We present the implications for cosmic inflation of the Planck measurements of the cosmic microwave background (CMB) anisotropies in both temperature and polarization based on the full Planck survey, which includes more than twice the integration time of the nominal survey used for the 2013 release papers. The Planck full mission temperature data and a first release of polarization data on large angular scales measure the spectral index of curvature perturbations to be n s = 0.968 ± 0.006 and tightly constrain its scale dependence to dn s /dln k = −0.003 ± 0.007 when combined with the Planck lensing likelihood. When the Planck high-polarization data are included, the results are consistent and uncertainties are further reduced. The upper bound on the tensor-to-scalar ratio is r 0.002 < 0.11 (95% CL). This upper limit is consistent with the B-mode polarization constraint r < 0.12 (95% CL) obtained from a joint analysis of the BICEP2/Keck Array and Planck data. These results imply that V(φ) ∝ φ 2 and natural inflation are now disfavoured compared to models predicting a smaller tensor-to-scalar ratio, such as R 2 inflation. We search for several physically motivated deviations from a simple power-law spectrum of curvature perturbations, including those motivated by a reconstruction of the inflaton potential not relying on the slow-roll approximation. We find that such models are not preferred, either according to a Bayesian model comparison or according to a frequentist simulation-based analysis. Three independent methods reconstructing the primordial power spectrum consistently recover a featureless and smooth P R (k) over the range of scales 0.008 Mpc −1 < ∼ k < ∼ 0.1 Mpc −1 . At large scales, each method finds deviations from a power law, connected to a deficit at multipoles ≈ 20−40 in the temperature power spectrum, but at an uncompelling statistical significance owing to the large cosmic variance present at these multipoles. By combining power spectrum and non-Gaussianity bounds, we constrain models with generalized Lagrangians, including Galileon models and axion monodromy models. The Planck data are consistent with adiabatic primordial perturbations, and the estimated values for the parameters of the base Λ cold dark matter (ΛCDM) model are not significantly altered when more general initial conditions are admitted. In correlated mixed adiabatic and isocurvature models, the 95% CL upper bound for the non-adiabatic contribution to the observed CMB temperature variance is |α non-adi | < 1.9%, 4.0%, and 2.9% for CDM, neutrino density, and neutrino velocity isocurvature modes, respectively. We have tested inflationary models producing an anisotropic modulation of the primordial curvature power spectrum finding that the dipolar modulation in the CMB temperature field induced by a CDM isocurvature perturbation is not preferred at a statistically significant level. We also establish tight constraints on a possible quadrupolar modulation of the curvature perturbation. These results are consistent with the Pl...

We analyse the implications of the Planck data for cosmic inflation. The Planck nominal mission temperature anisotropy measurements, combined with the WMAP large-angle polarization, constrain the scalar spectral index to be n s = 0.9603 ± 0.0073, ruling out exact scale invariance at over 5σ. Planck establishes an upper bound on the tensor-to-scalar ratio of r < 0.11 (95% CL). The Planck data thus shrink the space of allowed standard inflationary models, preferring potentials with V < 0. Exponential potential models, the simplest hybrid inflationary models, and monomial potential models of degree n ≥ 2 do not provide a good fit to the data. Planck does not find statistically significant running of the scalar spectral index, obtaining dn s /dln k = −0.0134 ± 0.0090. We verify these conclusions through a numerical analysis, which makes no slowroll approximation, and carry out a Bayesian parameter estimation and model-selection analysis for a number of inflationary models including monomial, natural, and hilltop potentials. For each model, we present the Planck constraints on the parameters of the potential and explore several possibilities for the post-inflationary entropy generation epoch, thus obtaining nontrivial data-driven constraints. We also present a direct reconstruction of the observable range of the inflaton potential. Unless a quartic term is allowed in the potential, we find results consistent with second-order slow-roll predictions. We also investigate whether the primordial power spectrum contains any features. We find that models with a parameterized oscillatory feature improve the fit by ∆χ 2 eff ≈ 10; however, Bayesian evidence does not prefer these models. We constrain several single-field inflation models with generalized Lagrangians by combining power spectrum data with Planck bounds on f NL. Planck constrains with unprecedented accuracy the amplitude and possible correlation (with the adiabatic mode) of non-decaying isocurvature fluctuations. The fractional primordial contributions of cold dark matter (CDM) isocurvature modes of the types expected in the curvaton and axion scenarios have upper bounds of 0.25% and 3.9% (95% CL), respectively. In models with arbitrarily correlated CDM or neutrino isocurvature modes, an anticorrelated isocurvature component can improve the χ 2 eff by approximately 4 as a result of slightly lowering the theoretical prediction for the < ∼ 40 multipoles relative to the higher multipoles. Nonetheless, the data are consistent with adiabatic initial conditions.

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.

