Publications (193)458.01 Total impact
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ABSTRACT: The lensinginduced $B$mode signal is a valuable probe of the dark matter distribution integrated back to the lastscattering surface, with a broad kernel that peaks at $z\simeq2$. It also constitutes an important contaminant for the extraction of the primary CMB $B$modes from inflation. Combining allsky coverage and high resolution and sensitivity, Planck provides accurate nearly allsky measurements of both the polarization $E$mode signal and the integrated mass distribution via the reconstruction of the CMB gravitational lensing. By combining these two data products, we have produced an allsky template map of the secondary CMB $B$modes using a realspace algorithm that minimizes the impact of sky masks. The crosscorrelation of this template with an observed (primordial and secondary) $B$mode map can be used to measure the lensing $B$mode power spectrum at all angular scales. In particular when crosscorrelating with the $B$mode contribution directly derived from the Planck polarization maps, we obtain lensinginduced $B$mode power spectrum measurements at a significance of $12\,\sigma$, which are in agreement with the theoretical expectation derived from the \Planck\ bestfit $\Lambda$CDM model. This unique nearly allsky secondary $B$mode template, which includes the lensinginduced information from intermediate to small ($10\lesssim \ell\lesssim 1000$) angular scales, is delivered as part of the Planck 2015 public data release. It will be particularly useful for experiments searching for primordial $B$modes, such as BICEP2/Keck Array or LiteBIRD, since it will enable an estimate to be made of the secondary (i.e., lensing) contribution to the measured total CMB $B$modes.  [Show abstract] [Hide abstract]
ABSTRACT: The Virgo cluster is the largest SunyaevZeldovich (SZ) source in the sky, both in terms of angular size and total integrated flux. Planck's wide angular scale and frequency coverage, together with its high sensitivity, allow a detailed study of this large object through the SZ effect. Virgo is well resolved by Planck, showing an elongated structure, which correlates well with the morphology observed from Xrays, but extends beyond the observed Xray signal. We find a good agreement between the SZ signal (or Compton paranmeter, y_c) observed by Planck and the expected signal inferred from Xray observations and simple analytical models. Due to its proximity to us, the gas beyond the virial radius can be studied with unprecedented sensitivity by integrating the SZ signal over tens of square degrees. We study the signal in the outskirts of Virgo and compare it with analytical models and a constrained simulation of the environment of Virgo. Planck data suggest that significant amounts of lowdensity plasma surround Virgo out to twice the virial radius. We find the SZ signal in the outskirts of Virgo to be consistent with a simple model that extrapolates the inferred pressure at lower radii while assuming that the temperature stays in the keV range beyond the virial radius. The observed signal is also consistent with simulations and points to a shallow pressure profile in the outskirts of the cluster. This reservoir of gas at large radii can be linked with the hottest phase of the elusive warm/hot intergalactic medium. Taking the lack of symmetry of Virgo into account, we find that a prolate model is favoured by the combination of SZ and Xray data, in agreement with predictions.  [Show abstract] [Hide abstract]
ABSTRACT: We present the 8th Full Focal Plane simulation set (FFP8), deployed in support of the Planck 2015 results. FFP8 consists of 10 fiducial mission realizations reduced to 18144 maps, together with the most massive suite of Monte Carlo realizations of instrument noise and CMB ever generated, comprising $10^4$ mission realizations reduced to about $10^6$ maps. The resulting maps incorporate the dominant instrumental, scanning, and data analysis effects; remaining subdominant effects will be included in future updates. Generated at a cost of some 25 million CPUhours spread across multiple highperformancecomputing (HPC) platforms, FFP8 is used for the validation and verification of analysis algorithms, as well as their implementations, and for removing biases from and quantifying uncertainties in the results of analyses of the real data.  [Show abstract] [Hide abstract]
ABSTRACT: We update the allsky Planck catalogue of 1227 clusters and cluster candidates (PSZ1) published in March 2013, derived from detections of the SunyaevZeldovich (SZ) effect using the first 15.5 months of Planck satellite observations. As an addendum, we deliver an updated version of the PSZ1 catalogue, reporting the further confirmation of 86 Planckdiscovered clusters. In total, the PSZ1 now contains 947 confirmed clusters, of which 214 were confirmed as newly discovered clusters through followup observations undertaken by the Planck Collaboration. The updated PSZ1 contains redshifts for 913 systems, of which 736 (similar to 80.6%) are spectroscopic, and associated mass estimates derived from the Yz mass proxy. We also provide a new SZ quality flag for the remaining 280 candidates. This flag was derived from a novel artificial neuralnetwork classification of the SZ signal. Based on this assessment, the purity of the updated PSZ1 catalogue is estimated to be 94%. In this release, we provide the full updated catalogue and an additional readme file with further information on the Planck SZ detections. 
