Planck 2015 results XXIV. Cosmology from Sunyaev-Zeldovich cluster counts

Acknowledgements. 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.We present cluster counts and corresponding cosmological constraints from the Planck full mission data set. Our catalogue consists of 439 clusters detected via their Sunyaev-Zeldovich (SZ) signal down to a signal-to-noise ratio of 6, and is more than a factor of 2 larger than the 2013 Planck cluster cosmology sample. The counts are consistent with those from 2013 and yield compatible constraints under the same modelling assumptions. Taking advantage of the larger catalogue, we extend our analysis to the two-dimensional distribution in redshift and signal-to-noise. We use mass estimates from two recent studies of gravitational lensing of background galaxies by Planck clusters to provide priors on the hydrostatic bias parameter, (1−b). In addition, we use lensing of cosmic microwave background (CMB) temperature fluctuations by Planck clusters as an independent constraint on this parameter. These various calibrations imply constraints on the present-day amplitude of matter fluctuations in varying degrees of tension with those from the Planck analysis of primary fluctuations in the CMB; for the lowest estimated values of (1−b) the tension is mild, only a little over one standard deviation, while it remains substantial (3.7σ) for the largest estimated value. We also examine constraints on extensions to the base flat ΛCDM model by combining the cluster and CMB constraints. The combination appears to favour non-minimal neutrino masses, but this possibility does little to relieve the overall tension because it simultaneously lowers the implied value of the Hubble parameter, thereby exacerbating the discrepancy with most current astrophysical estimates. Improving the precision of cluster mass calibrations from the current 10%-level to 1% would significantly strengthen these combined analyses and provide a stringent test of the base ΛCDM model.European Space AgencyCentre National D'etudes SpatialesCNRS/INSU-IN2P3-INP (France)Italian Space Agency (ASI)Italian National Research CouncilIstituto Nazionale Astrofisica (INAF)National Aeronautics & Space Administration (NASA)United States Department of Energy (DOE)UKSA (UK)Consejo Superior de Investigaciones Cientificas (CSIC)MINECO (Spain)JA (Spain)RES (Spain)Finnish Funding Agency for Technology & Innovation (TEKES)AoF (Finland)CSC (Finland)Helmholtz AssociationGerman Aerospace Centre (DLR)Max Planck SocietyCSA (Canada)DTU Space (Denmark)SER/SSO (Switzerland)RCN (Norway)Science Foundation IrelandPortuguese Foundation for Science and TechnologyERC (EU)European Union (EU)Science & Technology Facilities Council (STFC) ST/L000768/1 ST/L000393/

Planck 2015 results XXVII. The second Planck catalogue of Sunyaev-Zeldovich sources

Acknowledgements. 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. We thank Ian McCarthy for providing images and profiles of simulated clusters from cosmo-OWLS. This research has made use of the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration, and the SIMBAD database, operated at CDS, Strasbourg, France This research made use of data retrieved from SDSS-III. Funding for SDSSIII has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, and the US Department of Energy Office of Science; the SDSS-III web site is http://www.sdss3.org/. This research has made use of data processed by the Centre d’Analyse de Données Étendues (http://cade.irap.omp.eu/) and has made use of the HEALPix pixelization software (http://healpix.sourceforge.net; Górski et al. 2005). Some of this work was performed using the Darwin Supercomputer of the University of Cambridge High Performance Computing Service (http: //www.hpc.cam.ac.uk/), provided by Dell Inc. using Strategic Research Infrastructure Funding from the Higher Education Funding Council for England and funding from the Science and Technology Facilities Council.We present the all-sky Planck catalogue of Sunyaev-Zeldovich (SZ) sources detected from the 29 month full-mission data. The catalogue (PSZ2) is the largest SZ-selected sample of galaxy clusters yet produced and the deepest systematic all-sky surveyof galaxy clusters. It contains 1653 detections, of which 1203 are confirmed clusters with identified counterparts in external data sets, and is the first SZ-selected cluster survey containing >103 confirmed clusters. We present a detailed analysis of the survey selection function in terms of its completeness and statistical reliability, placing a lower limit of 83% on the purity. Using simulations, we find that the estimates of the SZ strength parameter Y5R500are robust to pressure-profile variation and beam systematics, but accurate conversion to Y500 requires the use of prior information on the cluster extent. We describe the multi-wavelength search for counterparts in ancillary data, which makes use of radio, microwave, infra-red, optical, and X-ray data sets, and which places emphasis on the robustness of the counterpart match. We discuss the physical properties of the new sample and identify a population of low-redshift X-ray under-luminous clusters revealed by SZ selection. These objects appear in optical and SZ surveys with consistent properties for their mass, but are almost absent from ROSAT X-ray selected samples.European Space AgencyCentre National D'etudes SpatialesCNRS/INSU-IN2P3-INP (France)Italian Space Agency (ASI)Italian National Research CouncilIstituto Nazionale Astrofisica (INAF)National Aeronautics & Space Administration (NASA)Max Planck SocietyCSA (Canada)DTU Space (Denmark)SER/SSO (Switzerland)RCN (Norway)Science Foundation IrelandPortuguese Foundation for Science and TechnologyERC (EU)European Union (EU)Higher Education Funding Council for EnglandAlfred P. Sloan FoundationNational Science Foundation (NSF)United States Department of Energy (DOE)Science & Technology Facilities Council (STFC) ST/F01239X/1 ST/L000393/1 ST/K001051/1 ST/K004131/1 ST/L000768/1 ST/N001206/1 ST/M001172/1 ST/H001239/