The European Space Agency's Planck satellite, dedicated to studying the early Universe and its subsequent evolution, was launched 14 May 2009 and has been scanning the microwave and submillimetre sky continuously since 12 August 2009. In March 2013, ESA and the Planck Collaboration released the initial cosmology products based on the first 15.5 months of Planck data, along with a set of scientific and technical papers and a web-based explanatory supplement. This paper gives an overview of the mission and its performance, the processing, analysis, and characteristics of the data, the scientific results, and the science data products and papers in the release. The science products include maps of the cosmic microwave background (CMB) and diffuse extragalactic foregrounds, a catalogue of compact Galactic and extragalactic sources, and a list of sources detected through the Sunyaev-Zeldovich effect. The likelihood code used to assess cosmological models against the Planck data and a lensing likelihood are described. Scientific results include robust support for the standard six-parameter ΛCDM model of cosmology and improved measurements of its parameters, including a highly significant deviation from scale invariance of the primordial power spectrum. The Planck values for these parameters and others derived from them are significantly different from those previously determined. Several large-scale anomalies in the temperature distribution of the CMB, first detected by WMAP, are confirmed with higher confidence. Planck sets new limits on the number and mass of neutrinos, and has measured gravitational lensing of CMB anisotropies at greater than 25σ. Planck finds no evidence for non-Gaussianity in the CMB. Planck's results agree well with results from the measurements of baryon acoustic oscillations. Planck finds a lower Hubble constant than found in some more local measures. Some tension is also present between the amplitude of matter fluctuations (σ 8 ) derived from CMB data and that derived from Sunyaev-Zeldovich data. The Planck and WMAP power spectra are offset from each other by an average level of about 2% around the first acoustic peak. Analysis of Planck polarization data is not yet mature, therefore polarization results are not released, although the robust detection of E-mode polarization around CMB hot and cold spots is shown graphically.

The two fundamental assumptions of the standard cosmological model -that the initial fluctuations are statistically isotropic and Gaussian -are rigorously tested using maps of the cosmic microwave background (CMB) anisotropy from the Planck satellite. The detailed results are based on studies of four independent estimates of the CMB that are compared to simulations using a fiducial ΛCDM model and incorporating essential aspects of the Planck measurement process. Deviations from isotropy have been found and demonstrated to be robust against component separation algorithm, mask choice, and frequency dependence. Many of these anomalies were previously observed in the WMAP data, and are now confirmed at similar levels of significance (about 3σ). However, we find little evidence of non-Gaussianity, with the exception of a few statistical signatures that seem to be associated with specific anomalies. In particular, we find that the quadrupole-octopole alignment is also connected to a low observed variance in the CMB signal. A power asymmetry is now found to persist on scales corresponding to about = 600 and can be described in the low-regime by a phenomenological dipole modulation model. However, any primordial power asymmetry is strongly scale-dependent and does not extend to arbitrarily small angular scales. Finally, it is plausible that some of these features may be reflected in the angular power spectrum of the data, which shows a deficit of power on similar scales. Indeed, when the power spectra of two hemispheres defined by a preferred direction are considered separately, one shows evidence of a deficit in power, while its opposite contains oscillations between odd and even modes that may be related to the parity violation and phase correlations also detected in the data. Although these analyses represent a step forward in building an understanding of the anomalies, a satisfactory explanation based on physically motivated models is still lacking.

The European Space Agency's Planck satellite, which is 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. In February 2015, ESA and the Planck Collaboration released the second set of cosmology products based on data from the entire Planck mission, including both temperature and polarization, along with a set of scientific and technical papers and a web-based explanatory supplement. This paper gives an overview of the main characteristics of the data and the data products in the release, as well as the associated cosmological and astrophysical science results and papers. The data products include maps of the cosmic microwave background (CMB), the thermal Sunyaev-Zeldovich effect, diffuse foregrounds in temperature and polarization, catalogues of compact Galactic and extragalactic sources (including separate catalogues of Corresponding author: C. R. Lawrence, e-mail: charles.lawrence@jpl.nasa.govArticle published by EDP Sciences A1, page 1 of 38 A&A 594, A1 (2016) Sunyaev-Zeldovich clusters and Galactic cold clumps), and extensive simulations of signals and noise used in assessing uncertainties and the performance of the analysis methods. The likelihood code used to assess cosmological models against the Planck data is described, along with a CMB lensing likelihood. Scientific results include cosmological parameters derived from CMB power spectra, gravitational lensing, and cluster counts, as well as constraints on inflation, non-Gaussianity, primordial magnetic fields, dark energy, and modified gravity, and new results on low-frequency Galactic foregrounds.

We test the statistical isotropy and Gaussianity of the cosmic microwave background (CMB) anisotropies using observations made by the Planck satellite. Our results are based mainly on the full Planck mission for temperature, but also include some polarization measurements. In particular, we consider the CMB anisotropy maps derived from the multi-frequency Planck data by several component-separation methods. For the temperature anisotropies, we find excellent agreement between results based on these sky maps over both a very large fraction of the sky and a broad range of angular scales, establishing that potential foreground residuals do not affect our studies. Tests of skewness, kurtosis, multi-normality, N-point functions, and Minkowski functionals indicate consistency with Gaussianity, while a power deficit at large angular scales is manifested in several ways, for example low map variance. The results of a peak statistics analysis are consistent with the expectations of a Gaussian random field. The "Cold Spot" is detected with several methods, including map kurtosis, peak statistics, and mean temperature profile. We thoroughly probe the large-scale dipolar power asymmetry, detecting it with several independent tests, and address the subject of a posteriori correction. Tests of directionality suggest the presence of angular clustering from large to small scales, but at a significance that is dependent on the details of the approach. We perform the first examination of polarization data, finding the morphology of stacked peaks to be consistent with the expectations of statistically isotropic simulations. Where they overlap, these results are consistent with the Planck 2013 analysis based on the nominal mission data and provide our most thorough view of the statistics of the CMB fluctuations to date.

The idea that we live near the center of a large, nonlinear void has attracted attention recently as an alternative to dark energy or modified gravity. We show that an appropriate void profile can fit both the latest cosmic microwave background and supernova data. However, this requires either a fine-tuned primordial spectrum or a Hubble rate so low as to rule these models out. We also show that measurements of the radial baryon acoustic scale can provide very strong constraints. Our results present a serious challenge to void models of acceleration.