Conference Paper: Simulations of directed energy thrust on rotating asteroids
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ABSTRACT: Asteroids that threaten Earth could be deflected from their orbits using directed energy to vaporize the surface, as the ejected plume creates a reaction thrust that alters the asteroid's trajectory. In this situation, a critical issue is the rotation of the asteroid relative to the directed energy beam, as this will reduce the average thrust magnitude and modify the thrust direction. Flux levels required to evaporate surface material depend on the surface material composition, rotation rate, albedo, and thermal and bulk mechanical properties of the asteroid. The observed distribution of asteroid rotation rates is used, along with an estimated range of material and mechanical properties, as input to a 4D thermalphysical model to calculate the resultant thrust vector. The model uses a directed energy beam, striking the surface of a rotating sphere with specified material properties, beam profile, and rotation rate. The model calculates thermal changes in the sphere, including vaporization and mass ejection of the target material. The amount of vaporization integrated over the target is used to determine the thrust magnitude and the phase shift relative to the nonrotating case. As the object rotates beneath the beam, the energy spreads out, decreasing temperature and vaporization causing both a phase shift and magnitude decrease in the average thrust vector. This produces a 4D analytical model of the expected thrust profile for rotating objects.  [Show abstract] [Hide abstract]
ABSTRACT: This paper presents the Planck 2015 likelihoods, statistical descriptions of the 2point correlation functions of CMB temperature and polarization. They use the hybrid approach employed previously: pixelbased at low multipoles, $\ell$, and a Gaussian approximation to the distribution of crosspower spectra at higher $\ell$. The main improvements are the use of more and better processed data and of Planck polarization data, and more detailed foreground and instrumental models. More than doubling the data allows further checks and enhanced immunity to systematics. Progress in foreground modelling enables a larger sky fraction, contributing to enhanced precision. Improvements in processing and instrumental models further reduce uncertainties. Extensive tests establish robustness and accuracy, from temperature, from polarization, and from their combination, and show that the {\Lambda}CDM model continues to offer a very good fit. We further validate the likelihood against specific extensions to this baseline, such as the effective number of neutrino species. For this first detailed analysis of Planck polarization, we concentrate at high $\ell$ on E modes. At low $\ell$ we use temperature at all Planck frequencies along with a subset of polarization. These data take advantage of Planck's wide frequency range to improve the separation of CMB and foregrounds. Within the baseline cosmology this requires a reionization optical depth $\tau=0.078\pm0.019$, significantly lower than without highfrequency data for explicit dust monitoring. At high $\ell$ we detect residual errors in E, typically at the {\mu}K$^2$ level; we thus recommend temperature alone as the high$\ell$ baseline. Nevertheless, Planck high$\ell$ polarization spectra are already good enough to allow a separate highaccuracy determination of the {\Lambda}CDM parameters, consistent with those established from temperature alone.  [Show abstract] [Hide abstract]
ABSTRACT: The Second Planck Catalogue of Compact Sources is a catalogue of sources detected in singlefrequency maps from the full duration of the Planck mission and supersedes previous versions of the Planck compact source catalogues. It consists of compact sources, both Galactic and extragalactic, detected over the entire sky. Compact sources detected in the lower frequency channels are assigned to the PCCS2, while at higher frequencies they are assigned to one of two subcatalogues, the PCCS2 or PCCS2E, depending on their location on the sky. The first of these catalogues covers most of the sky and allows the user to produce subsamples at higher reliabilities than the target 80% integral reliability of the catalogue. The PCCS2E contains sources detected in sky regions where the diffuse emission makes it difficult to quantify the reliability of the detections. Both the PCCS2 and PCCS2E include polarization measurements, in the form of polarized flux densities, or upper limits, and orientation angles for all seven polarizationsensitive Planck channels. The improved dataprocessing of the fullmission maps and their reduced noise levels allow us to increase the number of objects in the catalogue, improving its completeness for the target 80 % reliability as compared with the previous versions, the PCCS and ERCSC catalogues.  [Show abstract] [Hide abstract]
