-set split maps. For component-separation purposes, important improvements include: maps that retain the CMB Solar dipole, allowing for high-precision relative calibration in higher-level analyses; well-defined single-detector maps, allowing for robust CO extraction; and HFI temperature maps between 217 and 857 GHz that are binned into 0′.9 pixels (Nside = 4096), ensuring that the full angular information in the data is represented in the maps even at the highest Planck resolutions. The net effect of these improvements is lower levels of noise and systematics in both frequency and component maps at essentially all angular scales, as well as notably improved internal consistency between the various frequency channels. Based on the NPIPE maps, we present the first estimate of the Solar dipole determined through component separation across all nine Planck frequencies. The amplitude is (3366.6 ± 2.7) μK, consistent with, albeit slightly higher than, earlier estimates. From the large-scale polarization data, we derive an updated estimate of the optical depth of reionization of τ = 0.051 ± 0.006, which appears robust with respect to data and sky cuts. There are 600 complete signal, noise and systematics simulations of the full-frequency and detector-set maps. As a Planck first, these simulations include full time-domain processing of the beam-convolved CMB anisotropies. The release of NPIPE maps and simulations is accompanied with a complete suite of raw and processed time-ordered data and the software, scripts, auxiliary data, and parameter files needed to improve further on the analysis and to run matching simulations.

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 ΛCDM 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 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 ΛCDM 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 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 closely 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° regions. We derive a conservative estimate of the mean spectral index of polarized thermal dust emission of βd = 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 βs = -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 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 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 optimal modal bispectrum estimators, finding consistent values for the local, equilateral, and orthogonal bispectrum amplitudes. Our combined temperature and polarization analysis produces the following final results: flocalNL= -0.9 ± 5.1; fequilNL= -26 ± 47; and forthoNL= -38 ± 24 (68% CL, statistical). These results include low-multipole (4 ≤ ℓ < 40) polarization data that are not included in our previous analysis. The results also pass an extensive battery of tests (with additional tests regarding foreground residuals compared to 2015), and they are stable with respect to our 2015 measurements (with small fluctuations, at the level of a fraction of a standard deviation, which is consistent with changes in data processing). Polarizationonly bispectra display a significant improvement in robustness; they can now be used independently to set primordial NG constraints with a sensitivity comparable to WMAP temperature-based results and they give excellent agreement. In addition to the analysis of the standard local, equilateral, and orthogonal bispectrum shapes, we consider a large number of additional cases, such as 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 nonprimordial lensing bispectrum is, however, detected with an improved significance compared to 2015, excluding the null hypothesis at 3.5σ. Beyond estimates of individual shape amplitudes, we also present model-independent reconstructions and analyses of the Planck CMB bispectrum. Our final constraint on the local primordial trispectrum shape is glocalNL= (-5.8 ± 6.5) × 104(68% CL, statistical), while constraints for other trispectrum shapes are also determined. Exploiting the tight limits on various bispectrum and trispectrum shapes, we constrain the parameter space of different early-Universe scenarios that generate primordial NG, including general single-field models of inflation, multi-field models (e.g. curvaton models), models of inflation with axion fields producing parity-violation bispectra in the tensor sector, and inflationary models involving vector-like fields with directionally-dependent bispectra. Our results provide a high-precision test for structure-formation scenarios, showing complete agreement with the basic picture of the CDM cosmology regarding the statistics of the initial conditions, with cosmic structures arising from adiabatic, passive, Gaussian, and primordial seed perturbations.

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 ΛCDM 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 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 ΛCDM 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 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 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 optimal modal bispectrum estimators, finding consistent values for the local, equilateral, and orthogonal bispectrum amplitudes. Our combined temperature and polarization analysis produces the following final results: flocalNL= -0.9 ± 5.1; fequilNL= -26 ± 47; and forthoNL= -38 ± 24 (68% CL, statistical). These results include low-multipole (4 ≤ ℓ < 40) polarization data that are not included in our previous analysis. The results also pass an extensive battery of tests (with additional tests regarding foreground residuals compared to 2015), and they are stable with respect to our 2015 measurements (with small fluctuations, at the level of a fraction of a standard deviation, which is consistent with changes in data processing). Polarizationonly bispectra display a significant improvement in robustness; they can now be used independently to set primordial NG constraints with a sensitivity comparable to WMAP temperature-based results and they give excellent agreement. In addition to the analysis of the standard local, equilateral, and orthogonal bispectrum shapes, we consider a large number of additional cases, such as 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 nonprimordial lensing bispectrum is, however, detected with an improved significance compared to 2015, excluding the null hypothesis at 3.5σ. Beyond estimates of individual shape amplitudes, we also present model-independent reconstructions and analyses of the Planck CMB bispectrum. Our final constraint on the local primordial trispectrum shape is glocalNL= (-5.8 ± 6.5) × 104(68% CL, statistical), while constraints for other trispectrum shapes are also determined. Exploiting the tight limits on various bispectrum and trispectrum shapes, we constrain the parameter space of different early-Universe scenarios that generate primordial NG, including general single-field models of inflation, multi-field models (e.g. curvaton models), models of inflation with axion fields producing parity-violation bispectra in the tensor sector, and inflationary models involving vector-like fields with directionally-dependent bispectra. Our results provide a high-precision test for structure-formation scenarios, showing complete agreement with the basic picture of the CDM cosmology regarding the statistics of the initial conditions, with cosmic structures arising from adiabatic, passive, Gaussian, and primordial seed perturbations.

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.

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 μK, 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.

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 closely 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° regions. We derive a conservative estimate of the mean spectral index of polarized thermal dust emission of βd = 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 βs = -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.

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 μK, 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.

