A simple cosmological model with only six parameters (matter density, m h 2 , baryon density, b h 2 , Hubble constant, H 0 , amplitude of fluctuations, 8 , optical depth, , and a slope for the scalar perturbation spectrum, n s ) fits not only the 3 year WMAP temperature and polarization data, but also small-scale CMB data, light element abundances, large-scale structure observations, and the supernova luminosity/distance relationship. Using WMAP data only, the bestfit values for cosmological parameters for the power-law flat à cold dark matter (ÃCDM) model are ( m h 2 ; b h 2 ; h; n s ; ; 8 ) ¼ (0:1277 þ0:0080 À0:0079 ;0:02229 AE 0:00073;0:732 þ0:031 À0:032 ;0:958 AE 0:016;0:089 AE 0:030; 0:761 þ0:049 À0:048 ). The 3 year data dramatically shrink the allowed volume in this six-dimensional parameter space. Assuming that the primordial fluctuations are adiabatic with a power-law spectrum, the WMAP data alone require dark matter and favor a spectral index that is significantly less than the Harrison-Zel'dovich-Peebles scale-invariant spectrum (n s ¼ 1; r ¼ 0). Adding additional data sets improves the constraints on these components and the spectral slope. For power-law models, WMAP data alone puts an improved upper limit on the tensor-to-scalar ratio, r 0:002 < 0:65 (95% CL) and the combination of WMAP and the lensing-normalized SDSS galaxy survey implies r 0:002 < 0:30 (95% CL). Models that suppress largescale power through a running spectral index or a large-scale cutoff in the power spectrum are a better fit to the WMAP and small-scale CMB data than the power-law ÃCDM model; however, the improvement in the fit to the WMAP data is only Á 2 ¼ 3 for 1 extra degree of freedom. Models with a running-spectral index are consistent with a higher amplitude of gravity waves. In a flat universe, the combination of WMAP and the Supernova Legacy Survey (SNLS) data yields a significant constraint on the equation of state of the dark energy, w ¼ À0:967 þ0:073 À0:072 . If we assume w ¼ À1, then the deviations from the critical density, K , are small: the combination of WMAP and the SNLS data implies k ¼ À0:011 AE 0:012. The combination of WMAP 3 year data plus the HST Key Project constraint on H 0 implies k ¼ À0:014 AE 0:017 and à ¼ 0:716 AE 0:055. Even if we do not include the prior that the universe is flat, by combining WMAP, large-scale structure, and supernova data, we can still put a strong constraint on the dark energy equation of state, w ¼ À1:08 AE 0:12. For a flat universe, the combination of WMAP and other astronomical data yield a constraint on the sum of the neutrino masses, P m < 0:66 eV (95%CL). Consistent with the predictions of simple inflationary theories, we detect no significant deviations from Gaussianity in the CMB maps using Minkowski functionals, the bispectrum, trispectrum, and a new statistic designed to detect large-scale anisotropies in the fluctuations. Subject headingg s: cosmic microwave background -cosmology: observations

This paper presents cosmological results based on full-mission Planck observations of temperature and polarization anisotropies of the cosmic microwave background (CMB) radiation. Our results are in very good agreement with the 2013 analysis of the Planck nominal-mission temperature data, but with increased precision. The temperature and polarization power spectra are consistent with the standard spatially-flat 6-parameter ΛCDM cosmology with a power-law spectrum of adiabatic scalar perturbations (denoted "base ΛCDM" in this paper). From the Planck temperature data combined with Planck lensing, for this cosmology we find a Hubble constant, H 0 = (67.8 ± 0.9) km s −1 Mpc −1 , a matter density parameter Ω m = 0.308 ± 0.012, and a tilted scalar spectral index with n s = 0.968 ± 0.006, consistent with the 2013 analysis. Note that in this abstract we quote 68% confidence limits on measured parameters and 95% upper limits on other parameters. We present the first results of polarization measurements with the Low Frequency Instrument at large angular scales. Combined with the Planck temperature and lensing data, these measurements give a reionization optical depth of τ = 0.066 ± 0.016, corresponding to a reionization redshift of z re = 8.8+1.7 −1.4 . These results are consistent with those from WMAP polarization measurements cleaned for dust emission using 353-GHz polarization maps from the High Frequency Instrument. We find no evidence for any departure from base ΛCDM in the neutrino sector of the theory; for example, combining Planck observations with other astrophysical data we find N eff = 3.15 ± 0.23 for the effective number of relativistic degrees of freedom, consistent with the value N eff = 3.046 of the Standard Model of particle physics. The sum of neutrino masses is constrained to m ν < 0.23 eV. The spatial curvature of our Universe is found to be very close to zero, with |Ω K | < 0.005. Adding a tensor component as a single-parameter extension to base ΛCDM we find an upper limit on the tensor-to-scalar ratio of r 0.002 < 0.11, consistent with the Planck 2013 results and consistent with the B-mode polarization constraints from a joint analysis of BICEP2, Keck Array, and Planck (BKP) data. Adding the BKP B-mode data to our analysis leads to a tighter constraint of r 0.002 < 0.09 and disfavours inflationary models with a V(φ) ∝ φ 2 potential. The addition of Planck polarization data leads to strong constraints on deviations from a purely adiabatic spectrum of fluctuations. We find no evidence for any contribution from isocurvature perturbations or from cosmic defects. Combining Planck data with other astrophysical data, including Type Ia supernovae, the equation of state of dark energy is constrained to w = −1.006 ± 0.045, consistent with the expected Corresponding author: G. Efstathiou, e-mail: gpe@ast.cam.ac.ukArticle published by EDP Sciences A13, page 1 of 63 A&A 594, A13 (2016) value for a cosmological constant. The standard big bang nucleosynthesis predictions for the helium and deuterium abundanc...