Planck 2015 results XIX. Constraints on primordial magnetic fields

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 research used resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the US Department of Energy under Contract No. DE-AC02-05CH11231. Some of the results in this paper have been derived using the HEALPix package.We compute and investigate four types of imprint of a stochastic background of primordial magnetic fields (PMFs) on the cosmic microwave background (CMB) anisotropies: the impact of PMFs on the CMB temperature and polarization spectra, which is related to their contribution to cosmological perturbations; the effect on CMB polarization induced by Faraday rotation; the impact of PMFs on the ionization history; magnetically-induced non-Gaussianities and related non-zero bispectra; and the magnetically-induced breaking of statistical isotropy. We present constraints on the amplitude of PMFs that are derived from different Planck data products, depending on the specific effect that is being analysed. Overall, Planck data constrain the amplitude of PMFs to less than a few nanoGauss, with different bounds that depend on the considered model. In particular, individual limits coming from the analysis of the CMB angular power spectra, using the Planck likelihood, are B1 Mpc < 4:4 nG (where B1 Mpc is the comoving field amplitude at a scale of 1 Mpc) at 95% confidence level, assuming zero helicity. By considering the Planck likelihood, based only on parity-even angular power spectra, we obtain B1 Mpc < 5:6 nG for a maximally helical field. For nearly scale-invariant PMFs we obtain B1 Mpc < 2:0 nG and B1 Mpc < 0:9 nG if the impact of PMFs on the ionization history of the Universe is included in the analysis. From the analysis of magnetically-induced non-Gaussianity, we obtain three different values, corresponding to three applied methods, all below 5 nG. The constraint from the magnetically-induced passive-tensor bispectrum is B1 Mpc < 2:8 nG. A search for preferred directions in the magneticallyinduced passive bispectrum yields B1 Mpc < 4:5 nG, whereas the compensated-scalar bispectrum gives B1 Mpc < 3 nG. The analysis of the Faraday rotation of CMB polarization by PMFs uses the Planck power spectra in EE and BB at 70 GHz and gives B1 Mpc < 1380 nG. In our final analysis, we consider the harmonic-space correlations produced by Alfvén waves, finding no significant evidence for the presence of these waves. Together, these results comprise a comprehensive set of constraints on possible PMFs with Planck dataEuropean Space AgencyCentre National D'etudes SpatialesCNRS/INSU-IN2P3-INP (France)Italian Space Agency (ASI)Italian National Research CouncilIstituto Nazionale Astrofisica (INAF)National Aeronautics & Space Administration (NASA)UKSA (UK)Consejo Superior de Investigaciones Cientificas (CSIC)MINECO (Spain)JA (Spain)RES (Spain)Finnish Funding Agency for Technology & Innovation (TEKES)AoF (Finland)CSC (Finland)Helmholtz AssociationGerman Aerospace Centre (DLR)Max Planck SocietyCSA (Canada)DTU Space (Denmark)SER/SSO (Switzerland)RCN (Norway)Science Foundation IrelandPortuguese Foundation for Science and TechnologyERC (EU)European Union (EU)United States Department of Energy (DOE) DE-AC02-05CH11231Science & Technology Facilities Council (STFC) ST/L000393/1 ST/L000768/1Villum Fonden 1005