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 ΛCDM 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 (θ∗) now known to 0.03%. We describe the multi-component sky as seen by Planck, the success of the ΛCDM 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 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 ns = 0.9649 ± 0.0042 at 68% CL. We find no evidence for a scale dependence of ns, 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, r0.002 < 0.10, is further tightened by combining with the BICEP2/Keck Array BK15 data to obtain r0.002 < 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″(φ) < 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 k 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 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 0.5σ level. We find good consistency with the standard spatially-flat 6-parameter ΛCDM cosmology having a power-law spectrum of adiabatic scalar perturbations (denoted "base ΛCDM"in this paper), from polarization, temperature, and lensing, separately and in combination. A combined analysis gives dark matter density ωch2 = 0.120 ± 0.001, baryon density ωbh2 = 0.0224 ± 0.0001, scalar spectral index ns = 0.965 ± 0.004, and optical depth τ = 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 100θ∗ = 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-ΛCDM cosmology, the inferred (model-dependent) late-Universe parameters are: Hubble constant H0 = (67.4 ± 0.5) km s-1 Mpc-1; matter density parameter ωm = 0.315 ± 0.007; and matter fluctuation amplitude σ8 = 0.811 ± 0.006. We find no compelling evidence for extensions to the base-ΛCDM model. Combining with baryon acoustic oscillation (BAO) measurements (and considering single-parameter extensions) we constrain the effective extra relativistic degrees of freedom to be Neff = 2.99 ± 0.17, in agreement with the Standard Model prediction Neff = 3.046, and find that the neutrino mass is tightly constrained to mν < 0.12 eV. The CMB spectra continue to prefer higher lensing amplitudes than predicted in base ΛCDM at over 2σ, which pulls some parameters that affect the lensing amplitude away from the ΛCDM 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, ωK = 0.001 ± 0.002. Also combining with Type Ia supernovae (SNe), the dark-energy equation of state parameter is measured to be w0 = -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 r0.002 < 0.06. Standard big-bang nucleosynthesis predictions for the helium and deuterium abundances for the base-ΛCDM cosmology are in excellent agreement with observations. The Planck base-ΛCDM 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, 3.6σ, 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.

The study of polarized dust emission has become entwined with the analysis of the cosmic microwave background (CMB) polarization in the quest for the curl-like B-mode polarization from primordial gravitational waves and the low-multipole E-mode polarization associated with the reionization of the Universe. We used the new Planck PR3 maps to characterize Galactic dust emission at high latitudes as a foreground to the CMB polarization and use end-to-end simulations to compute uncertainties and assess the statistical significance of our measurements. We present Planck EE, BB, and TE power spectra of dust polarization at 353 GHz for a set of six nested high-Galactic-latitude 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, which for the largest sky region are αEE = -2.42 ± 0.02 and αBB = -2.54 ± 0.02, respectively. The spectra show that the TE correlation and E/B power asymmetry discovered by Planck extend to low multipoles that were not included in earlier Planck polarization papers due to residual data systematics. We also report evidence for a positive TB dust signal. Combining data from Planck and WMAP, we have determined 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 that is required for measuring the low-ℓ reionization CMB E-mode signal and 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 black-body emission law from 353 GHz to below 70 GHz. For a dust temperature of 19.6 K, the mean dust spectral index for dust polarization is βdP = 1.53±0.02. The difference between indices for polarization and total intensity is βdP-βdI = 0.05±0.03. By fitting multi-frequency cross-spectra between Planck data at 100, 143, 217, and 353 GHz, we examine the correlation of the dust polarization maps across frequency. We find no evidence for a loss of correlation and provide lower limits to the correlation ratio that are tighter than values we derive from the correlation of the 217- and 353 GHz maps alone. If the Planck limit on decorrelation for the largest sky region applies to the smaller sky regions observed by sub-orbital experiments, then frequency decorrelation of dust polarization might not be a problem for CMB experiments aiming at a primordial B-mode detection limit on the tensor-to-scalar ratio r≃ 0.01 at the recombination peak. However, the Planck sensitivity precludes identifying how difficult the component-separation problem will be for more ambitious experiments targeting lower limits on r.

We present measurements of the cosmic microwave background (CMB) lensing potential using the final Planck 2018 temperature and polarization data. Using polarization maps filtered to account for the noise anisotropy, we increase the significance of the detection of lensing in the polarization maps from 5σ to 9σ. Combined with temperature, lensing is detected at 40σ. We present an extensive set of tests of the robustness of the lensingpotential power spectrum, and construct a minimum-variance estimator likelihood over lensing multipoles 8 ≤ L ≤ 400 (extending the range to lower L compared to 2015), which we use to constrain cosmological parameters. We find good consistency between lensing constraints and the results from the Planck CMB power spectra within the σCDM model. Combined with baryon density and other weak priors, the lensing analysis alone constrains σ8Ω0.25m= 0.589 ± 0.020 (1σ errors). Also combining with baryon acoustic oscillation data, we find tight individual parameter constraints, σ8 = 0.811 ± 0.019, H0 = 67.9+1.2-1.3km s-1Mpc-1, and m = 0.303+0.016-0.018. Combining with Planck CMB power spectrum data, we measure σ8 to better than 1% precision, finding σ8 = 0.811 ± 0.006. CMB lensing reconstruction data are complementary to galaxy lensing data at lower redshift, having a different degeneracy direction in σ8 - m space; we find consistency with the lensing results from the Dark Energy Survey, and give combined lensing-only parameter constraints that are tighter than joint results using galaxy clustering. Using the Planck cosmic infrared background (CIB) maps as an additional tracer of high-redshift matter, we make a combined Planck-only estimate of the lensing potential over 60% of the sky with considerably more small-scale signal.We additionally demonstrate delensing of the Planck power spectra using the joint and individual lensing potential estimates, detecting a maximum removal of 40% of the lensing-induced power in all spectra. The improvement in the sharpening of the acoustic peaks by including both CIB and the quadratic lensing reconstruction is detected at high significance.

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.