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.

This paper presents the first cosmological results based on Planck measurements of the cosmic microwave background (CMB) temperature and lensing-potential power spectra. We find that the Planck spectra at high multipoles ( > ∼ 40) are extremely well described by the standard spatiallyflat six-parameter ΛCDM cosmology with a power-law spectrum of adiabatic scalar perturbations. Within the context of this cosmology, the Planck data determine the cosmological parameters to high precision: the angular size of the sound horizon at recombination, the physical densities of baryons and cold dark matter, and the scalar spectral index are estimated to be θ * = (1.04147 ± 0.00062) × 10 −2 , Ω b h 2 = 0.02205 ± 0.00028, Ω c h 2 = 0.1199 ± 0.0027, and n s = 0.9603 ± 0.0073, respectively (note that in this abstract we quote 68% errors on measured parameters and 95% upper limits on other parameters). For this cosmology, we find a low value of the Hubble constant, H 0 = (67.3 ± 1.2) km s −1 Mpc −1 , and a high value of the matter density parameter, Ω m = 0.315 ± 0.017. These values are in tension with recent direct measurements of H 0 and the magnituderedshift relation for Type Ia supernovae, but are in excellent agreement with geometrical constraints from baryon acoustic oscillation (BAO) surveys. Including curvature, we find that the Universe is consistent with spatial flatness to percent level precision using Planck CMB data alone. We use high-resolution CMB data together with Planck to provide greater control on extragalactic foreground components in an investigation of extensions to the six-parameter ΛCDM model. We present selected results from a large grid of cosmological models, using a range of additional astrophysical data sets in addition to Planck and high-resolution CMB data. None of these models are favoured over the standard six-parameter ΛCDM cosmology. The deviation of the scalar spectral index from unity is insensitive to the addition of tensor modes and to changes in the matter content of the Universe. We find an upper limit of r 0.002 < 0.11 on the tensor-to-scalar ratio. There is no evidence for additional neutrino-like relativistic particles beyond the three families of neutrinos in the standard model. Using BAO and CMB data, we find N eff = 3.30 ± 0.27 for the effective number of relativistic degrees of freedom, and an upper limit of 0.23 eV for the sum of neutrino masses. Our results are in excellent agreement with big bang nucleosynthesis and the standard value of N eff = 3.046. We find no evidence for dynamical dark energy; using BAO and CMB data, the dark energy equation of state parameter is constrained to be w = −1.13 +0.13 −0.10 . We also use the Planck data to set limits on a possible variation of the fine-structure constant, dark matter annihilation and primordial magnetic fields. Despite the success of the six-parameter ΛCDM model in describing the Planck data at high multipoles, we note that this cosmology does not provide a good fit to the temperature power spectrum at low multipoles. T...

