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Publication# Planck 2013 results. XXXI. Consistency of the Planck data

Résumé

The Planck design and scanning strategy provide many levels of redundancy that can be exploited to provide tests of internal consistency. One of the most important is the comparison of the 70 GHz (amplifier) and 100 GHz (bolometer) channels. Based on different instrument technologies, with feeds located differently in the focal plane, analysed independently by different teams using different software, and near the minimum of diffuse foreground emission, these channels are in effect two different experiments. The 143 GHz channel has the lowest noise level on Planck, and is near the minimum of unresolved foreground emission. In this paper, we analyse the level of consistency achieved in the 2013 Planck data. We concentrate on comparisons between the 70, 100, and 143 GHz channel maps and power spectra, particularly over the angular scales of the first and second acoustic peaks, on maps masked for diffuse Galactic emission and for strong unresolved sources. Difference maps covering angular scales from 8 degrees to 15 ' are consistent with noise, and show no evidence of cosmic microwave background structure. Including small but important corrections for unresolved-source residuals, we demonstrate agreement (measured by deviation of the ratio from unity) between 70 and 100 GHz power spectra averaged over 70

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Fabio Finelli, Jan Hamann, Julien Lesgourgues

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 greater than or similar to 40) are extremely well described by the standard spatially-flat six-parameter ACDM 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 theta* = (1.04147 +/- 0.00062) x 10(-2), Omega(b)h(2) = 0.02205 +/- 0.00028, Omega(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, Omega(m) = 0.315 +/- 0.017. These values are in tension with recent direct measurements of H-0 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 ACDM 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 ACDM 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(-0.10)(+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 ACDM 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 less than or similar to l less than or similar to 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.

Fabio Finelli, Julien Lesgourgues

This paper presents the Planck 2013 likelihood, a complete statistical description of the two-point correlation function of the CMB temperature fluctuations that accounts for all known relevant uncertainties, both instrumental and astrophysical in nature. We use this likelihood to derive our best estimate of the CMB angular power spectrum from Planck over three decades in multipole moment, t, covering 2 2500. The main source of uncertainty at S 1500 is cosmic variance. Uncertainties in small-scale foreground modelling and instrumental noise dominate the error budget at higher Es. For < 50, our likelihood exploits all Planck frequency channels from 30 to 353 GHz, separating the cosmological CMB signal from diffuse Galactic foregrounds through a physically motivated Bayesian component separation technique. At 50, we employ a correlated Gaussian likelihood approximation based on a fine-grained set of angular cross-spectra derived from multiple detector combinations between the 100, 143, and 217 GHz frequency channels, marginalising over power spectrum foreground templates. We validate our likelihood through an extensive suite of consistency tests, and assess the impact of residual foreground and instrumental uncertainties on the final cosmological parameters. We find good internal agreement among the high- cross-spectra with residuals below a few fiK2 at S 1000, in agreement with estimated calibration uncertainties. We compare our results with foreground-cleaned CMB maps derived from all Planck frequencies, as well as with cross-spectra derived from the 70 GHz Planck map, and find broad agreement in terms of spectrum residuals and cosmological parameters. We further show that the best-fit ACDM cosmology is in excellent agreement with preliminary Planck EE and T E polarisation spectra. We find that the standard ACDM cosmology is well constrained by Planck from the measurements at C 1500. One specific example is the spectral index of scalar perturbations, for which we report a 5.4o- deviation from scale invariance, ns = 1. Increasing the multipole range beyond = 1500 does not increase our accuracy for the ACDM parameters, but instead allows us to study extensions beyond the standard model. We find no indication of significant departures from the ACDM framework. Finally, we report a tension between the Planck best-fit ACDM model and the low- spectrum in the form of a power deficit of 5-10% at 40, with a statistical significance of 2.5-3o-. Without a theoretically motivated model for this power deficit, we do not elaborate further on its cosmological implications, but note that this is our most puzzling finding in an otherwise remarkably consistent data set.

Fabio Finelli, Julien Lesgourgues

We present new measurements of cosmic infrared background (CIB) anisotropies using Planck. Combining HFI data with IRAS, the angular auto-and cross-frequency power spectrum is measured from 143 to 3000 GHz, and the auto-bispectrum from 217 to 545 GHz. The total areas used to compute the CIB power spectrum and bispectrum are about 2240 and 4400 deg(2), respectively. After careful removal of the contaminants (cosmic microwave background anisotropies, Galactic dust, and Sunyaev-Zeldovich emission), and a complete study of systematics, the CIB power spectrum is measured with unprecedented signal to noise ratio from angular multipoles l similar to 150 to 2500. The bispectrum due to the clustering of dusty, star-forming galaxies is measured from l similar to 130 to 1100, with a total signal to noise ratio of around 6, 19, and 29 at 217, 353, and 545 GHz, respectively. Two approaches are developed for modelling CIB power spectrum anisotropies. The first approach takes advantage of the unique measurements by Planck at large angular scales, and models only the linear part of the power spectrum, with a mean bias of dark matter haloes hosting dusty galaxies at a given redshift weighted by their contribution to the emissivities. The second approach is based on a model that associates star-forming galaxies with dark matter haloes and their subhaloes, using a parametrized relation between the dust-processed infrared luminosity and (sub-) halo mass. The two approaches simultaneously fit all auto-and cross-power spectra very well. We find that the star formation history is well constrained up to redshifts around 2, and agrees with recent estimates of the obscured star-formation density using Spitzer and Herschel. However, at higher redshift, the accuracy of the star formation history measurement is strongly degraded by the uncertainty in the spectral energy distribution of CIB galaxies. We also find that the mean halo mass which is most efficient at hosting star formation is log (M-eff/ M-circle dot) = 12.6 and that CIB galaxies have warmer temperatures as redshift increases. The CIB bispectrum is steeper than that expected from the power spectrum, although well fitted by a power law; this gives some information about the contribution of massive haloes to the CIB bispectrum. Finally, we show that the same halo occupation distribution can fit all power spectra simultaneously. The precise measurements enabled by Planck pose new challenges for the modelling of CIB anisotropies, indicating the power of using CIB anisotropies to understand the process of galaxy formation.