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 ΛCDM 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 (θ∗) now known to 0.03%. We describe the multi-component sky as seen by Planck, the success of the ΛCDM 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 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 ns = 0.9649 ± 0.0042 at 68% CL. We find no evidence for a scale dependence of ns, 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, r0.002 < 0.10, is further tightened by combining with the BICEP2/Keck Array BK15 data to obtain r0.002 < 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″(φ) < 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 k 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 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 0.5σ level. We find good consistency with the standard spatially-flat 6-parameter ΛCDM cosmology having a power-law spectrum of adiabatic scalar perturbations (denoted "base ΛCDM"in this paper), from polarization, temperature, and lensing, separately and in combination. A combined analysis gives dark matter density ωch2 = 0.120 ± 0.001, baryon density ωbh2 = 0.0224 ± 0.0001, scalar spectral index ns = 0.965 ± 0.004, and optical depth τ = 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 100θ∗ = 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-ΛCDM cosmology, the inferred (model-dependent) late-Universe parameters are: Hubble constant H0 = (67.4 ± 0.5) km s-1 Mpc-1; matter density parameter ωm = 0.315 ± 0.007; and matter fluctuation amplitude σ8 = 0.811 ± 0.006. We find no compelling evidence for extensions to the base-ΛCDM model. Combining with baryon acoustic oscillation (BAO) measurements (and considering single-parameter extensions) we constrain the effective extra relativistic degrees of freedom to be Neff = 2.99 ± 0.17, in agreement with the Standard Model prediction Neff = 3.046, and find that the neutrino mass is tightly constrained to mν < 0.12 eV. The CMB spectra continue to prefer higher lensing amplitudes than predicted in base ΛCDM at over 2σ, which pulls some parameters that affect the lensing amplitude away from the ΛCDM 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, ωK = 0.001 ± 0.002. Also combining with Type Ia supernovae (SNe), the dark-energy equation of state parameter is measured to be w0 = -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 r0.002 < 0.06. Standard big-bang nucleosynthesis predictions for the helium and deuterium abundances for the base-ΛCDM cosmology are in excellent agreement with observations. The Planck base-ΛCDM 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, 3.6σ, 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 present measurements of the cosmic microwave background (CMB) lensing potential using the final Planck 2018 temperature and polarization data. Using polarization maps filtered to account for the noise anisotropy, we increase the significance of the detection of lensing in the polarization maps from 5σ to 9σ. Combined with temperature, lensing is detected at 40σ. We present an extensive set of tests of the robustness of the lensingpotential power spectrum, and construct a minimum-variance estimator likelihood over lensing multipoles 8 ≤ L ≤ 400 (extending the range to lower L compared to 2015), which we use to constrain cosmological parameters. We find good consistency between lensing constraints and the results from the Planck CMB power spectra within the σCDM model. Combined with baryon density and other weak priors, the lensing analysis alone constrains σ8Ω0.25m= 0.589 ± 0.020 (1σ errors). Also combining with baryon acoustic oscillation data, we find tight individual parameter constraints, σ8 = 0.811 ± 0.019, H0 = 67.9+1.2-1.3km s-1Mpc-1, and m = 0.303+0.016-0.018. Combining with Planck CMB power spectrum data, we measure σ8 to better than 1% precision, finding σ8 = 0.811 ± 0.006. CMB lensing reconstruction data are complementary to galaxy lensing data at lower redshift, having a different degeneracy direction in σ8 - m space; we find consistency with the lensing results from the Dark Energy Survey, and give combined lensing-only parameter constraints that are tighter than joint results using galaxy clustering. Using the Planck cosmic infrared background (CIB) maps as an additional tracer of high-redshift matter, we make a combined Planck-only estimate of the lensing potential over 60% of the sky with considerably more small-scale signal.We additionally demonstrate delensing of the Planck power spectra using the joint and individual lensing potential estimates, detecting a maximum removal of 40% of the lensing-induced power in all spectra. The improvement in the sharpening of the acoustic peaks by including both CIB and the quadratic lensing reconstruction is detected at high significance.

The study of polarized dust emission has become entwined with the analysis of the cosmic microwave background (CMB) polarization in the quest for the curl-like B-mode polarization from primordial gravitational waves and the low-multipole E-mode polarization associated with the reionization of the Universe. We used the new Planck PR3 maps to characterize Galactic dust emission at high latitudes as a foreground to the CMB polarization and use end-to-end simulations to compute uncertainties and assess the statistical significance of our measurements. We present Planck EE, BB, and TE power spectra of dust polarization at 353 GHz for a set of six nested high-Galactic-latitude 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, which for the largest sky region are αEE = -2.42 ± 0.02 and αBB = -2.54 ± 0.02, respectively. The spectra show that the TE correlation and E/B power asymmetry discovered by Planck extend to low multipoles that were not included in earlier Planck polarization papers due to residual data systematics. We also report evidence for a positive TB dust signal. Combining data from Planck and WMAP, we have determined 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 that is required for measuring the low-ℓ reionization CMB E-mode signal and 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 black-body emission law from 353 GHz to below 70 GHz. For a dust temperature of 19.6 K, the mean dust spectral index for dust polarization is βdP = 1.53±0.02. The difference between indices for polarization and total intensity is βdP-βdI = 0.05±0.03. By fitting multi-frequency cross-spectra between Planck data at 100, 143, 217, and 353 GHz, we examine the correlation of the dust polarization maps across frequency. We find no evidence for a loss of correlation and provide lower limits to the correlation ratio that are tighter than values we derive from the correlation of the 217- and 353 GHz maps alone. If the Planck limit on decorrelation for the largest sky region applies to the smaller sky regions observed by sub-orbital experiments, then frequency decorrelation of dust polarization might not be a problem for CMB experiments aiming at a primordial B-mode detection limit on the tensor-to-scalar ratio r≃ 0.01 at the recombination peak. However, the Planck sensitivity precludes identifying how difficult the component-separation problem will be for more ambitious experiments targeting lower limits on r.

Modifications of General Relativity leave their imprint both on the cosmic expansion history through a non-trivial dark energy equation of state, and on the evolution of cosmological perturbations in the scalar and in the tensor sectors. In particular, the modification in the tensor sector gives rise to a notion of gravitational-wave (GW) luminosity distance, different from the standard electromagnetic luminosity distance, that can be studied with standard sirens at GW detectors such as LISA or third-generation ground based experiments. We discuss the predictions for modified GW propagation from some of the best studied theories of modified gravity, such as Horndeski or the more general degenerate higher order scalar-tensor (DHOST) theories, non-local infrared modifications of gravity, bigravity theories and the corresponding phenomenon of GW oscillation, as well as theories with extra or varying dimensions. We show that modified GW propagation is a completely generic phenomenon in modified gravity. We then use a simple parametrization of the effect in terms of two parameters (Ξ0,n), that is shown to fit well the results from a large class of models, to study the prospects of observing modified GW propagation using supermassive black hole binaries as standard sirens with LISA. We construct mock source catalogs and perform detailed Markov Chain Monte Carlo studies of the likelihood obtained from LISA standard sirens alone, as well as by combining them with CMB, BAO and SNe data to reduce the degeneracies between cosmological parameters. We find that the combination of LISA with the other cosmological datasets allows one to measure the parameter Ξ0 that characterizes modified GW propagation to the percent level accuracy, sufficient to test several modified gravity theories. LISA standard sirens can also improve constraints on GW oscillations induced by extra field content by about three orders of magnitude relative to the current capability of ground detectors. We also update the forecasts on the accuracy on H0 and on the dark-energy equation of state using more recent estimates for the LISA sensitivity.

