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Register a new userPlanck 2018 results. VI. Cosmological parameters
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We present cosmological parameter results from the final full-mission Planck measurements of the CMB anisotropies. We find good consistency with the standard spatially-flat 6-parameter $Lambda$CDM cosmology having a power-law spectrum of adiabatic scalar perturbations (denoted base $Lambda$CDM in this paper), from polarization, temperature, and lensing, separately and in combination. A combined analysis gives dark matter density $Omega_c h^2 = 0.120pm 0.001$, baryon density $Omega_b h^2 = 0.0224pm 0.0001$, scalar spectral index $n_s = 0.965pm 0.004$, and optical depth $tau = 0.054pm 0.007$ (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 $100theta_*=1.0411pm 0.0003$. These results are only weakly dependent on the cosmological model and remain stable, with somewhat increased errors, in many commonly considered extensions. Assuming the base-$Lambda$CDM cosmology, the inferred late-Universe parameters are: Hubble constant $H_0 = (67.4pm 0.5)$km/s/Mpc; matter density parameter $Omega_m = 0.315pm 0.007$; and matter fluctuation amplitude $sigma_8 = 0.811pm 0.006$. We find no compelling evidence for extensions to the base-$Lambda$CDM model. Combining with BAO we constrain the effective extra relativistic degrees of freedom to be $N_{rm eff} = 2.99pm 0.17$, and the neutrino mass is tightly constrained to $sum m_ u< 0.12$eV. The CMB spectra continue to prefer higher lensing amplitudes than predicted in base -$Lambda$CDM at over $2,sigma$, which pulls some parameters that affect the lensing amplitude away from the base-$Lambda$CDM model; however, this is not supported by the lensing reconstruction or (in models that also change the background geometry) BAO data. (Abridged)
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We present the first results based on Planck measurements of the CMB temperature and lensing-potential power spectra. The Planck spectra at high multipoles are extremely well described by the standard spatially-flat six-parameter LCDM cosmology. In this model Planck data determine the cosmological parameters to high precision. We find a low value of the Hubble constant, H0=67.3+/-1.2 km/s/Mpc and a high value of the matter density parameter, Omega_m=0.315+/-0.017 (+/-1 sigma errors) in excellent agreement with 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 present results from an analysis of extensions to the standard cosmology, using astrophysical data sets in addition to Planck and high-resolution CMB data. None of these models are favoured significantly over standard LCDM. 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 a 95% upper limit of r<0.11 on the tensor-to-scalar ratio. There is no evidence for additional neutrino-like relativistic particles. 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 summed neutrino mass. 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. Despite the success of the standard LCDM model, this cosmology does not provide a good fit to the CMB power spectrum at low multipoles, as noted previously by the WMAP team. While not of decisive significance, this is an anomaly in an otherwise self-consistent analysis of the Planck temperature data.
We present results based on full-mission Planck observations of temperature and polarization anisotropies of the CMB. These data are consistent with the six-parameter inflationary LCDM cosmology. From the Planck temperature and lensing data, for this cosmology we find a Hubble constant, H0= (67.8 +/- 0.9) km/s/Mpc, a matter density parameter Omega_m = 0.308 +/- 0.012 and a scalar spectral index with n_s = 0.968 +/- 0.006. (We quote 68% errors on measured parameters and 95% limits on other parameters.) Combined with Planck temperature and lensing data, Planck LFI polarization measurements lead to a reionization optical depth of tau = 0.066 +/- 0.016. Combining Planck with other astrophysical data we find N_ eff = 3.15 +/- 0.23 for the effective number of relativistic degrees of freedom and the sum of neutrino masses is constrained to < 0.23 eV. Spatial curvature is found to be |Omega_K| < 0.005. For LCDM we find a limit on the tensor-to-scalar ratio of r <0.11 consistent with the B-mode constraints from an analysis of BICEP2, Keck Array, and Planck (BKP) data. Adding the BKP data leads to a tighter constraint of r < 0.09. We find no evidence for isocurvature perturbations or cosmic defects. The equation of state of dark energy is constrained to w = -1.006 +/- 0.045. Standard big bang nucleosynthesis predictions for the Planck LCDM cosmology are in excellent agreement with observations. We investigate annihilating dark matter and deviations from standard recombination, finding no evidence for new physics. The Planck results for base LCDM are in agreement with BAO data and with the JLA SNe sample. However the amplitude of the fluctuations is found to be higher than inferred from rich cluster counts and weak gravitational lensing. Apart from these tensions, the base LCDM cosmology provides an excellent description of the Planck CMB observations and many other astrophysical data sets.
The European Space Agencys 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 857GHz. 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 LCDM model continues to provide an excellent fit to the cosmic microwave background data at high and low redshift, describing the cosmological information in over a billion map pixels with just six parameters. With 18 peaks in the temperature and polarization angular power spectra constrained well, Planck measures five of the six parameters to better than 1% (simultaneously), with the best-determined parameter (theta_*) now known to 0.03%. We describe the multi-component sky as seen by Planck, the success of the LCDM 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 explore the 2013 Planck likelihood function with a high-precision multi-dimensional minimizer (Minuit). This allows a refinement of the Lambda-cdm best-fit solution with respect to previously-released results, and the construction of frequentist confidence intervals using profile likelihoods. The agreement with the cosmological results from the Bayesian framework is excellent, demonstrating the robustness of the Planck results to the statistical methodology. We investigate the inclusion of neutrino masses, where more significant differences may appear due to the non-Gaussian nature of the posterior mass distribution. By applying the Feldman--Cousins prescription, we again obtain results very similar to those of the Bayesian methodology. However, the profile-likelihood analysis of the CMB combination (Planck+WP+highL) reveals a minimum well within the unphysical negative-mass region. We show that inclusion of the Planck CMB-lensing information regularizes this issue, and provide a robust frequentist upper limit $M_ u < 0.26 eV$ ($95%$ confidence) from the CMB+lensing+BAO data combination.
We present measurements of the cosmic microwave background (CMB) lensing potential using the final $textit{Planck}$ 2018 temperature and polarization data. We increase the significance of the detection of lensing in the polarization maps from $5,sigma$ to $9,sigma$. Combined with temperature, lensing is detected at $40,sigma$. We present an extensive set of tests of the robustness of the lensing-potential power spectrum, and construct a minimum-variance estimator likelihood over lensing multipoles $8 le L le 400$. We find good consistency between lensing constraints and the results from the $textit{Planck}$ CMB power spectra within the $rm{Lambda CDM}$ model. Combined with baryon density and other weak priors, the lensing analysis alone constrains $sigma_8 Omega_{rm m}^{0.25}=0.589pm 0.020$ ($1,sigma$ errors). Also combining with baryon acoustic oscillation (BAO) data, we find tight individual parameter constraints, $sigma_8=0.811pm0.019$, $H_0=67.9_{-1.3}^{+1.2},text{km},text{s}^{-1},rm{Mpc}^{-1}$, and $Omega_{rm m}=0.303^{+0.016}_{-0.018}$. Combining with $textit{Planck}$ CMB power spectrum data, we measure $sigma_8$ to better than $1,%$ precision, finding $sigma_8=0.811pm 0.006$. 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 $textit{Planck}$ cosmic infrared background (CIB) maps we make a combined estimate of the lensing potential over $60,%$ of the sky with considerably more small-scale signal. We demonstrate delensing of the $textit{Planck}$ power spectra, 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 (abridged).
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