Planck 2015 results. XI. CMB power spectra, likelihoods, and robustness of parameters

Abstract

This paper presents the Planck 2015 likelihoods, statistical descriptions of the 2-point correlations of CMB data, using the hybrid approach employed previously: pixel-based at $\ell <30$ and a Gaussian approximation to the distribution of spectra at higher $\ell$. The main improvements are the use of more and better processed data and of Planck polarization data, and more detailed foreground and instrumental models, allowing further checks and enhanced immunity to systematics. Progress in foreground modelling enables a larger sky fraction. Improvements in processing and instrumental models further reduce uncertainties. For temperature, we perform an analysis of end-to-end instrumental simulations fed into the data processing pipeline; this does not reveal biases from residual instrumental systematics. The $\Lambda$CDM cosmological model continues to offer a very good fit to Planck data. The slope of primordial scalar fluctuations, $n_s$, is confirmed smaller than unity at more than 5σ from Planck alone. We further validate robustness against specific extensions to the baseline cosmology. E.g., the effective number of neutrino species remains compatible with the canonical value of 3.046. This first detailed analysis of Planck polarization concentrates on E modes. At low $\ell$ we use temperature at all frequencies and a subset of polarization. The frequency range improves CMB-foreground separation. Within the baseline model this requires a reionization optical depth $\tau =0.078\pm 0.019$, significantly lower than without high-frequency data for explicit dust monitoring. At high $\ell$ we detect residual errors in E, typically O($\mu$K${}^2$); we recommend temperature alone as the high-$\ell$ baseline. Nevertheless, Planck high-$\ell$ polarization allows a separate determination of $\Lambda$CDM parameters consistent with those from temperature alone.

This paper is associated with the 2015 Planck release (see http://www.cosmos.esa.int/web/planck/publications). Likelihood code & data available at http://www.cosmos.esa.int/web/planck/pla. Version accepted by A&A. Substancially extended (104 pages) with analysis of end-to-simulations of systematics further confirming the results. Abstract abridged

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• Inflation as an amplifier: the case of Lorentz violation
• Exploring cosmic origins with CORE: mitigation of systematic effects
• An Improved Diffuse Foreground Subtraction by ILC method: CMB Map and Angular Power Spectrum using Planck and WMAP Observations
• Local Group timing argument and virial theorem mass estimators from cosmological simulations
• Unraveling the interplay between SIDM and baryons in MW halos: defining where baryons dictate heat transfer
• Radion induced inflation on non-flat brane and modulus stabilization
• The BAHAMAS project: Effects of dynamical dark energy on large-scale structure
• Full-sky, arcminute-scale, 3D models of Galactic microwave foreground dust emission based on filaments
• Magnetic Moments of Leptons, Charged Lepton Flavor Violations and Dark Matter Phenomenology of a Minimal Radiative Dirac Neutrino Mass Model
• The arbitrariness of potentials in interacting quintessence models
• On the impact of large angle CMB polarization data on cosmological parameters
• Modeling the large-scale power deficit with smooth and discontinuous primordial spectra
• Dark energy versus modified gravity: Impacts on measuring neutrino mass
• Observable Predictions for Massive-Neutrino Cosmologies with Model-Independent Dark Energy
• Joining bits and pieces of reionization history
• Improving cosmological parameter estimation with the future 21 cm observation from SKA
• Improved model-independent constraints on the recombination era and development of a direct projection method
• A novel CMB polarization likelihood package for large angular scales built from combined WMAP and Planck LFI legacy maps
• Lack-of-correlation anomaly in CMB large scale polarisation maps
• A Hint of a Blue Axion Isocurvature Spectrum?