Modifications of General Relativity leave their imprint both on the cosmic expansion history through a non-trivial dark energy equation of state, and on the evolution of cosmological perturbations in the scalar and in the tensor sectors. In particular, the modification in the tensor sector gives rise to a notion of gravitational-wave (GW) luminosity distance, different from the standard electromagnetic luminosity distance, that can be studied with standard sirens at GW detectors such as LISA or third-generation ground based experiments. We discuss the predictions for modified GW propagation from some of the best studied theories of modified gravity, such as Horndeski or the more general degenerate higher order scalar-tensor (DHOST) theories, non-local infrared modifications of gravity, bigravity theories and the corresponding phenomenon of GW oscillation, as well as theories with extra or varying dimensions. We show that modified GW propagation is a completely generic phenomenon in modified gravity. We then use a simple parametrization of the effect in terms of two parameters (Ξ0,n), that is shown to fit well the results from a large class of models, to study the prospects of observing modified GW propagation using supermassive black hole binaries as standard sirens with LISA. We construct mock source catalogs and perform detailed Markov Chain Monte Carlo studies of the likelihood obtained from LISA standard sirens alone, as well as by combining them with CMB, BAO and SNe data to reduce the degeneracies between cosmological parameters. We find that the combination of LISA with the other cosmological datasets allows one to measure the parameter Ξ0 that characterizes modified GW propagation to the percent level accuracy, sufficient to test several modified gravity theories. LISA standard sirens can also improve constraints on GW oscillations induced by extra field content by about three orders of magnitude relative to the current capability of ground detectors. We also update the forecasts on the accuracy on H0 and on the dark-energy equation of state using more recent estimates for the LISA sensitivity.

Our current understanding of the Universe is established through the pristinemeasurements of structure in the cosmic microwave background (CMB) and thedistribution and shapes of galaxies tracing the large scale structure (LSS) ofthe Universe. One key ingredient that underlies cosmological observables isthat the field that sources the observed structure is assumed to be initiallyGaussian with high precision. Nevertheless, a minimal deviation fromGaussianityis perhaps the most robust theoretical prediction of models thatexplain the observed Universe; itis necessarily present even in the simplestscenarios. In addition, most inflationary models produce far higher levels ofnon-Gaussianity. Since non-Gaussianity directly probes the dynamics in theearly Universe, a detection would present a monumental discovery in cosmology,providing clues about physics at energy scales as high as the GUT scale.

This paper presents the Planck Multi-frequency Catalogue of Non-thermal (i.e. synchrotron-dominated) Sources (PCNT) observed between 30 and 857 GHz by the ESA Planck mission. This catalogue was constructed by selecting objects detected in the full mission all-sky temperature maps at 30 and 143 GHz, with a signal-to-noise ratio (S/N)> 3 in at least one of the two channels after filtering with a particular Mexican hat wavelet. As a result, 29 400 source candidates were selected. Then, a multi-frequency analysis was performed using the Matrix Filters methodology at the position of these objects, and flux densities and errors were calculated for all of them in the nine Planck channels. This catalogue was built using a different methodology than the one adopted for the Planck Catalogue of Compact Sources (PCCS) and the Second Planck Catalogue of Compact Sources (PCCS2), although the initial detection was done with the same pipeline that was used to produce them. The present catalogue is the first unbiased, full-sky catalogue of synchrotron-dominated sources published at millimetre and submillimetre wavelengths and constitutes a powerful database for statistical studies of non-thermal extragalactic sources, whose emission is dominated by the central active galactic nucleus. Together with the full multi-frequency catalogue, we also define the Bright Planck Multi-frequency Catalogue of Non-thermal Sources (PCNTb), where only those objects with a S/N > 4 at both 30 and 143 GHz were selected. In this catalogue 1146 compact sources are detected outside the adopted Planck GAL070 mask; thus, these sources constitute a highly reliable sample of extragalactic radio sources. We also flag the high-significance subsample (PCNThs), a subset of 151 sources that are detected with S/Na, >, 4 in all nine Planck channels, 75 of which are found outside the Planck mask adopted here. The remaining 76 sources inside the Galactic mask are very likely Galactic objects.

This paper presents the Planck Multi-frequency Catalogue of Non-thermal (i.e. synchrotron-dominated) Sources (PCNT) observed between 30 and 857 GHz by the ESA Planck mission. This catalogue was constructed by selecting objects detected in the full mission all-sky temperature maps at 30 and 143 GHz, with a signal-to-noise ratio (S/N)> 3 in at least one of the two channels after filtering with a particular Mexican hat wavelet. As a result, 29 400 source candidates were selected. Then, a multi-frequency analysis was performed using the Matrix Filters methodology at the position of these objects, and flux densities and errors were calculated for all of them in the nine Planck channels. This catalogue was built using a different methodology than the one adopted for the Planck Catalogue of Compact Sources (PCCS) and the Second Planck Catalogue of Compact Sources (PCCS2), although the initial detection was done with the same pipeline that was used to produce them. The present catalogue is the first unbiased, full-sky catalogue of synchrotron-dominated sources published at millimetre and submillimetre wavelengths and constitutes a powerful database for statistical studies of non-thermal extragalactic sources, whose emission is dominated by the central active galactic nucleus. Together with the full multi-frequency catalogue, we also define the Bright Planck Multi-frequency Catalogue of Non-thermal Sources (PCNTb), where only those objects with a S/N > 4 at both 30 and 143 GHz were selected. In this catalogue 1146 compact sources are detected outside the adopted Planck GAL070 mask; thus, these sources constitute a highly reliable sample of extragalactic radio sources. We also flag the high-significance subsample (PCNThs), a subset of 151 sources that are detected with S/Na, >, 4 in all nine Planck channels, 75 of which are found outside the Planck mask adopted here. The remaining 76 sources inside the Galactic mask are very likely Galactic objects.

Using the Planck full-mission data, we present a detection of the temperature (and therefore velocity) dispersion due to the kinetic Sunyaev-Zeldovich (kSZ) effect from clusters of galaxies. To suppress the primary CMB and instrumental noise we derive a matched filter and then convolve it with the Planck foreground-cleaned "2D-ILC" maps. By using the Meta Catalogue of X-ray detected Clusters of galaxies (MCXC), we determine the normalized rms dispersion of the temperature fluctuations at the positions of clusters, finding that this shows excess variance compared with the noise expectation. We then build an unbiased statistical estimator of the signal, determining that the normalized mean temperature dispersion of 1526 clusters is ((ΔT/T)2) = (1.64 ± 0.48) × 10-11. However, comparison with analytic calculations and simulations suggest that around 0.7 σ of this result is due to cluster lensing rather than the kSZ effect. By correcting this, the temperature dispersion is measured to be ((ΔT/T)2) = (1.35 ± 0.48) × 10-11, which gives a detection at the 2.8 σ level. We further convert uniform-weight temperature dispersion into a measurement of the line-of-sight velocity dispersion, by using estimates of the optical depth of each cluster (which introduces additional uncertainty into the estimate). We find that the velocity dispersion is (υ2) = (123 000 ± 71 000) (km s-1)2, which is consistent with findings from other large-scale structure studies, and provides direct evidence of statistical homogeneity on scales of 600 h-1 Mpc. Our study shows the promise of using cross-correlations of the kSZ effect with large-scale structure in order to constrain the growth of structure.

