Planck 2013 results. XVI. Cosmological parameters
TL;DR: In this paper, the authors present the first results based on Planck measurements of the CMB temperature and lensing-potential power spectra, which are extremely well described by the standard spatially-flat six-parameter LCDM cosmology.
Abstract: 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.
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TL;DR: In this paper, the authors present results based on full-mission Planck observations of temperature and polarization anisotropies of the CMB, which are consistent with the six-parameter inflationary LCDM cosmology.
Abstract: 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.
9,745 citations
TL;DR: In this paper, the authors present the first cosmological results based on Planck measurements of the cosmic microwave background (CMB) temperature and lensing-potential power spectra, which are extremely well described by the standard spatially-flat six-parameter ΛCDM cosmology with a power-law spectrum of adiabatic scalar perturbations.
Abstract: 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 (l ≳ 40) are extremely well described by the standard spatially-flat 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, Ωbh2 = 0.02205 ± 0.00028, Ωch2 = 0.1199 ± 0.0027, and ns = 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, H0 = (67.3 ± 1.2) km s-1 Mpc-1, and a high value of the matter density parameter, Ωm = 0.315 ± 0.017. These values are in tension with recent direct measurements of H0 and the magnitude-redshift 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 isinsensitive to the addition of tensor modes and to changes in the matter content of the Universe. We find an upper limit of r0.002< 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 Neff = 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 Neff = 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 = -1.13-0.10+0.13. 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. The unusual shape of the spectrum in the multipole range 20 ≲ l ≲ 40 was seen previously in the WMAP data and is a real feature of the primordial CMB anisotropies. The poor fit to the spectrum at low multipoles is not of decisive significance, but is an “anomaly” in an otherwise self-consistent analysis of the Planck temperature data.
7,060 citations
TL;DR: In this article, a critical review of the current status of cosmological nucleosynthesis is given, where the baryon-to-photon ratio of deuterium and helium-4 is consistent with the independent determination of $\eta$ from observations of anisotropies in the cosmic microwave background.
Abstract: A critical review is given of the current status of cosmological nucleosynthesis. In the framework of the Standard Model with 3 types of relativistic neutrinos, the baryon-to-photon ratio, $\eta$, corresponding to the inferred primordial abundances of deuterium and helium-4 is consistent with the independent determination of $\eta$ from observations of anisotropies in the cosmic microwave background. However the primordial abundance of lithium-7 inferred from observations is significantly below its expected value. Taking systematic uncertainties in the abundance estimates into account, there is overall concordance in the range $\eta = (5.7-6.7)\times 10^{-10}$ at 95% CL (corresponding to a cosmological baryon density $\Omega_B h^2 = 0.021 - 0.025$). The D and He-4 abundances, when combined with the CMB determination of $\eta$, provide the bound $N_
u=3.28 \pm 0.28$ on the effective number of neutrino species. Other constraints on new physics are discussed briefly.
5,144 citations
TL;DR: In this article, the authors present cosmological parameter results from the full-mission Planck measurements of the cosmic microwave background (CMB) anisotropies, combining information from the temperature and polarization maps and the lensing reconstruction.
Abstract: 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 manyparameters,withresidualmodellinguncertaintiesestimatedtoaffectthemonlyatthe05σlevelWefindgoodconsistencywiththestandard spatially-flat6-parameter ΛCDMcosmologyhavingapower-lawspectrumofadiabaticscalarperturbations(denoted“base ΛCDM”inthispaper), from polarization, temperature, and lensing, separately and in combination A combined analysis gives dark matter density Ωch2 = 0120±0001, baryon density Ωbh2 = 00224±00001, scalar spectral index ns = 0965±0004, and optical depth τ = 0054±0007 (in this abstract we quote 68% confidence regions on measured parameters and 95% on upper limits) The angular acoustic scale is measured to 003% precision, with 100θ∗ = 10411±00003Theseresultsareonlyweaklydependentonthecosmologicalmodelandremainstable,withsomewhatincreasederrors, in many commonly considered extensions Assuming the base-ΛCDM cosmology, the inferred (model-dependent) late-Universe parameters are: HubbleconstantH0 = (674±05)kms−1Mpc−1;matterdensityparameterΩm = 0315±0007;andmatterfluctuationamplitudeσ8 = 0811±0006 We find no compelling evidence for extensions to the base-ΛCDM model Combining with baryon acoustic oscillation (BAO) measurements (and consideringsingle-parameterextensions)weconstraintheeffectiveextrarelativisticdegreesoffreedomtobe Neff = 299±017,inagreementwith the Standard Model prediction Neff = 3046, and find that the neutrino mass is tightly constrained toPmν < 012 eV The CMB spectra continue to prefer higher lensing amplitudesthan predicted in base ΛCDM at over 2σ, which pulls some parameters that affect thelensing amplitude away from the ΛCDM model; however, this is not supported by the lensing reconstruction or (in models that also change the background geometry) BAOdataThejointconstraintwithBAOmeasurementsonspatialcurvatureisconsistentwithaflatuniverse, ΩK = 0001±0002Alsocombining with Type Ia supernovae (SNe), the dark-energy equation of state parameter is measured to be w0 = −103±003, 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 r0002 < 006 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, 36σ, 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
4,688 citations
TL;DR: In this article, the authors report on the implications for cosmic inflation of the 2018 Release of the Planck CMB anisotropy measurements, which are fully consistent with the two previous Planck cosmological releases, but have smaller uncertainties thanks to improvements in the characterization of polarization at low and high multipoles.
