Primordial black hole formation with non-Gaussian curvature perturbations

In the context of transient constant-roll inflation near a local maximum, we derive the non-perturbative field redefinition that relates a Gaussian random field with the true non-Gaussian curvature perturbation. Our analysis shows the emergence of a new critical amplitude $\zeta_*$, corresponding to perturbations that prevent the inflaton from overshooting the local maximum, thus becoming trapped in the false minimum of the potential. For potentials with a mild curvature at the local maximum (and thus small non-Gaussianity), we recover the known perturbative field redefinition. We apply these results to the formation of primordial black holes, and discuss the cases for which $\zeta_*$ is smaller or of the same order than the critical value for collapse of spherically symmetric overdensities. In the latter case, we present a simple potential for which the power spectrum needs an amplitude 10 times smaller that in the Gaussian case for producing a sizeable amount of primordial black holes.Comment: 13 pages, 8 figures. v2: expanded explanations + small changes. v3: small typos correcte

Radial derivatives as a test of pre-big bang events on the Planck data

Although the search for azimuthal patterns in cosmological surveys is useful to characterize some effects depending exclusively on an angular distance within the standard model, they are considered as a key distinguishing feature of some exotic scenarios, such as bubble collisions or conformal cyclic cosmology (CCC). In particular, the CCC is a non-stardard framework that predicts circular patterns on the cosmic microwave background intensity fluctuations. Motivated by some previous works that explore the presence of radial gradients, we apply a methodology based on the radial derivatives to the latest release of Planck data. The new approach allows exhaustive studies to be performed at all-sky directions at a HEALPIX resolution of Nside = 1024. Specifically, two different analyses are performed focusing on weight functions in both small (up to a 5-deg radius) and large scales. We present a comparison between our results and those shown by An, Meissner & Nurowski (2017) and An et al. (2018). In addition, a possible polarization counterpart of these circular patterns is also analysed for the most promising case. Taking into account the limitations to characterize the significance of the results, including the possibility of suffering a look-elsewhere effect, no strong evidence of the kind of circular patterns expected from CCC is found in the Planck data for either the small or the large scales.The authors would like to thank Spanish Agencia Estatal de Investigacion (AEI, MICIU) for the financial support provided under ´the projects with references ESP2017-83921-C2-1-R and AYA2017-90675-REDC, co-funded with European Union ‘Fondo Europeo de Desarrollo Regional’ (EU FEDER) funds, and also acknowledge the funding from Unidad de Excelencia Mar´ıa de Maeztu (MDM 2017-0765). AM-C acknowledges the postdoctoral contract from the University of the Basque Country UPV/EHU ‘Especializacion´ de personal investigador doctor’ program, and the financial Support from the Spanish Ministry MINECO, MCIU/AEI/FEDER grant (PGC2018-094626-B-C21), the Basque Government grant (IT979-16). This research used resources of the National Energy Research Scientific Computing Center (NERSC), a U.S. Department of Energy Office of Science User Facility operated under Contract No. DEAC02-05CH11231

The group structure of non-Abelian NS-NS transformations

We study the transformations of the worldvolume fields of a system of multiple coinciding D-branes under gauge transformations of the supergravity Kalb-Ramond field. We find that the pure gauge part of these NS-NS transformations can be written as a U(N) symmetry of the underlying Yang-Mills group, but that in general the full NS-NS variations get mixed up non-trivially with the U(N). We compute the commutation relations and the Jacobi identities of the bigger group formed by the NS-NS and U(N) transformations.Comment: Latex, 11 pages. v2: Typos corrected; version to appear in JHEP