Using the Planck full-mission data, we present a detection of the temperature (and therefore velocity) dispersion due to the kinetic Sunyaev-Zeldovich (kSZ) effect from clusters of galaxies. To suppress the primary CMB and instrumental noise we derive a matched filter and then convolve it with the Planck foreground-cleaned "2D-ILC" maps. By using the Meta Catalogue of X-ray detected Clusters of galaxies (MCXC), we determine the normalized rms dispersion of the temperature fluctuations at the positions of clusters, finding that this shows excess variance compared with the noise expectation. We then build an unbiased statistical estimator of the signal, determining that the normalized mean temperature dispersion of 1526 clusters is ((ΔT/T)2) = (1.64 ± 0.48) × 10-11. However, comparison with analytic calculations and simulations suggest that around 0.7 σ of this result is due to cluster lensing rather than the kSZ effect. By correcting this, the temperature dispersion is measured to be ((ΔT/T)2) = (1.35 ± 0.48) × 10-11, which gives a detection at the 2.8 σ level. We further convert uniform-weight temperature dispersion into a measurement of the line-of-sight velocity dispersion, by using estimates of the optical depth of each cluster (which introduces additional uncertainty into the estimate). We find that the velocity dispersion is (υ2) = (123 000 ± 71 000) (km s-1)2, which is consistent with findings from other large-scale structure studies, and provides direct evidence of statistical homogeneity on scales of 600 h-1 Mpc. Our study shows the promise of using cross-correlations of the kSZ effect with large-scale structure in order to constrain the growth of structure.

We describe a space-borne, multi-band, multi-beam polarimeter aiming at a precise and accurate measurement of the polarization of the Cosmic Microwave Background. The instrument is optimized to be compatible with the strict budget requirements of a medium-size space mission within the Cosmic Vision Programme of the European Space Agency. The instrument has no moving parts, and uses arrays of diffraction-limited Kinetic Inductance Detectors to cover the frequency range from 60 GHz to 600 GHz in 19 wide bands, in the focal plane of a 1.2 m aperture telescope cooled at 40 K, allowing for an accurate extraction of the CMB signal from polarized foreground emission. The projected CMB polarization survey sensitivity of this instrument, after foregrounds removal, is 1.7 μKċarcmin. The design is robust enough to allow, if needed, a downscoped version of the instrument covering the 100 GHz to 600 GHz range with a 0.8 m aperture telescope cooled at 85 K, with a projected CMB polarization survey sensitivity of 3.2 μKċarcmin.

Lensing of the cosmic microwave background (CMB) is now a well-developed probe of the clustering of the large-scale mass distribution over a broad range of redshifts. By exploiting the non-Gaussian imprints of lensing in the polarization of the CMB, the CORE mission will allow production of a clean map of the lensing deflections over nearly the full-sky. The number of high-S/N modes in this map will exceed current CMB lensing maps by a factor of 40, and the measurement will be sample-variance limited on all scales where linear theory is valid. Here, we summarise this mission product and discuss the science that will follow from its power spectrum and the cross-correlation with other clustering data. For example, the summed mass of neutrinos will be determined to an accuracy of 17 meV combining CORE lensing and CMB two-point information with contemporaneous measurements of the baryon acoustic oscillation feature in the clustering of galaxies, three times smaller than the minimum total mass allowed by neutrino oscillation measurements. Lensing has applications across many other science goals of CORE, including the search for B-mode polarization from primordial gravitational waves. Here, lens-induced B-modes will dominate over instrument noise, limiting constraints on the power spectrum amplitude of primordial gravitational waves. With lensing reconstructed by CORE, one can "delens" the observed polarization internally, reducing the lensing B-mode power by 60 %. This can be improved to 70 % by combining lensing and measurements of the cosmic infrared background from CORE, leading to an improvement of a factor of 2.5 in the error on the amplitude of primordial gravitational waves compared to no delensing (in the null hypothesis of no primordial B-modes). Lensing measurements from CORE will allow calibration of the halo masses of the tens of thousands of galaxy clusters that it will find, with constraints dominated by the clean polarization-based estimators. The 19 frequency channels proposed for CORE will allow accurate removal of Galactic emission from CMB maps. We present initial findings that show that residual Galactic foreground contamination will not be a significant source of bias for lensing power spectrum measurements with CORE.

We present an analysis of the main systematic effects that could impact the measurement of CMB polarization with the proposed CORE space mission. We employ timeline-to-map simulations to verify that the CORE instrumental set-up and scanning strategy allow us to measure sky polarization to a level of accuracy adequate to the mission science goals. We also show how the CORE observations can be processed to mitigate the level of contamination by potentially worrying systematics, including intensity-to-polarization leakage due to bandpass mismatch, asymmetric main beams, pointing errors and correlated noise. We use analysis techniques that are well validated on data from current missions such as Planck to demonstrate how the residual contamination of the measurements by these effects can be brought to a level low enough not to hamper the scientific capability of the mission, nor significantly increase the overall error budget. We also present a prototype of the CORE photometric calibration pipeline, based on that used for Planck, and discuss its robustness to systematics, showing how CORE can achieve its calibration requirements. While a fine-grained assessment of the impact of systematics requires a level of knowledge of the system that can only be achieved in a future study phase, the analysis presented here strongly suggests that the main areas of concern for the CORE mission can be addressed using existing knowledge, techniques and algorithms.

Future observations of cosmic microwave background (CMB) polarisation have the potential to answer some of the most fundamental questions of modern physics and cosmology, including: what physical process gave birth to the Universe we see today? What are the dark matter and dark energy that seem to constitute 95% of the energy density of the Universe? Do we need extensions to the standard model of particle physics and fundamental interactions? Is the ΛCDM cosmological scenario correct, or are we missing an essential piece of the puzzle? In this paper, we list the requirements for a future CMB polarisation survey addressing these scientific objectives, and discuss the design drivers of the COREmfive space mission proposed to ESA in answer to the "M5" call for a medium-sized mission. The rationale and options, and the methodologies used to assess the mission's performance, are of interest to other future CMB mission design studies. COREmfive has 19 frequency channels, distributed over a broad frequency range, spanning the 60-600 GHz interval, to control astrophysical foreground emission. The angular resolution ranges from 2′ to 18′, and the aggregate CMB sensitivity is about 2 μKċarcmin. The observations are made with a single integrated focal-plane instrument, consisting of an array of 2100 cryogenically-cooled, linearly-polarised detectors at the focus of a 1.2-m aperture cross-Dragone telescope. The mission is designed to minimise all sources of systematic effects, which must be controlled so that no more than 10-4 of the intensity leaks into polarisation maps, and no more than about 1% of E-type polarisation leaks into B-type modes. COREmfive observes the sky from a large Lissajous orbit around the Sun-Earth L2 point on an orbit that offers stable observing conditions and avoids contamination from sidelobe pick-up of stray radiation originating from the Sun, Earth, and Moon. The entire sky is observed repeatedly during four years of continuous scanning, with a combination of three rotations of the spacecraft over different timescales. With about 50% of the sky covered every few days, this scan strategy provides the mitigation of systematic effects and the internal redundancy that are needed to convincingly extract the primordial B-mode signal on large angular scales, and check with adequate sensitivity the consistency of the observations in several independent data subsets. COREmfive is designed as a "near-ultimate" CMB polarisation mission which, for optimal complementarity with ground-based observations, will perform the observations that are known to be essential to CMB polarisation science and cannot be obtained by any other means than a dedicated space mission. It will provide well-characterised, highly-redundant multi-frequency observations of polarisation at all the scales where foreground emission and cosmic variance dominate the final uncertainty for obtaining precision CMB science, as well as 2′ angular resolution maps of high-frequency foreground emission in the 300-600 GHz frequency range, essential for complementarity with future ground-based observations with large telescopes that can observe the CMB with the same beamsize.

