Predictions of Spectral Parameters by Several Inflationary Universe Models in Light of the Planck Results

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 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. 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 \(n_\mathrm{s} = 0.968 \pm 0.006\) and tightly constrain its scale dependence to \(d n_s/d \ln k =-0.003 \pm 0.007\) when combined with the Planck lensing likelihood. When the high-\(\ell\) polarization data is included, the results are consistent and uncertainties are reduced. The upper bound on the tensor-to-scalar ratio is \(r_{0.002} < 0.11\) (95% CL), consistent with the B-mode polarization constraint \(r< 0.12\) (95% CL) obtained from a joint BICEP2/Keck Array and Planck analysis. These results imply that \(V(\phi) \propto \phi^2\) and natural inflation are now disfavoured compared to models predicting a smaller tensor-to-scalar ratio, such as \(R^2\) inflation. Three independent methods reconstructing the primordial power spectrum are investigated. The Planck data are consistent with adiabatic primordial perturbations. We investigate inflationary models producing an anisotropic modulation of the primordial curvature power spectrum as well as generalized models of inflation not governed by a scalar field with a canonical kinetic term. The 2015 results are consistent with the 2013 analysis based on the nominal mission data.