Planck 2015 results XIV. Dark energy and modified gravity

We study the implications of Planck data for models of dark energy (DE) and modified gravity (MG) beyond the standard cosmological constant scenario. We start with cases where the DE only directly affects the background evolution, considering Taylor expansions of the equation of state w(a), as well as principal component analysis and parameterizations related to the potential of a minimally coupled DE scalar field. When estimating the density of DE at early times, we significantly improve present constraints and find that it has to be below ~2% (at 95% confidence) of the critical density, even when forced to play a role for z < 50 only. We then move to general parameterizations of the DE or MG perturbations that encompass both effective field theories and the phenomenology of gravitational potentials in MG models. Lastly, we test a range of specific models, such as k-essence, f(R) theories, and coupled DE. In addition to the latest Planck data, for our main analyses, we use background constraints from baryonic acoustic oscillations, type-Ia supernovae, and local measurements of the Hubble constant. We further show the impact of measurements of the cosmological perturbations, such as redshift-space distortions and weak gravitational lensing. These additional probes are important tools for testing MG models and for breaking degeneracies that are still present in the combination of Planck and background data sets. All results that include only background parameterizations (expansion of the equation of state, early DE, general potentials in minimally-coupled scalar fields or principal component analysis) are in agreement with ΛCDM. When testing models that also change perturbations (even when the background is fixed to ΛCDM), some tensions appear in a few scenarios: the maximum one found is ~2σ for Planck TT+lowP when parameterizing observables related to the gravitational potentials with a chosen time dependence; the tension increases to, at most, 3σ when external data sets are included. It however disappears when including CMB lensing.German Research Foundation (DFG)Swiss National Science Foundation (SNSF)European Space AgencyCentre National D'etudes SpatialesCNRS/INSU-IN2P3-INP (France)Italian Space Agency (ASI)Italian National Research CouncilIstituto Nazionale Astrofisica (INAF)National Aeronautics & Space Administration (NASA)United States Department of Energy (DOE)UKSA (UK)Consejo Superior de Investigaciones Cientificas (CSIC)MINECO (Spain)JA (Spain)RES (Spain)Finnish Funding Agency for Technology & Innovation (TEKES)AoF (Finland)CSC (Finland)Helmholtz AssociationGerman Aerospace Centre (DLR)Max Planck SocietyCSA (Canada)DTU Space (Denmark)SER/SSO (Switzerland)RCN (Norway)Science Foundation IrelandPortuguese Foundation for Science and TechnologyERC (EU)European Union (EU)Science & Technology Facilities Council (STFC) ST/J005673/1 ST/M007065/1 ST/M00418X/1 ST/L000393/1 ST/L000768/1 ST/K00333X/