• Constraints on running vacuum model with $H(z)$ and $f{\sigma }_8$
• Pure E and B polarization maps via Wiener filtering
• Probing the Neutrino Mass Hierarchy beyond $\Lambda$CDM Model
• Consistency of the Planck CMB data and $\Lambda$CDM cosmology
• Robust predictions for an oscillatory bispectrum in Planck 2015 data from transient reductions in the speed of sound of the inflaton
• Universe opacity and CMB
• BeyondPlanck XII. Cosmological parameter constraints with end-to-end error propagation
• De Broglie-Bohm Quantum Mechanics
• Constraining quantum collapse inflationary models with CMB data
• BeyondPlanck XI. Bayesian CMB analysis with sample-based end-to-end error propagation
• Probing the Seesaw Mechanism with Cosmological Data
• On general features of warm dark matter with reduced relativistic gas
• Cosmoglobe DR1 results. I. Improved Wilkinson Microwave Anisotropy Probe maps through Bayesian end-to-end analysis
• No Slip CMB
• V-mode Polarization in Axion Inflation and Preheating
• Constraining quantum collapse inflationary models with current data: The semiclassical approach
• Radiative stability and observational constraints on dark energy and modified gravity
• Forecast constraints on Anisotropic Stress in Dark Energy using gravitational-waves
• Hybrid-basis inference for large-scale galaxy clustering: combining spherical and Cartesian Fourier analyses
• High-resolution CMB bispectrum estimator with flexible modal basis
• Modified Gravity Away from a $\Lambda$CDM Background
• Planck Limits on Non-canonical Generalizations of Large-field Inflation Models
• Primordial power spectrum features in phenomenological descriptions of inflation
• Lensing covariance on cut sky and SPT-Planck lensing tensions
• A Two-point Diagnostic for the HII Galaxy Hubble Diagram
• CMB Lens Sample Covariance and Consistency Relations
• Brane inflation and the robustness of the Starobinsky inflationary model
• Real space lensing reconstruction using cosmic microwave background polarization
• Cosmological constraints on sterile neutrino oscillations from Planck
• Anomalous spectral lines and relic quantum nonequilibrium
• Bandpass mismatch error for satellite CMB experiments I: Estimating the spurious signal
• Phenomenology of the gauge symmetry for right-handed fermions
• Marginalized Fisher Forecast for Horndeski Dark Energy Models
• Ultrahigh energy cosmic rays and neutrinos from light nuclei composition
• Beyond optical depth: Future determination of ionization history from the CMB
• How much primordial tensor mode is allowed?
• Cluster counts. II. Tensions, massive neutrinos, and modified gravity
• Model-Independent Predictions for Smooth Cosmic Acceleration Scenarios
• Joint Bayesian analysis of large angular scale CMB temperature anomalies
• Was there an early reionization component in our universe?
• Cosmological stealths with nonconformal couplings
• Finding structure in the dark: coupled dark energy, weak lensing, and the mildly nonlinear regime
• Fermionic Minimal Dark Matter in 5D Gauge-Higgs Unification
• Eternal inflation and the quantum birth of cosmic structure
• Optimal cosmic microwave background map-making in the presence of cross-correlated noise
• Testing the growth rate in homogeneous and inhomogeneous interacting vacuum models
• The magnetic field strength of the Faraday screen surrounding the radio galaxy Coma A
• Impact of $1/f$ noise on cosmological parameter constraints for SKA intensity mapping
• Reionization in the dark and the light from Cosmic Microwave Background
• Integrated Sachs-Wolfe map reconstruction in the presence of systematic errors
• A Novel CMB Component Separation Method: Hierarchical Generalized Morphological Component Analysis
• Entropy production in inflation from spectator loops
• Prospects for weighing neutrinos in interacting dark energy models using joint observations of gravitational waves and $\gamma$-ray bursts
• Constraining the Break of Spatial Diffeomorphism Invariance with Planck Data
• Cosmological N-body simulations with generic hot dark matter
• Understanding the neutrino mass constraints achievable by combining CMB lensing and spectroscopic galaxy surveys
• SU(2)${}_{\mathrm{CMB}}$ and the cosmological model: angular power spectra
• Searching for local features in primordial power spectrum using genetic algorithms
• Self-interacting neutrinos, the Hubble parameter tension, and the Cosmic Microwave Background
• Impact of SZ cluster residuals in CMB maps and CMB-LSS cross-correlations
• Lensed CMB power spectrum biases from masking extragalactic sources
• Reconstructing the EFT of Inflation from Cosmological Data
• Testing statistical Isotropy in Cosmic Microwave Background Polarization maps
• Isotropic non-Gaussian $g_{\mathrm{NL}}$-like toy models that reproduce the cosmic microwave background anomalies
• A note on the semiclassicality of cosmological perturbations
• A Generalized Doppler and Aberration Kernel for Frequency-Dependent Cosmological Observables
• Is it Mixed dark matter or neutrino masses?