Abstract: We report on the implications for cosmic inflation of the 2018 Release of the Planck CMB anisotropy measurements. The results are fully consistent with 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 $n_\mathrm{s}=0.9649\pm 0.0042$ at 68% CL and show no evidence for a scale dependence of $n_\mathrm{s}.$ Spatial flatness is confirmed at a precision of 0.4% at 95% CL with the combination with BAO data. The Planck 95% CL upper limit on the tensor-to-scalar ratio, $r_{0.002}<0.10$, is further tightened by combining with the BICEP2/Keck Array BK15 data to obtain $r_{0.002}<0.056$. In the framework of single-field inflationary models with Einstein gravity, these results imply that: (a) slow-roll models with a concave potential, $V" (\phi) < 0,$ are increasingly favoured by the data; and (b) two different methods for reconstructing the inflaton potential find no evidence for dynamics beyond slow roll. Non-parametric reconstructions of the primordial power spectrum consistently confirm a pure power law. A complementary analysis also finds no evidence for theoretically motivated parameterized features in the Planck power spectrum, a result further strengthened for certain oscillatory models by a new combined analysis that includes Planck bispectrum data. The new Planck polarization data provide a stringent test of the adiabaticity of the initial conditions. The polarization data also provide improved constraints on inflationary models that predict a small statistically anisotropic quadrupolar modulation of the primordial fluctuations. However, the polarization data do not confirm physical models for a scale-dependent dipolar modulation.
3,438 citations
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TL;DR: The theory and phenomenology of reheating and preheating after inflation is reviewed in this paper, providing a unified discussion of both the gravitational and nongravitational features of multifield inflation.
Abstract: The theory of inflation with single and multiple fields is reviewed paying particular attention to the dynamics of adiabatic and entropy/isocurvature perturbations which provide the primary means of testing inflationary models. The theory and phenomenology of reheating and preheating after inflation is reviewed providing a unified discussion of both the gravitational and nongravitational features of multifield inflation. In addition inflation in theories with extra dimensions and models such as the curvaton scenario and modulated reheating which provide alternative ways of generating large-scale density perturbations are covered. Finally interesting observational implications are discussed that can result from adiabatic-isocurvature correlations and non-Gaussianity.
1,042 citations
TL;DR: In this article, a formalism for analyzing a full-sky temperature and polarization map of the cosmic microwave background is presented, where temperature maps are analyzed by expanding over the set of spherical harmonics to give multipole moments of the two-point correlation function.
Abstract: We present a formalism for analyzing a full-sky temperature and polarization map of the cosmic microwave background. Temperature maps are analyzed by expanding over the set of spherical harmonics to give multipole moments of the two-point correlation function. Polarization, which is described by a second-rank tensor, can be treated analogously by expanding in the appropriate tensor spherical harmonics. We provide expressions for the complete set of temperature and polarization multipole moments for scalar and tensor metric perturbations. Four sets of multipole moments completely describe isotropic temperature and polarization correlations; for scalar metric perturbations one set is identically zero, giving the possibility of a clean determination of the vector and tensor contributions. The variance with which the multipole moments can be measured in idealized experiments is evaluated, including the effects of detector noise, sky coverage, and beam width. Finally, we construct coordinate-independent polarization two-point correlation functions, express them in terms of the multipole moments, and derive small-angle limits.
896 citations
TL;DR: A variety of observations suggest that magnetic fields are present in all galaxies and galaxy clusters as mentioned in this paper, but fundamental questions concerning the nature of the dynamo as well as the origin of the seed fields necessary to prime it remain unclear.
Abstract: A variety of observations suggest that magnetic fields are present in all galaxies and galaxy clusters. These fields are characterized by a modest strength ${(10}^{\ensuremath{-}7}\char21{}{10}^{\ensuremath{-}5}\mathrm{G})$ and huge spatial scale $(\ensuremath{\lesssim}1\mathrm{Mpc}).$ It is generally assumed that magnetic fields in spiral galaxies arise from the combined action of differential rotation and helical turbulence, a process known as the \ensuremath{\alpha}\ensuremath{\omega} dynamo. However, fundamental questions concerning the nature of the dynamo as well as the origin of the seed fields necessary to prime it remain unclear. Moreover, the standard \ensuremath{\alpha}\ensuremath{\omega} dynamo does not explain the existence of magnetic fields in elliptical galaxies and clusters. The author summarizes what is known observationally about magnetic fields in galaxies, clusters, superclusters, and beyond. He then reviews the standard dynamo paradigm, the challenges that have been leveled against it, and several alternative scenarios. He concludes with a discussion of astrophysical and early-Universe candidates for seed fields.
861 citations
TL;DR: The results of a search for time variability of the fine structure constant alpha using absorption systems in the spectra of distant quasars find no systematic effects which can explain the results.
Abstract: We describe the results of a search for time variability of the fine structure constant $\ensuremath{\alpha}$ using absorption systems in the spectra of distant quasars. Three large optical data sets and two $21\mathrm{cm}$ and mm absorption systems provide four independent samples, spanning $\ensuremath{\sim}23%$ to $87%$ of the age of the universe. Each sample yields a smaller $\ensuremath{\alpha}$ in the past and the optical sample shows a $4\ensuremath{\sigma}$ deviation: $\ensuremath{\Delta}\ensuremath{\alpha}/\ensuremath{\alpha}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}0.72\ifmmode\pm\else\textpm\fi{}0.18\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ over the redshift range $0.5lzl3.5$. We find no systematic effects which can explain our results. The only potentially significant systematic effects push $\ensuremath{\Delta}\ensuremath{\alpha}/\ensuremath{\alpha}$ towards positive values; i.e., our results would become more significant were we to correct for them.
765 citations
TL;DR: In this article, the effect of three-neutrino flavour oscillations on the decoupling process of neutrinos has been studied by solving the momentum-dependent kinetic equations for the neutrino spectra.
757 citations