Planck 2013 results. XXII. Constraints on inflation

We analyse the implications of the Planck data for cosmic inflation. The Planck nominal mission temperature anisotropy measurements, combined with the WMAP large-angle polarization, constrain the scalar spectral index to be ns = 0.9603 ± 0.0073, ruling out exact scale invariance at over 5σ.Planck establishes an upper bound on the tensor-to-scalar ratio of r< 0.11 (95% CL). The Planck data thus shrink the space of allowed standard inflationary models, preferring potentials with V′′< 0. Exponential potential models, the simplest hybrid inflationary models, and monomial potential models of degree n ≥ 2 do not provide a good fit to the data. Planck does not find statistically significant running of the scalar spectral index, obtaining dns/ dlnk = − 0.0134 ± 0.0090. We verify these conclusions through a numerical analysis, which makes no slow-roll approximation, and carry out a Bayesian parameter estimation and model-selection analysis for a number of inflationary models including monomial, natural, and hilltop potentials. For each model, we present the Planck constraints on the parameters of the potential and explore several possibilities for the post-inflationary entropy generation epoch, thus obtaining nontrivial data-driven constraints. We also present a direct reconstruction of the observable range of the inflaton potential. Unless a quartic term is allowed in the potential, we find results consistent with second-order slow-roll predictions. We also investigate whether the primordial power spectrum contains any features. We find that models with a parameterized oscillatory feature improve the fit by Δχ2eff ≈ 10; however, Bayesian evidence does not prefer these models. We constrain several single-field inflation models with generalized Lagrangians by combining power spectrum data with Planck bounds on fNL. Planck constrains with unprecedented accuracy the amplitude and possible correlation (with the adiabatic mode) of non-decaying isocurvature fluctuations. The fractional primordial contributions of cold dark matter (CDM) isocurvature modes of the types expected in the curvaton and axion scenarios have upper bounds of 0.25% and 3.9% (95% CL), respectively. In models with arbitrarily correlated CDM or neutrino isocurvature modes, an anticorrelated isocurvature component can improve the χ2eff by approximately 4 as a result of slightly lowering the theoretical prediction for the ℓ ≲ 40 multipoles relative to the higher multipoles. Nonetheless, the data are consistent with adiabatic initial conditions.European Space AgencyCentre National D'etudes SpatialesCNRS/INSU-IN2P3-INP (France)Italian Space Agency (ASI)Italian National Research CouncilIstituto Nazionale Astrofisica (INAF)National Aeronautics & Space Administration (NASA)United States Department of Energy (DOE)Science & Technology Facilities Council (STFC)UKSA (UK)Consejo Superior de Investigaciones Cientificas (CSIC)Spanish GovernmentJARES (Spain)Finnish Funding Agency for Technology & Innovation (TEKES)AoFCSC (Finland)Helmholtz AssociationGerman Aerospace Centre (DLR)Max Planck SocietyCSA (Canada)DTU Space (Denmark)SER/SSO (Switzerland)RCN (Norway)Science Foundation IrelandPortuguese Foundation for Science and TechnologyEuropean Union (EU)Science & Technology Facilities Council (STFC) ST/K001051/1 ST/K004131/1 ST/L000768/1 ST/K00106X/1 ST/H008586/1 ST/K003674/1 ST/I000976/1 ST/K002899/1 ST/G003874/1 ST/K000985/1 ST/J005673/1 ST/J004812/1 ST/J001368/1 ST/J000388/1 ST/L001314/1 ST/L000393/1 ST/I005765/1 ST/H001239/1 ST/I002006/1 ST/M007685/1 ST/K002805/1 ST/K00333X/

Planck 2013 results. XX. Cosmology from Sunyaev–Zeldovich cluster counts

We present constraints on cosmological parameters using number counts as a function of redshift for a sub-sample of 189 galaxy clusters from the Planck SZ (PSZ) catalogue. The PSZ is selected through the signature of the Sunyaev-Zeldovich (SZ) effect, and the sub-sample used here has a signal-to-noise threshold of seven, with each object confirmed as a cluster and all but one with a redshift estimate. We discuss the completeness of the sample and our construction of a likelihood analysis. Using a relation between mass M and SZ signal Y calibrated to X-ray measurements, we derive constraints on the power spectrum amplitude σ8 and matter density parameter Ωm in a flat ΛCDM model. We test the robustness of our estimates and find that possible biases in the Y–M relation and the halo mass function are larger than the statistical uncertainties from the cluster sample. Assuming the X-ray determined mass to be biased low relative to the true mass by between zero and 30%, motivated by comparison of the observed mass scaling relations to those from a set of numerical simulations, we find that σ8 = 0.75 ± 0.03, Ωm = 0.29 ± 0.02, and σ8(Ωm/ 0.27)0.3 = 0.764 ± 0.025. The value of σ8 is degenerate with the mass bias; if the latter is fixed to a value of 20% (the central value from numerical simulations) we find σ8(Ωm/0.27)0.3 = 0.78 ± 0.01 and a tighter one-dimensional range σ8 = 0.77 ± 0.02. We find that the larger values of σ8 and Ωm preferred by Planck’s measurements of the primary CMB anisotropies can be accommodated by a mass bias of about 40%. Alternatively, consistency with the primary CMB constraints can be achieved by inclusion of processes that suppress power on small scales relative to the ΛCDM model, such as a component of massive neutrinos. We place our results in the context of other determinations of cosmologicalparameters, and discuss issues that need to be resolved in order to make further progress in this field.Science & Technology Facilities Council (STFC) ST/K004131/1 ST/J001368/1 ST/J000388/1 ST/G003874/1 ST/M007685/1 ST/L001314/1 ST/J004812/1 ST/K00333X/1 ST/I005129/1 ST/K002805/1 ST/H008586/1 ST/K000985/1 ST/K002899/1 ST/K003674/1 ST/L000768/1 ST/J005673/1 ST/K006606/1 ST/I002006/1 ST/H001239/1 ST/K001051/1 ST/I005765/