• Polarization of the Cosmic Infrared Background Fluctuations
• Radiative Corrections to Aid the Direct Detection of the Higgsino-like Neutralino Dark Matter: Spin-Independent Interactions
• Constraints on the Spacetime Dynamics of an Early Dark Energy Component
• Constraints on circum-galactic media from Sunyaev-Zel'dovich effects and X-ray data
• Limits on Entanglement Effects in the String Landscape from Planck and BICEP/Keck Data
• The Atacama Cosmology Telescope: Semi-Analytic Covariance Matrices for the DR6 CMB Power Spectra
• The Atacama Cosmology Telescope: DR6 Power Spectrum Foreground Model and Validation
• Data driven foreground clustering approach to component separation in multifrequency CMB experiments: A new Planck CMB map
• Perturbations and quantum relaxation
• Estimation of spectrum and parameters of relic gravitational waves using space-borne interferometers
• Small-scale CMB anisotropies induced by the primordial magnetic fields
• Cosmological bounds on neutrino statistics
• Reassessing Dust's Role in Forming the CMB
• Measuring inflaton couplings via dark radiation as $\Delta N_{\mathrm{eff}}$ in CMB
• On tachyonic stability priors for dark energy
• Uncalibrated Cosmic Standards as a Robust Test on Late-Time Cosmological Models
• New Constraints on Decaying Dark Matter from INTEGRAL/SPI
• Observational constraints on running vacuum model
• CMB statistical isotropy confirmation at all scales using multipole vectors
• Consistency of CMB experiments beyond cosmic variance
• ISW in $\Lambda$CDM or something else?
• Accurate estimation of angular power spectra for maps with correlated masks
• Inference of the optical depth to reionization $\tau$ from $\text{Planck}$ CMB maps with convolutional neural networks
• Doubly Blind Spots in Scalar Dark Matter Models
• Constraining Parameters for the Accelerating Universe in $f(R,{\mathcal{L}}_m)$ Gravity
• Finsler space-time can explain both parity asymmetry and power deficit seen in CMB temperature anisotropies
• Study of systematics effects on the Cross Power Spectrum of 21 cm Line and Cosmic Microwave Background using Murchison Widefield Array Data
• Impact of Low ell's on Large Scale Structure Anomalies
• Looking beyond lambda
• Statistical imprints of CMB B-type polarization leakage in an incomplete sky survey analysis
• An SU(2) gauge principle for the Cosmic Microwave Background: Perspectives on the Dark Sector of the Cosmological Model
• Cosmological parameters from Planck data in SU(2)${}_{\mathrm{CMB}}$, their local $\Lambda$CDM values, and the modified photon Boltzmann equation
• Optimal strategy for polarization modulation in the LSPE-SWIPE experiment
• Limit on the dark matter mass from its interaction with photons
• Elucidating Dark Energy with Future 21 cm Observations at the Epoch of Reionization
• Strange stars admixed with dark matter: equiparticle model in a two fluid approach
• Thermal gravitational-wave background in the general pre-inflationary scenario
• A forecast of the sensitivity on the measurement of the optical depth to reionization with the GroundBIRD experiment
• Possible Impact of non-Gaussianities on cosmological constraints in neutrino physics
• Cosmological constraints on $\Lambda (\alpha )$CDM models with time-varying fine structure constant
• Anisotropic power spectrum and the observed low-l power in PLANCK CMB data
• Brane inflation driven by an arctan potential: CMB constraints and Reheating
• Scale invariance of the primordial tensor power spectrum
• Is the lack of power anomaly in the CMB correlated with the orientation of the Galactic plane?