We discuss the potential of a next generation space-borne Cosmic Microwave Background (CMB) experiment for studies of extragalactic sources. Our analysis has particular bearing on the definition of the future space project, CORE, that has been submitted in response to ESA's call for a Medium-size mission opportunity as the successor of the Planck satellite. Even though the effective telescope size will be somewhat smaller than that of Planck, CORE will have a considerably better angular resolution at its highest frequencies, since, in contrast with Planck, it will be diffraction limited at all frequencies. The improved resolution implies a considerable decrease of the source confusion, i.e. substantially fainter detection limits. In particular, CORE will detect thousands of strongly lensed high-z galaxies distributed over the full sky. The extreme brightness of these galaxies will make it possible to study them, via follow-up observations, in extraordinary detail. Also, the CORE resolution matches the typical sizes of high-z galaxy proto-clusters much better than the Planck resolution, resulting in a much higher detection efficiency; these objects will be caught in an evolutionary phase beyond the reach of surveys in other wavebands. Furthermore, CORE will provide unique information on the evolution of the star formation in virialized groups and clusters of galaxies up to the highest possible redshifts. Finally, thanks to its very high sensitivity, CORE will detect the polarized emission of thousands of radio sources and, for the first time, of dusty galaxies, at mm and sub-mm wavelengths, respectively.

We describe a space-borne, multi-band, multi-beam polarimeter aiming at a precise and accurate measurement of the polarization of the Cosmic Microwave Background. The instrument is optimized to be compatible with the strict budget requirements of a medium-size space mission within the Cosmic Vision Programme of the European Space Agency. The instrument has no moving parts, and uses arrays of diffraction-limited Kinetic Inductance Detectors to cover the frequency range from 60 GHz to 600 GHz in 19 wide bands, in the focal plane of a 1.2 m aperture telescope cooled at 40 K, allowing for an accurate extraction of the CMB signal from polarized foreground emission. The projected CMB polarization survey sensitivity of this instrument, after foregrounds removal, is 1.7 μKċarcmin. The design is robust enough to allow, if needed, a downscoped version of the instrument covering the 100 GHz to 600 GHz range with a 0.8 m aperture telescope cooled at 85 K, with a projected CMB polarization survey sensitivity of 3.2 μKċarcmin.

We present an analysis of the main systematic effects that could impact the measurement of CMB polarization with the proposed CORE space mission. We employ timeline-to-map simulations to verify that the CORE instrumental set-up and scanning strategy allow us to measure sky polarization to a level of accuracy adequate to the mission science goals. We also show how the CORE observations can be processed to mitigate the level of contamination by potentially worrying systematics, including intensity-to-polarization leakage due to bandpass mismatch, asymmetric main beams, pointing errors and correlated noise. We use analysis techniques that are well validated on data from current missions such as Planck to demonstrate how the residual contamination of the measurements by these effects can be brought to a level low enough not to hamper the scientific capability of the mission, nor significantly increase the overall error budget. We also present a prototype of the CORE photometric calibration pipeline, based on that used for Planck, and discuss its robustness to systematics, showing how CORE can achieve its calibration requirements. While a fine-grained assessment of the impact of systematics requires a level of knowledge of the system that can only be achieved in a future study phase, the analysis presented here strongly suggests that the main areas of concern for the CORE mission can be addressed using existing knowledge, techniques and algorithms.

Future observations of cosmic microwave background (CMB) polarisation have the potential to answer some of the most fundamental questions of modern physics and cosmology, including: what physical process gave birth to the Universe we see today? What are the dark matter and dark energy that seem to constitute 95% of the energy density of the Universe? Do we need extensions to the standard model of particle physics and fundamental interactions? Is the ΛCDM cosmological scenario correct, or are we missing an essential piece of the puzzle? In this paper, we list the requirements for a future CMB polarisation survey addressing these scientific objectives, and discuss the design drivers of the COREmfive space mission proposed to ESA in answer to the "M5" call for a medium-sized mission. The rationale and options, and the methodologies used to assess the mission's performance, are of interest to other future CMB mission design studies. COREmfive has 19 frequency channels, distributed over a broad frequency range, spanning the 60-600 GHz interval, to control astrophysical foreground emission. The angular resolution ranges from 2′ to 18′, and the aggregate CMB sensitivity is about 2 μKċarcmin. The observations are made with a single integrated focal-plane instrument, consisting of an array of 2100 cryogenically-cooled, linearly-polarised detectors at the focus of a 1.2-m aperture cross-Dragone telescope. The mission is designed to minimise all sources of systematic effects, which must be controlled so that no more than 10-4 of the intensity leaks into polarisation maps, and no more than about 1% of E-type polarisation leaks into B-type modes. COREmfive observes the sky from a large Lissajous orbit around the Sun-Earth L2 point on an orbit that offers stable observing conditions and avoids contamination from sidelobe pick-up of stray radiation originating from the Sun, Earth, and Moon. The entire sky is observed repeatedly during four years of continuous scanning, with a combination of three rotations of the spacecraft over different timescales. With about 50% of the sky covered every few days, this scan strategy provides the mitigation of systematic effects and the internal redundancy that are needed to convincingly extract the primordial B-mode signal on large angular scales, and check with adequate sensitivity the consistency of the observations in several independent data subsets. COREmfive is designed as a "near-ultimate" CMB polarisation mission which, for optimal complementarity with ground-based observations, will perform the observations that are known to be essential to CMB polarisation science and cannot be obtained by any other means than a dedicated space mission. It will provide well-characterised, highly-redundant multi-frequency observations of polarisation at all the scales where foreground emission and cosmic variance dominate the final uncertainty for obtaining precision CMB science, as well as 2′ angular resolution maps of high-frequency foreground emission in the 300-600 GHz frequency range, essential for complementarity with future ground-based observations with large telescopes that can observe the CMB with the same beamsize.