Planck 2018 results: XII. Galactic astrophysics using polarized dust emission

Observations of the submillimetre emission from Galactic dust, in both total intensity I and polarization, have received tremendous interest thanks to the Planck full-sky maps. In this paper we make use of such full-sky maps of dust polarized emission produced from the third public release of Planck data. As the basis for expanding on astrophysical studies of the polarized thermal emission from Galactic dust, we present full-sky maps of the dust polarization fraction p, polarization angle ?, and dispersion function of polarization angles ??. The joint distribution (one-point statistics) of p and NH confirms that the mean and maximum polarization fractions decrease with increasing NH. The uncertainty on the maximum observed polarization fraction, pmax = 22.0?1.4+3.5% at 353 GHz and 80? resolution, is dominated by the uncertainty on the Galactic emission zero level in total intensity, in particular towards diffuse lines of sight at high Galactic latitudes. Furthermore, the inverse behaviour between p and ?? found earlier is seen to be present at high latitudes. This follows the ?????p?1 relationship expected from models of the polarized sky (including numerical simulations of magnetohydrodynamical turbulence) that include effects from only the topology of the turbulent magnetic field, but otherwise have uniform alignment and dust properties. Thus, the statistical properties of p, ?, and ?? for the most part reflect the structure of the Galactic magnetic field. Nevertheless, we search for potential signatures of varying grain alignment and dust properties. First, we analyse the product map ???×?p, looking for residual trends. While the polarization fraction p decreases by a factor of 3?4 between NH?=?1020?cm?2 and NH?=?2?×?1022?cm?2, out of the Galactic plane, this product ???×?p only decreases by about 25%. Because ?? is independent of the grain alignment efficiency, this demonstrates that the systematic decrease in p with NH is determined mostly by the magnetic-field structure and not by a drop in grain alignment. This systematic trend is observed both in the diffuse interstellar medium (ISM) and in molecular clouds of the Gould Belt. Second, we look for a dependence of polarization properties on the dust temperature, as we would expect from the radiative alignment torque (RAT) theory. We find no systematic trend of ???×?p with the dust temperature Td, whether in the diffuse ISM or in the molecular clouds of the Gould Belt. In the diffuse ISM, lines of sight with high polarization fraction p and low polarization angle dispersion ?? tend, on the contrary, to have colder dust than lines of sight with low p and high ??. We also compare the Planck thermal dust polarization with starlight polarization data in the visible at high Galactic latitudes. The agreement in polarization angles is remarkable, and is consistent with what we expect from the noise and the observed dispersion of polarization angles in the visible on the scale of the Planck beam. The two polarization emission-to-extinction ratios, RP/p and RS/V, which primarily characterize dust optical properties, have only a weak dependence on the column density, and converge towards the values previously determined for translucent lines of sight. We also determine an upper limit for the polarization fraction in extinction, pV/E(B???V), of 13% at high Galactic latitude, compatible with the polarization fraction p???20% observed at 353 GHz. Taken together, these results provide strong constraints for models of Galactic dust in diffuse gas

Planck 2018 results: IV. Diffuse component separation

We present full-sky maps of the cosmic microwave background (CMB) and polarized synchrotron and thermal dust emission, derived from the third set of Planck frequency maps. These products have significantly lower contamination from instrumental systematic effects than previous versions. The methodologies used to derive these maps follow closely those described in earlier papers, adopting four methods (Commander, NILC, SEVEM, and SMICA) to extract the CMB component, as well as three methods (Commander, GNILC, and SMICA) to extract astrophysical components. Our revised CMB temperature maps agree with corresponding products in the Planck 2015 delivery, whereas the polarization maps exhibit significantly lower large-scale power, reflecting the improved data processing described in companion papers; however, the noise properties of the resulting data products are complicated, and the best available end-to-end simulations exhibit relative biases with respect to the data at the few percent level. Using these maps, we are for the first time able to fit the spectral index of thermal dust independently over 3° regions. We derive a conservative estimate of the mean spectral index of polarized thermal dust emission of ?d?=?1.55? ± ?0.05, where the uncertainty marginalizes both over all known systematic uncertainties and different estimation techniques. For polarized synchrotron emission, we find a mean spectral index of ?s?=??3.1? ± ?0.1, consistent with previously reported measurements. We note that the current data processing does not allow for construction of unbiased single-bolometer maps, and this limits our ability to extract CO emission and correlated components. The foreground results for intensity derived in this paper therefore do not supersede corresponding Planck 2015 products. For polarization the new results supersede the corresponding 2015 products in all respects.The Planck Collaboration acknowledges the support of: ESA; CNES, and CNRS/INSU-IN2P3-INP (France); ASI, CNR, and INAF (Italy); NASA and DoE (USA); STFC and UKSA (UK); CSIC, MINECO, JA, and RES (Spain); Tekes, AoF, and CSC (Finland); DLR and MPG (Germany); CSA (Canada); DTU Space (Denmark); SER/SSO (Switzerland); RCN (Norway); SFI (Ireland); FCT/MCTES (Portugal); ERC and PRACE (EU). A description of the Planck Collaboration and a list of its members, indicating which technical or scientific activities they have been involved in, can be found at http: //www.cosmos.esa.int/web/planck/planck-collaboration. This work has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement numbers 687312, 776282 and 772253

