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Register a new userPlanck intermediate results. LI. Features in the cosmic microwave background temperature power spectrum and shifts in cosmological parameters
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The six parameters of the standard $Lambda$CDM model have best-fit values derived from the Planck temperature power spectrum that are shifted somewhat from the best-fit values derived from WMAP data. These shifts are driven by features in the Planck temperature power spectrum at angular scales that had never before been measured to cosmic-variance level precision. We investigate these shifts to determine whether they are within the range of expectation and to understand their origin in the data. Taking our parameter set to be the optical depth of the reionized intergalactic medium $tau$, the baryon density $omega_{rm b}$, the matter density $omega_{rm m}$, the angular size of the sound horizon $theta_*$, the spectral index of the primordial power spectrum, $n_{rm s}$, and $A_{rm s}e^{-2tau}$ (where $A_{rm s}$ is the amplitude of the primordial power spectrum), we examine the change in best-fit values between a WMAP-like large angular-scale data set (with multipole moment $ell<800$ in the Planck temperature power spectrum) and an all angular-scale data set ($ell<2500$ Planck temperature power spectrum), each with a prior on $tau$ of $0.07pm0.02$. We find that the shifts, in units of the 1$sigma$ expected dispersion for each parameter, are ${Delta tau, Delta A_{rm s} e^{-2tau}, Delta n_{rm s}, Delta omega_{rm m}, Delta omega_{rm b}, Delta theta_*} = {-1.7, -2.2, 1.2, -2.0, 1.1, 0.9}$, with a $chi^2$ value of 8.0. We find that this $chi^2$ value is exceeded in 15% of our simulated data sets, and that a parameter deviates by more than 2.2$sigma$ in 9% of simulated data sets, meaning that the shifts are not unusually large. Comparing $ell<800$ instead to $ell>800$, or splitting at a different multipole, yields similar results. We examine the $ell<800$ model residuals in the $ell>800$ power spectrum data and find that the features there... [abridged]
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We explore the relationship between features in the Planck 2015 temperature and polarization data, shifts in the cosmological parameters, and features from inflation. Residuals in the temperature data at low multipole $ell$, which are responsible for the high $H_0approx 70$ km s$^{-1}$Mpc$^{-1}$ and low $sigma_8Omega_m^{1/2}$ values from $ell<1000$ in power-law $Lambda$CDM models, are better fit to inflationary features with a $1.9sigma$ preference for running of the running of the tilt or a stronger $99%$ CL local significance preference for a sharp drop in power around $k=0.004$ Mpc$^{-1}$ in generalized slow roll and a lower $H_0approx 67$ km s$^{-1}$Mpc$^{-1}$. The same in-phase acoustic residuals at $ell>1000$ that drive the global $H_0$ constraints and appear as a lensing anomaly also favor running parameters which allow even lower $H_0$, but not once lensing reconstruction is considered. Polarization spectra are intrinsically highly sensitive to these parameter shifts, and even more so in the Planck 2015 TE data due to an outlier at $ell approx 165$, which disfavors the best fit $H_0$ $Lambda$CDM solution by more than $2sigma$, and high $H_0$ value at almost $3sigma$. Current polarization data also slightly enhance the significance of a sharp suppression of large-scale power but leave room for large improvements in the future with cosmic variance limited $E$-mode measurements.
Using Planck maps of six regions of low Galactic dust emission with a total area of about 140 square degrees, we determine the angular power spectra of cosmic infrared background (CIB) anisotropies from multipole l = 200 to l = 2000 at 217, 353, 545 and 857 GHz. We use 21-cm observations of HI as a tracer of thermal dust emission to reduce the already low level of Galactic dust emission and use the 143 GHz Planck maps in these fields to clean out cosmic microwave background anisotropies. Both of these cleaning processes are necessary to avoid significant contamination of the CIB signal. We measure correlated CIB structure across frequencies. As expected, the correlation decreases with increasing frequency separation, because the contribution of high-redshift galaxies to CIB anisotropies increases with wavelengths. We find no significant difference between the frequency spectrum of the CIB anisotropies and the CIB mean, with Delta I/I=15% from 217 to 857 GHz. In terms of clustering properties, the Planck data alone rule out the linear scale- and redshift-independent bias model. Non-linear corrections are significant. Consequently, we develop an alternative model that couples a dusty galaxy, parametric evolution model with a simple halo-model approach. It provides an excellent fit to the measured anisotropy angular power spectra and suggests that a different halo occupation distribution is required at each frequency, which is consistent with our expectation that each frequency is dominated by contributions from different redshifts. In our best-fit model, half of the anisotropy power at l=2000 comes from redshifts z<0.8 at 857 GHz and z<1.5 at 545 GHz, while about 90% come from redshifts z>2 at 353 and 217 GHz, respectively.
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.
Angular power spectrum of the cosmic microwave background (CMB) temperature anisotropies is one of the most important on characteristics of the Universe such as its geometry and total density. Using flat sky approximation and Fourier analysis, we estimate the angular power spectrum from an ensemble of least foreground-contaminated square patches from WMAP W and V frequency band map. This method circumvents the issue of foreground cleaning and that of breaking orthogonality in spherical harmonic analysis due to masking out the bright Galactic plane region, thereby rendering a direct measurement of the angular power spectrum. We test and confirm Gaussian statistical characteristic of the selected patches, from which the first and second acoustic peak of the power spectrum are reproduced, and the third peak is clearly visible albeit with some noise residual at the tail.
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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