We demonstrate that, for the baseline design of the CORE satellite mission, the polarized foregrounds can be controlled at the level required to allow the detection of the primordial cosmic microwave background (CMB) B-mode polarization with the desired accuracy at both reionization and recombination scales, for tensor-to-scalar ratio values of r 5× 10-3. We consider detailed sky simulations based on state-of-the-art CMB observations that consist of CMB polarization with τ=0.055 and tensor-to-scalar values ranging from r=10-2 to 10-3, Galactic synchrotron, and thermal dust polarization with variable spectral indices over the sky, polarized anomalous microwave emission, polarized infrared and radio sources, and gravitational lensing effects. Using both parametric and blind approaches, we perform full component separation and likelihood analysis of the simulations, allowing us to quantify both uncertainties and biases on the reconstructed primordial B-modes. Under the assumption of perfect control of lensing effects, CORE would measure an unbiased estimate of r=(5 ± 0.4)× 10-3 after foreground cleaning. In the presence of both gravitational lensing effects and astrophysical foregrounds, the significance of the detection is lowered, with CORE achieving a 4σ-measurement of r=5× 10-3 after foreground cleaning and 60% delensing. For lower tensor-to-scalar ratios (r=10-3) the overall uncertainty on r is dominated by foreground residuals, not by the 40% residual of lensing cosmic variance. Moreover, the residual contribution of unprocessed polarized point-sources can be the dominant foreground contamination to primordial B-modes at this r level, even on relatively large angular scales, ℓ ∼ 50. Finally, we report two sources of potential bias for the detection of the primordial B-modes by future CMB experiments: (i) the use of incorrect foreground models, e.g. a modelling error of Δβs = 0.02 on the synchrotron spectral indices may result in an excess in the recovered reionization peak corresponding to an effective Δ r > 10-3; (ii) the average of the foreground line-of-sight spectral indices by the combined effects of pixelization and beam convolution, which adds an effective curvature to the foreground spectral energy distribution and may cause spectral degeneracies with the CMB in the frequency range probed by the experiment.

We forecast the main cosmological parameter constraints achievable with the CORE space mission which is dedicated to mapping the polarisation of the Cosmic Microwave Background (CMB). CORE was recently submitted in response to ESA's fifth call for medium-sized mission proposals (M5). Here we report the results from our pre-submission study of the impact of various instrumental options, in particular the telescope size and sensitivity level, and review the great, transformative potential of the mission as proposed. Specifically, we assess the impact on a broad range of fundamental parameters of our Universe as a function of the expected CMB characteristics, with other papers in the series focusing on controlling astrophysical and instrumental residual systematics. In this paper, we assume that only a few central CORE frequency channels are usable for our purpose, all others being devoted to the cleaning of astrophysical contaminants. On the theoretical side, we assume ΛCDM as our general framework and quantify the improvement provided by CORE over the current constraints from the Planck 2015 release. We also study the joint sensitivity of CORE and of future Baryon Acoustic Oscillation and Large Scale Structure experiments like DESI and Euclid. Specific constraints on the physics of inflation are presented in another paper of the series. In addition to the six parameters of the base ΛCDM, which describe the matter content of a spatially flat universe with adiabatic and scalar primordial fluctuations from inflation, we derive the precision achievable on parameters like those describing curvature, neutrino physics, extra light relics, primordial helium abundance, dark matter annihilation, recombination physics, variation of fundamental constants, dark energy, modified gravity, reionization and cosmic birefringence. In addition to assessing the improvement on the precision of individual parameters, we also forecast the post-CORE overall reduction of the allowed parameter space with figures of merit for various models increasing by as much as ∼ 107 as compared to Planck 2015, and 105 with respect to Planck 2015 + future BAO measurements.

We examine the cosmological constraints that can be achieved with a galaxy cluster survey with the future CORE space mission. Using realistic simulations of the millimeter sky, produced with the latest version of the Planck Sky Model, we characterize the CORE cluster catalogues as a function of the main mission performance parameters. We pay particular attention to telescope size, key to improved angular resolution, and discuss the comparison and the complementarity of CORE with ambitious future ground-based CMB experiments that could be deployed in the next decade. A possible CORE mission concept with a 150 cm diameter primary mirror can detect of the order of 50,000 clusters through the thermal Sunyaev-Zeldovich effect (SZE). The total yield increases (decreases) by 25% when increasing (decreasing) the mirror diameter by 30 cm. The 150 cm telescope configuration will detect the most massive clusters (>1014 Mo) at redshift z>1.5 over the whole sky, although the exact number above this redshift is tied to the uncertain evolution of the cluster SZE flux-mass relation; assuming self-similar evolution, CORE will detect 0∼ 50 clusters at redshift z>1.5. This changes to 800 (200) when increasing (decreasing) the mirror size by 30 cm. CORE will be able to measure individual cluster halo masses through lensing of the cosmic microwave background anisotropies with a 1-σ sensitivity of 4×1014 Mo, for a 120 cm aperture telescope, and 1014 Mo for a 180 cm one. From the ground, we estimate that, for example, a survey with about 150,000 detectors at the focus of 350 cm telescopes observing 65% of the sky would be shallower than CORE and detect about 11,000 clusters, while a survey with the same number of detectors observing 25% of sky with a 10 m telescope is expected to be deeper and to detect about 70,000 clusters. When combined with the latter, CORE would reach a limiting mass of M500 ∼ 2-3 × 1013 Mo and detect 220,000 clusters (5 sigma detection limit). Cosmological constraints from CORE cluster counts alone are competitive with other scheduled large scale structure surveys in the 2020's for measuring the dark energy equation-of-state parameters w0 and wa (σw0=0.28, σwa=0.31). In combination with primary CMB constraints, CORE cluster counts can further reduce these error bars on w0 and wa to 0.05 and 0.13 respectively, and constrain the sum of the neutrino masses, Σ mν, to 39 meV (1 sigma). The wide frequency coverage of CORE, 60-600 GHz, will enable measurement of the relativistic thermal SZE by stacking clusters. Contamination by dust emission from the clusters, however, makes constraining the temperature of the intracluster medium difficult. The kinetic SZE pairwise momentum will be extracted with 0S/N=7 in the foreground-cleaned CMB map. Measurements of TCMB(z) using CORE clusters will establish competitive constraints on the evolution of the CMB temperature: (1+z)1-β, with an uncertainty of σβ ≲ 2.7× 10-3 at low redshift (z ≲ 1). The wide frequency coverage also enables clean extraction of a map of the diffuse SZE signal over the sky, substantially reducing contamination by foregrounds compared to the Planck SZE map extraction. Our analysis of the one-dimensional distribution of Compton-y values in the simulated map finds an order of magnitude improvement in constraints on σ8 over the Planck result, demonstrating the potential of this cosmological probe with CORE.