La radiación del fondo cósmico de microondas a gran escala y la teoría de picos

ABSTRACT: In this PhD thesis, the large-scale anisotropies in the Cosmic Microwave Background (CMB) radiation are analysed. In particular, the theory of peaks in a Gaussian random field on the sphere is reviewed and applied to the CMB temperature and polarization fields, including the eccentricity of the peaks in the formalism. Previous to the characterization of the large-scale peaks, a general study of the derivatives up to second order of the Planck CMB temperature data is performed at different scales, identifying the most significant deviations from the standard cosmological model prediction. A more detailed anaylsis is applied to the largest peaks on the CMB temperature and the Cold Spot. The formalism of the multipolar profiles is used to characterize the shape and geometry of those peaks. Finally, the large-scale anisotropies produced by the Integrated Sachs-Wolfe (ISW) effect are analysed in the last two chapters. In the first one, the claim that the Cold Spot can be originated by the imprint on the CMB temperature of a supervoid is analysed, considering different dark energy models and void geometries. On the other hand, in the last chapter, the ISW effect is detected from the cross-correlation between the CMB temperature and large-scale structure tracers. In particular, the redshift distribution and angular power spectrum of the NRAO VLA Sky Survey (NVSS) are studied in order to have a theoretical model of the angular cross-power spectrum between the CMB temperature and this galaxy catalogue. Some results presented in the latter chapter are included in the çcolaboración Planck en los artículos dedicados al estudio del efecto Sachs-Wolfe integrado.RESUMEN: En esta tesis doctoral, se analizan las anisotropías de la radiación del fondo cósmico de microondas (FCM) a gran escala. En particular, se estudia la teoría de picos que surgen en campos gaussianos aleatorios sobre una superficie esférica, incluyendo la excentricidad de los picos como parámetro. Dicha teoría se aplica al caso particular del la temperatura y la polarización de la radiación del FCM. Para poder caracterizar los picos, es necesario conocer los campos de las derivadas hasta segundo orden. Tomando como banco de pruebas los datos de la misión Planck de la ESA, se realiza un análisis de las derivadas a diferentes escalas, estudiando aquellos lugares que presentan una mayor desviación del modelo cosmológico estándar. Posteriormente, se realiza un análisis más detallado de los picos que forman las estructuras más grandes del FCM, además de la región conocida como el Cold Spot (mancha fría). El formalismo de los perfiles multipolares, desarrollado previamente, se aplica a dichos picos para poder caracterizar su forma y geometría particular. Finalmente, en los dos últimos capítulos, se procede a estudiar las anisotropías del FCM a gran escala producidas por el efecto Sachs-Wolfe Integrado (ISW). En el primero de ellos, se estudia el efecto producido por un supervacío alineado con el Cold Spot, considerando diferentes modelos de energía oscura y geometrías del vacío. Por otro lado, se estudia la correlación cruzada del la temperatura del FCM y de diferentes trazadores de la estructura a gran escala del Universo. En particular, se modeliza el catálogo de galaxias denominado NRAO VLA Sky Survey (NVSS) en términos de su espectro angular de potencias y de su distribución en redshift, para poder tener un modelo teórico adecuado para describir tanto su auto-correlación, como la cruzada con el FCM. Algunos de los resultados presentados en este último capítulo han sido publicados por la colaboración Planck en los artículos dedicados al estudio del efecto Sachs-Wolfe integrado