Planck 2015 results XV. Gravitational lensing

Acknowledgements. 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. Some of the results in this paper have been derived using the HEALPix package. We acknowledge support from the Science and Technology Facilities Council [grant number ST/L000652/1]. The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013)/ ERC Grant Agreement No. [616170]. Part of this work was undertaken on the STFC DiRAC HPC Facilities at the University of Cambridge funded by UK BIS National E-infrastructure capital grants.We present the most significant measurement of the cosmic microwave background (CMB) lensing potential to date (at a level of 40σ), using temperature and polarization data from the Planck 2015 full-mission release. Using a polarization-only estimator, we detect lensing at a significance of 5σ. We cross-check the accuracy of our measurement using the wide frequency coverage and complementarity of the temperature and polarization measurements. Public products based on this measurement include an estimate of the lensing potential over approximately 70% of the sky, an estimate of the lensing potential power spectrum in bandpowers for the multipole range 40 ≤ L ≤ 400, and an associated likelihood for cosmological parameter constraints. We find good agreement between our measurement of the lensing potential power spectrum and that found in the ΛCDM model that best fits the Planck temperature and polarization power spectra. Using the lensing likelihood alone we obtain a percent-level measurement of the parameter combination σ8Ω0.25m = 0.591 ± 0.021. We combine our determination of the lensing potential with the E-mode polarization, also measured by Planck, to generate an estimate of the lensing B-mode. We show that this lensing B-mode estimate is correlated with the B-modes observed directly by Planck at the expected level and with a statistical significance of 10σ, confirming Planck’s sensitivity to this known sky signal. We also correlate our lensing potential estimate with the large-scale temperature anisotropies, detecting a cross-correlation at the 3σ level, as expected because of dark energy in the concordance ΛCDM model.European Space AgencyCentre National D'etudes SpatialesCNRS/INSU-IN2P3-INP (France)Italian Space Agency (ASI)Italian National Research CouncilIstituto Nazionale Astrofisica (INAF)National Aeronautics & Space Administration (NASA)United States Department of Energy (DOE)UKSA (UK)Consejo Superior de Investigaciones Cientificas (CSIC)MINECO (Spain)JA (Spain)RES (Spain)Finnish Funding Agency for Technology & Innovation (TEKES)AoF (Finland)CSC (Finland)Helmholtz AssociationGerman Aerospace Centre (DLR)Max Planck SocietyCSA (Canada)DTU Space (Denmark)SER/SSO (Switzerland)RCN (Norway)Science Foundation IrelandPortuguese Foundation for Science and TechnologyERC (EU)European Union (EU)Science & Technology Facilities Council (STFC) ST/L000652/1European Research Council (ERC) 616170UK BIS National E-infrastructure capital grantsScience & Technology Facilities Council (STFC) ST/L000768/1 ST/L000393/1 ST/L000636/

Planck 2013 results. XXXI. Consistency of the Planck data

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Planck intermediate results III : The relation between galaxy cluster mass and Sunyaev-Zeldovich signal

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Planck intermediate results IV : The XMM-Newton validation programme for new Planck galaxy clusters

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