We forecast the scientific capabilities to improve our understanding of cosmic inflation of CORE, a proposed CMB space satellite submitted in response to the ESA fifth call for a medium-size mission opportunity. The CORE satellite will map the CMB anisotropies in temperature and polarization in 19 frequency channels spanning the range 60-600 GHz. CORE will have an aggregate noise sensitivity of 1.7 μKċ arcmin and an angular resolution of 5' at 200 GHz. We explore the impact of telescope size and noise sensitivity on the inflation science return by making forecasts for several instrumental configurations. This study assumes that the lower and higher frequency channels suffice to remove foreground contaminations and complements other related studies of component separation and systematic effects, which will be reported in other papers of the series "Exploring Cosmic Origins with CORE." We forecast the capability to determine key inflationary parameters, to lower the detection limit for the tensor-to-scalar ratio down to the 10-3 level, to chart the landscape of single field slow-roll inflationary models, to constrain the epoch of reheating, thus connecting inflation to the standard radiation-matter dominated Big Bang era, to reconstruct the primordial power spectrum, to constrain the contribution from isocurvature perturbations to the 10-3 level, to improve constraints on the cosmic string tension to a level below the presumptive GUT scale, and to improve the current measurements of primordial non-Gaussianities down to the fNLlocal < 1 level. For all the models explored, CORE alone will improve significantly on the present constraints on the physics of inflation. Its capabilities will be further enhanced by combining with complementary future cosmological observations.

We discuss the effects on the cosmic microwave background (CMB), cosmic infrared background (CIB), and thermal Sunyaev-Zeldovich effect due to the peculiar motion of an observer with respect to the CMB rest frame, which induces boosting effects. After a brief review of the current observational and theoretical status, we investigate the scientific perspectives opened by future CMB space missions, focussing on the Cosmic Origins Explorer (CORE) proposal. The improvements in sensitivity offered by a mission like CORE, together with its high resolution over a wide frequency range, will provide a more accurate estimate of the CMB dipole. The extension of boosting effects to polarization and cross-correlations will enable a more robust determination of purely velocity-driven effects that are not degenerate with the intrinsic CMB dipole, allowing us to achieve an overall signal-to-noise ratio of 13; this improves on the Planck detection and essentially equals that of an ideal cosmic-variance-limited experiment up to a multipole ℓ2000. Precise inter-frequency calibration will offer the opportunity to constrain or even detect CMB spectral distortions, particularly from the cosmological reionization epoch, because of the frequency dependence of the dipole spectrum, without resorting to precise absolute calibration. The expected improvement with respect to COBE-FIRAS in the recovery of distortion parameters (which could in principle be a factor of several hundred for an ideal experiment with the CORE configuration) ranges from a factor of several up to about 50, depending on the quality of foreground removal and relative calibration. Even in the case of 1 % accuracy in both foreground removal and relative calibration at an angular scale of 1-, we find that dipole analyses for a mission like CORE will be able to improve the recovery of the CIB spectrum amplitude by a factor 17 in comparison with current results based on COBE-FIRAS. In addition to the scientific potential of a mission like CORE for these analyses, synergies with other planned and ongoing projects are also discussed.

Lensing of the cosmic microwave background (CMB) is now a well-developed probe of the clustering of the large-scale mass distribution over a broad range of redshifts. By exploiting the non-Gaussian imprints of lensing in the polarization of the CMB, the CORE mission will allow production of a clean map of the lensing deflections over nearly the full-sky. The number of high-S/N modes in this map will exceed current CMB lensing maps by a factor of 40, and the measurement will be sample-variance limited on all scales where linear theory is valid. Here, we summarise this mission product and discuss the science that will follow from its power spectrum and the cross-correlation with other clustering data. For example, the summed mass of neutrinos will be determined to an accuracy of 17 meV combining CORE lensing and CMB two-point information with contemporaneous measurements of the baryon acoustic oscillation feature in the clustering of galaxies, three times smaller than the minimum total mass allowed by neutrino oscillation measurements. Lensing has applications across many other science goals of CORE, including the search for B-mode polarization from primordial gravitational waves. Here, lens-induced B-modes will dominate over instrument noise, limiting constraints on the power spectrum amplitude of primordial gravitational waves. With lensing reconstructed by CORE, one can "delens" the observed polarization internally, reducing the lensing B-mode power by 60 %. This can be improved to 70 % by combining lensing and measurements of the cosmic infrared background from CORE, leading to an improvement of a factor of 2.5 in the error on the amplitude of primordial gravitational waves compared to no delensing (in the null hypothesis of no primordial B-modes). Lensing measurements from CORE will allow calibration of the halo masses of the tens of thousands of galaxy clusters that it will find, with constraints dominated by the clean polarization-based estimators. The 19 frequency channels proposed for CORE will allow accurate removal of Galactic emission from CMB maps. We present initial findings that show that residual Galactic foreground contamination will not be a significant source of bias for lensing power spectrum measurements with CORE.

We discuss the potential of a next generation space-borne Cosmic Microwave Background (CMB) experiment for studies of extragalactic sources. Our analysis has particular bearing on the definition of the future space project, CORE, that has been submitted in response to ESA's call for a Medium-size mission opportunity as the successor of the Planck satellite. Even though the effective telescope size will be somewhat smaller than that of Planck, CORE will have a considerably better angular resolution at its highest frequencies, since, in contrast with Planck, it will be diffraction limited at all frequencies. The improved resolution implies a considerable decrease of the source confusion, i.e. substantially fainter detection limits. In particular, CORE will detect thousands of strongly lensed high-z galaxies distributed over the full sky. The extreme brightness of these galaxies will make it possible to study them, via follow-up observations, in extraordinary detail. Also, the CORE resolution matches the typical sizes of high-z galaxy proto-clusters much better than the Planck resolution, resulting in a much higher detection efficiency; these objects will be caught in an evolutionary phase beyond the reach of surveys in other wavebands. Furthermore, CORE will provide unique information on the evolution of the star formation in virialized groups and clusters of galaxies up to the highest possible redshifts. Finally, thanks to its very high sensitivity, CORE will detect the polarized emission of thousands of radio sources and, for the first time, of dusty galaxies, at mm and sub-mm wavelengths, respectively.