Planck intermediate results: LVII. Joint Planck LFI and HFI data processing

We present the NPIPE processing pipeline, which produces calibrated frequency maps in temperature and polarization from data from the Planck Low Frequency Instrument (LFI) and High Frequency Instrument (HFI) using high-performance computers. NPIPE represents a natural evolution of previous Planck analysis efforts, and combines some of the most powerful features of the separate LFI and HFI analysis pipelines. For example, following the LFI 2018 processing procedure, NPIPE uses foreground polarization priors during the calibration stage in order to break scanning-induced degeneracies. Similarly, NPIPE employs the HFI 2018 time-domain processing methodology to correct for bandpass mismatch at all frequencies. In addition, NPIPE introduces several improvements, including, but not limited to: inclusion of the 8% of data collected during repointing manoeuvres; smoothing of the LFI reference load data streams; in-flight estimation of detector polarization parameters; and construction of maximally independent detector-set split maps. For component-separation purposes, important improvements include: maps that retain the CMB Solar dipole, allowing for high-precision relative calibration in higher-level analyses; well-defined single-detector maps, allowing for robust CO extraction; and HFI temperature maps between 217 and 857 GHz that are binned into 0?.9 pixels (Nside = 4096), ensuring that the full angular information in the data is represented in the maps even at the highest Planck resolutions. The net effect of these improvements is lower levels of noise and systematics in both frequency and component maps at essentially all angular scales, as well as notably improved internal consistency between the various frequency channels. Based on the NPIPE maps, we present the first estimate of the Solar dipole determined through component separation across all nine Planck frequencies. The amplitude is (3366.6?±?2.7) ?K, consistent with, albeit slightly higher than, earlier estimates. From the large-scale polarization data, we derive an updated estimate of the optical depth of reionization of ??=?0.051?±?0.006, which appears robust with respect to data and sky cuts. There are 600 complete signal, noise and systematics simulations of the full-frequency and detector-set maps. As a Planck first, these simulations include full time-domain processing of the beam-convolved CMB anisotropies. The release of NPIPE maps and simulations is accompanied with a complete suite of raw and processed time-ordered data and the software, scripts, auxiliary data, and parameter files needed to improve further on the analysis and to run matching simulations.The Planck Collaboration acknowledges the support of: ESA; CNES, and CNRS/INSU-IN2P3-INP (France); ASI, CNR, and INAF (Italy); NASA and DoE (USA); STFC and UKSA (UK); CSIC, MINECO, JA, and RES (Spain); Tekes, AoF, and CSC (Finland); DLR and MPG (Germany); CSA (Canada); DTU Space (Denmark); SER/SSO (Switzerland); RCN (Norway); SFI (Ireland); FCT/MCTES (Portugal); ERC and PRACE (EU). A description of the Planck Collaboration and a list of its members, indicating which technical or scientific activities they have been involved in, can be found at http://www.cosmos.esa.int/web/planck/planck-collaboration. This work has received funding from the European Union’s Horizon 2020 research and innovation programme under grant numbers 776282, 772253 and 819478. This research would not have been possible without the resources of the National Energy Research Scientific Computing Center (NERSC), a US Department of Energy Office of Science User Facility operated under Contract No. DE-AC02-05CH11231

Planck intermediate results: LV. Reliability and thermal properties of high-frequency sources in the Second Planck Catalogue of Compact Sources