We study the effect of primordial nongaussianity on large-scale structure, focusing upon the most massive virialized objects. Using analytic arguments and N-body simulations, we calculate the mass function and clustering of dark matter halos across a range of redshifts and levels of nongaussianity. We propose a simple fitting function for the mass function valid across the entire range of our simulations. We find pronounced effects of nongaussianity on the clustering of dark matter halos, leading to strongly scale-dependent bias. This suggests that the large-scale clustering of rare objects may provide a sensitive probe of primordial nongaussianity. We very roughly estimate that upcoming surveys can constrain nongaussianity at the level |fNL| < ∼ 10, competitive with forecasted constraints from the microwave background.

We present new full-sky temperature maps in five frequency bands from 23 to 94 GHz, based on data from the first 3 years of the WMAP sky survey. The new maps are consistent with the first-year maps and are more sensitive. The 3 year maps incorporate several improvements in data processing made possible by the additional years of data and by a more complete analysis of the polarization signal. These include several new consistency tests as well as refinements in the gain calibration and beam response models. We employ two forms of multifrequency analysis to separate astrophysical foreground signals from the CMB, each of which improves on our first-year analyses. First, we form an improved ''Internal Linear Combination'' (ILC) map, based solely on WMAP data, by adding a bias-correction step and by quantifying residual uncertainties in the resulting map. Second, we fit and subtract new spatial templates that trace Galactic emission; in particular, we now use low-frequency WMAP data to trace synchrotron emission instead of the 408 MHz sky survey. The WMAP point source catalog is updated to include 115 new sources whose detection is made possible by the improved sky map sensitivity. We derive the angular power spectrum of the temperature anisotropy using a hybrid approach that combines a maximum likelihood estimate at low l (large angular scales) with a quadratic cross-power estimate for l > 30. The resulting multifrequency spectra are analyzed for residual point source contamination. At 94 GHz the unmasked sources contribute 128 AE 27 K 2 to l(l þ 1)C l /2 at l ¼ 1000. After subtracting this contribution, our best estimate of the CMB power spectrum is derived by averaging cross-power spectra from 153 statistically independent channel pairs. The combined spectrum is cosmic variance limited to l ¼ 400, and the signal-to-noise ratio per l-mode exceeds unity up to l ¼ 850. For bins of width Ál/l ¼ 3%, the signal-to-noise ratio exceeds unity up to l ¼ 1000. The first two acoustic peaks are seen at l ¼ 220:8 AE 0:7 and l ¼ 530:9 AE 3:8, respectively, while the first two troughs are seen at l ¼ 412:4 AE 1:9 and l ¼ 675:2 AE 11:1. The rise to the third peak is unambiguous; when the WMAP data are combined with higher resolution CMB measurements, the existence of a third acoustic peak is well established. Spergel et al. use the 3 year temperature and polarization data to constrain cosmological model parameters. A simple six-parameter ÃCDM model continues to fit CMB data and other measures of large-scale structure remarkably well. The new polarization data produce a better measurement of the optical depth to reionization, ¼ 0:089 AE 0:03. This new and tighter constraint on helps break a degeneracy with the scalar spectral index, which is now found to be n s ¼ 0:960 AE 0:016. If additional cosmological data sets are included in the analysis, the spectral index is found to be n s ¼ 0:947 AE 0:015.

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 report the results of a joint analysis of data from BICEP2/Keck Array and Planck. BICEP2 and Keck Array have observed the same approximately 400 deg 2 patch of sky centered on RA 0 h, Dec. −57.5°. The combined maps reach a depth of 57 nK deg in Stokes Q and U in a band centered at 150 GHz. Planck has observed the full sky in polarization at seven frequencies from 30 to 353 GHz, but much less deeply in any given region (1.2 μK deg in Q and U at 143 GHz). We detect 150 × 353 cross-correlation in B modes at high significance. We fit the single-and cross-frequency power spectra at frequencies ≥ 150 GHz to a lensed-ΛCDM model that includes dust and a possible contribution from inflationary gravitational waves (as parametrized by the tensor-to-scalar ratio r), using a prior on the frequency spectral behavior of polarized dust emission from previous Planck analysis of other regions of the sky. We find strong evidence for dust and no statistically significant evidence for tensor modes. We probe various model variations and extensions, including adding a synchrotron component in combination with lower frequency data, and find that these make little difference to the r constraint. Finally, we present an alternative analysis which is similar to a map-based cleaning of the dust contribution, and show that this gives similar constraints. The final result is expressed as a likelihood curve for r, and yields an upper limit r 0.05 < 0.12 at 95% confidence. Marginalizing over dust and r, lensing B modes are detected at 7.0σ significance.