• WHIM-hunting through cross-correlation of optical and SZ effect data in the Virgo cluster filaments
• General solutions of the leakage in integral transforms and applications to the EB-leakage and detection of the cosmological gravitational wave background
• Novel vacuum conditions in inflationary collapse models
• The Simons Observatory: Assessing the Impact of Dust Complexity on the Recovery of Primordial $B$-modes
• The first direct measurement of gravitational potential decay rate at cosmological scales and improved dark energy constraint
• Comparison of results on $N_{\mathrm{eff}}$ from various Planck likelihoods
• Shapes and features of the primordial bispectrum
• A Pop III generated dust screen at z~16
• A probabilistic framework for cosmological inference of peculiar velocities
• Local Limit of Nonlocal Gravity: Cosmological Perturbations
• Does fractal Universe favour warm inflation: Observational support?
• On the regularity of the covariance matrix of a discretized scalar field on the sphere
• Cosmological Zero Modes
• An Introduction to the Planck Mission
• CHEX-MATE: The Impact of Triaxiality and Orientation on Planck SZ Cluster Selection and Weak Lensing Mass Measurements
• Is warm inflation quasi-stable?
• Influence of the correlation prior on reconstruction of the dark energy equation of state
• Cosmology with Planck T-E correlation coefficient
• Renormalization group computation of likelihood functions for cosmological data sets
• The choice of Planck CMB likelihood in cosmological analyses
• An Optimally Weighted Estimator of the Linear Power Spectrum Disentangling the Growth of Density Perturbations Across Galaxy Surveys
• The running of featureful primordial power spectra
• A Comparative Test of the LCDM and R_h=ct Cosmologies Based on Upcoming Redshift Drift Measurements
• Constraining the primordial power spectrum using a differentiable likelihood
• Impact of reionization history on constraining primordial gravitational waves in future all-sky cosmic microwave background experiments
• Approximate Likelihood Approaches for Detecting the Influence of Primordial Gravitational Waves in Cosmic Microwave Background Polarization
• Too small to succeed: the difficulty of sustaining star formation in low-mass haloes
• Improved renormalization group computation of likelihood functions for cosmological data sets
• Lensing anomalies from the epoch of reionisation
• Excessive shift of the CMB acoustic peaks of the Cold Spot area
• Accounting for Correlations When Fitting Extra Cosmological Parameters
• Confirmation of the detection of B-modes in the Planck polarization maps
• The CMB angular power spectrum via component separation: a study on Planck data
• How Many Bursts Does it Take to Form a Core at the Center of a Galaxy?
• Hartle-Hawking wave function and large-scale power suppression of CMB
• Minicharged Particle Sensitivity of the MAPP Outrigger Detector
• A comprehensive dynamical and phenomenological analysis of structure growth in curvature-modulated coupled quintessence scenario
• Does History Repeat Itself? Periodic Time Cosmology
• The Forward Physics Facility at the High-Luminosity LHC
• Internal dynamics and structure of Cepheus OB4. The asymmetric expansion of Berkeley 59
• CASCO: Cosmological and AStrophysical parameters from Cosmological simulations and Observations IV. Testing warm dark matter cosmologies with galaxy scaling relations: A joint simulation-observation study using DREAMS simulations
• Cross-tests of CMB features in the primordial spectra
• Non-Gaussianity in D3-brane inflation
• Beam-deconvolved Planck LFI maps
• Constraints on the velocity dispersion of Dark Matter from Cosmology and new bounds on scattering from the Cosmic Dawn
• The impact of the locally measured Hubble parameter on the mass of Sterile neutrino
• SU(2) Quantum Yang-Mills Thermodynamics: Some Theory and Some Applications
• Evaluation of multi-parameter likelihoods through iteration of two-dimensional slices