We describe an extension of the most recent version of the Planck Catalogue of Compact Sources (PCCS2), produced using a new multi-band Bayesian Extraction and Estimation Package (BeeP). BeeP assumes that the compact sources present in PCCS2 at 857 GHz have a dust-like spectral energy distribution (SED), which leads to emission at both lower and higher frequencies, and adjusts the parameters of the source and its SED to fit the emission observed in Planck?s three highest frequency channels at 353, 545, and 857 GHz, as well as the IRIS map at 3000 GHz. In order to reduce confusion regarding diffuse cirrus emission, BeeP?s data model includes a description of the background emission surrounding each source, and it adjusts the confidence in the source parameter extraction based on the statistical properties of the spatial distribution of the background emission. BeeP produces the following three new sets of parameters for each source: (a) fits to a modified blackbody (MBB) thermal emission model of the source; (b) SED-independent source flux densities at each frequency considered; and (c) fits to an MBB model of the background in which the source is embedded. BeeP also calculates, for each source, a reliability parameter, which takes into account confusion due to the surrounding cirrus. This parameter can be used to extract sub-samples of high-frequency sources with statistically well-understood properties. We define a high-reliability subset (BeeP/base), containing 26 083 sources (54.1% of the total PCCS2 catalogue), the majority of which have no information on reliability in the PCCS2. We describe the characteristics of this specific high-quality subset of PCCS2 and its validation against other data sets, specifically for: the sub-sample of PCCS2 located in low-cirrus areas; the Planck Catalogue of Galactic Cold Clumps; the Herschel GAMA15-field catalogue; and the temperature- and spectral-index-reconstructed dust maps obtained with Planck?s Generalized Needlet Internal Linear Combination method. The results of the BeeP extension of PCCS2, which are made publicly available via the Planck Legacy Archive, will enable the study of the thermal properties of well-defined samples of compact Galactic and extragalactic dusty sources.The Planck Collaboration acknowledges the support of: ESA; CNES and CNRS/INSU-IN2P3-INP (France); ASI, CNR, and INAF (Italy); NASA and DoE (USA); STFC and UKSA (UK); CSIC, MINECO, JA, and RES (Spain); Tekes, AoF and CSC (Finland); DLR and MPG (Germany); CSA (Canada); DTU Space (Denmark); SER/SSO (Switzerland); RCN (Norway); SFI (Ireland); FCT/MCTES (Portugal); and ERC and PRACE (EU). A description of the Planck Collaboration and a list of its members, indicating which technical or scientific activities they have been involved in, can be found at http://www.cosmos.esa.int/web/planck/planck-collaboration. We acknowledge support from the ESTEC Faculty Research Project Programme

Planck 2018 results: VI. Cosmological parameters

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 many parameters, with residual modelling uncertainties estimated to affect them only at the 0.5? level. We find good consistency with the standard spatially-flat 6-parameter ?CDM cosmology having a power-law spectrum of adiabatic scalar perturbations (denoted ?base ?CDM? in this paper), from polarization, temperature, and lensing, separately and in combination. A combined analysis gives dark matter density ?ch2?=?0.120?±?0.001, baryon density ?bh2?=?0.0224?±?0.0001, scalar spectral index ns?=?0.965?±?0.004, and optical depth ??=?0.054?±?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 100?*?=?1.0411?±?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-?CDM cosmology, the inferred (model-dependent) late-Universe parameters are: Hubble constant H0?=?(67.4?±?0.5)??km?s?1?Mpc?1; matter density parameter ?m?=?0.315?±?0.007; and matter fluctuation amplitude ?8?=?0.811?±?0.006. We find no compelling evidence for extensions to the base-?CDM model. Combining with baryon acoustic oscillation (BAO) measurements (and considering single-parameter extensions) we constrain the effective extra relativistic degrees of freedom to be Neff?=?2.99?±?0.17, in agreement with the Standard Model prediction Neff?=?3.046, and find that the neutrino mass is tightly constrained to ?m??< ?0.12??eV. The CMB spectra continue to prefer higher lensing amplitudes than predicted in base ?CDM at over 2?, which pulls some parameters that affect the lensing amplitude away from the ?CDM model; however, this is not supported by the lensing reconstruction or (in models that also change the background geometry) BAO data. The joint constraint with BAO measurements on spatial curvature is consistent with a flat universe, ?K?=?0.001?±?0.002. Also combining with Type Ia supernovae (SNe), the dark-energy equation of state parameter is measured to be w0?=??1.03?±?0.03, 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 r0.002?< ?0.06. Standard big-bang nucleosynthesis predictions for the helium and deuterium abundances for the base-?CDM cosmology are in excellent agreement with observations. The Planck base-?CDM 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, 3.6?, 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.The Planck Collaboration acknowledges the support of: ESA; CNES, and CNRS/INSU-IN2P3-INP (France); ASI, CNR, and INAF (Italy); NASA and DoE (USA); STFC and UKSA (UK); CSIC, MINECO, JA, and RES (Spain); Tekes, AoF, and CSC (Finland); DLR and MPG (Germany); CSA (Canada); DTU Space (Denmark); SER/SSO (Switzerland); RCN (Norway); SFI (Ireland); FCT/MCTES (Portugal); ERC and PRACE (EU). A description of the Planck Collaboration and a list of its members, indicating which technical or scientific activities they have been involved in, can be found at https://www.cosmos.esa.int/web/planck/planck-collaboration. We additionally acknowledge support from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013)/ERC Grant Agreement No. [616170]. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 725456, CMBSPEC). We thank Ofelia Pisanti for providing updated numerical BBN results from the PArthENoPE code, Cyril Pitrou for producing some results from the PRIMAT code, and the DES team for sharing their likelihoods. We also thank Marco Crisostomi, Ignacy Sawicky, Alessandra Silvestri, and Filippo Vernizzi for discussions on the dark-energy and modified-gravity models. Some of the results in this paper have been derived using the HEALPix package

Planck 2018 results: X. Constraints on inflation

We report on the implications for cosmic inflation of the 2018 release of the Planck cosmic microwave background (CMB) anisotropy measurements. The results are fully consistent with those reported using the data from 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 ns?=?0.9649?±?0.0042 at 68% CL. We find no evidence for a scale dependence of ns, either as a running or as a running of the running. The Universe is found to be consistent with spatial flatness with a precision of 0.4% at 95% CL by combining Planck with a compilation of baryon acoustic oscillation data. The Planck 95% CL upper limit on the tensor-to-scalar ratio, r0.002?< ?0.10, is further tightened by combining with the BICEP2/Keck Array BK15 data to obtain r0.002?< ?0.056. In the framework of standard single-field inflationary models with Einstein gravity, these results imply that: (a) the predictions of slow-roll models with a concave potential, V?(?) < 0, are increasingly favoured by the data; and (b) based on two different methods for reconstructing the inflaton potential, we find no evidence for dynamics beyond slow roll. Three different methods for the non-parametric reconstruction of the primordial power spectrum consistently confirm a pure power law in the range of comoving scales 0.005?Mpc?1???k???0.2?Mpc?1. A complementary analysis also finds no evidence for theoretically motivated parameterized features in the Planck power spectra. For the case of oscillatory features that are logarithmic or linear in k, this result is further strengthened by a new combined analysis including the Planck bispectrum data. The new Planck polarization data provide a stringent test of the adiabaticity of the initial conditions for the cosmological fluctuations. In correlated, mixed adiabatic and isocurvature models, the non-adiabatic contribution to the observed CMB temperature variance is constrained to 1.3%, 1.7%, and 1.7% at 95% CL for cold dark matter, neutrino density, and neutrino velocity, respectively. Planck power spectra plus lensing set constraints on the amplitude of compensated cold dark matter-baryon isocurvature perturbations that are consistent with current complementary measurements. The polarization data also provide improved constraints on inflationary models that predict a small statistically anisotropic quadupolar modulation of the primordial fluctuations. However, the polarization data do not support physical models for a scale-dependent dipolar modulation. All these findings support the key predictions of the standard single-field inflationary models, which will be further tested by future cosmological observations.We are grateful to Jan Hamann and Jim Zibin for extensive help with the final editing of this manuscript. The Planck Collaboration acknowledges the support of: ESA; CNES and CNRS/INSU-IN2P3-INP (France); ASI, CNR, and INAF (Italy); NASA and DoE (USA); STFC and UKSA (UK); CSIC, MINECO, JA, and RES (Spain); Tekes, AoF, and CSC (Finland); DLR and MPG (Germany); CSA (Canada); DTU Space (Denmark); SER/SSO (Switzerland); RCN (Norway); SFI (Ireland); FCT/MCTES (Portugal); ERC and PRACE (EU). A description of the Planck Collaboration and a list of its members, indicating which technical or scientific activities they have been involved in, can be found at http://www.cosmos.esa.int/web/planck/planck-collaboration