ABSTRACT: (abridged) We discuss the Galactic foreground emission between 20 and 100GHz based on observations by Planck/WMAP. The Commander componentseparation tool has been used to separate the various astrophysical processes in total intensity. Comparison with RRL templates verifies the recovery of the freefree emission along the Galactic plane. Comparison of the highlatitude Halpha emission with our freefree map shows residuals that correlate with dust optical depth, consistent with a fraction (~30%) of Halpha having been scattered by highlatitude dust. We highlight a number of diffuse spinning dust morphological features at high latitude. There is substantial spatial variation in the spinning dust spectrum, with the emission peak ranging from below 20GHz to more than 50GHz. There is a strong tendency for the spinning dust component near many prominent HII regions to have a higher peak frequency, suggesting that this increase in peak frequency is associated with dust in the photodissociation regions around the nebulae. The emissivity of spinning dust in these diffuse regions is of the same order as previous detections in the literature. Over the entire sky, the commander solution finds more anomalous microwave emission than the WMAP component maps, at the expense of synchrotron and freefree emission. This can be explained by the difficulty in separating multiple broadband components with a limited number of frequency maps. Future surveys (520GHz), will greatly improve the separation by constraining the synchrotron spectrum. We combine Planck/WMAP data to make the highest S/N ratio maps yet of the intensity of the allsky polarized synchrotron emission at frequencies above a few GHz. Most of the highlatitude polarized emission is associated with distinct largescale loops and spurs, and we rediscuss their structure...  [Show abstract] [Hide abstract]
ABSTRACT: We present a description of the pipeline used to calibrate the Planck Low Frequency Instrument (LFI) timelines into thermodynamic temperatures for the Planck 2015 data release, covering 4 years of uninterrupted operations. As in the 2013 data release, our calibrator is provided by the spinsynchronous modulation of the CMB dipole, exploiting both the orbital and solar components. Our 2015 LFI analysis provides an independent Solar dipole estimate in excellent agreement with that of HFI and within $1\sigma$ (0.3 % in amplitude) of the WMAP value. This 0.3 % shift in the peaktopeak dipole temperature from WMAP and a global overhaul of the iterative calibration code increases the overall level of the LFI maps by 0.45 % (30 GHz), 0.64 % (44 GHz), and 0.82 % (70 GHz) in temperature with respect to the 2013 Planck data release, thus reducing the discrepancy with the power spectrum measured by WMAP. We estimate that the LFI calibration uncertainty is at the level of 0.20 % for the 70 GHz map, 0.26 % for the 44 GHz map, and 0.35 % for the 30 GHz map. We provide a detailed description of the impact of all the changes implemented in the calibration since the previous data release.  [Show abstract] [Hide abstract]
ABSTRACT: We present foregroundreduced CMB maps derived from the full Planck data set in both temperature and polarization. Compared to the corresponding Planck 2013 temperature sky maps, the total data volume is larger by a factor of 3.2 for frequencies between 30 and 70 GHz, and by 1.9 for frequencies between 100 and 857 GHz. In addition, systematic errors in the forms of temperaturetopolarization leakage, analoguetodigital conversion uncertainties, and very long time constant errors have been dramatically reduced, to the extent that the cosmological polarization signal may now be robustly recovered on angular scales $\ell\gtrsim40$. On the very largest scales, instrumental systematic residuals are still nonnegligible compared to the expected cosmological signal, and modes with $\ell < 20$ are accordingly suppressed in the current polarization maps by highpass filtering. As in 2013, four different CMB component separation algorithms are applied to these observations, providing a measure of stability with respect to algorithmic and modelling choices. The resulting polarization maps have rms instrumental noise ranging between 0.21 and 0.27$\,\mu\textrm{K}$ averaged over 55 arcmin pixels, and between 4.5 and 6.1$\,\mu\textrm{K}$ averaged over 3.4 arcmin pixels. The cosmological parameters derived from the analysis of temperature power spectra are in agreement at the $1\sigma$ level with the Planck 2015 likelihood. Unresolved mismatches between the noise properties of the data and simulations prevent a satisfactory description of the higherorder statistical properties of the polarization maps. Thus, the primary applications of these polarization maps are those that do not require massive simulations for accurate estimation of uncertainties, for instance estimation of crossspectra and crosscorrelations, or stacking analyses.  [Show abstract] [Hide abstract]
ABSTRACT: 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 tensortoscalar ratio is $r_{0.002} < 0.11$ (95% CL), consistent with the Bmode 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 tensortoscalar 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.  [Show abstract] [Hide abstract]
ABSTRACT: We predict 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 spectra; the effect on CMB polarization induced by Faraday rotation; magneticallyinduced nonGaussianities; and the magneticallyinduced breaking of statistical isotropy. Overall, Planck data constrain the amplitude of PMFs to less than a few nanogauss. In particular, individual limits coming from the analysis of the CMB angular power spectra, using the Planck likelihood, are $B_{1\,\mathrm{Mpc}}< 4.4$ nG (where $B_{1\,\mathrm{Mpc}}$ is the comoving field amplitude at a scale of 1 Mpc) at 95% confidence level, assuming zero helicity, and $B_{1\,\mathrm{Mpc}}< 5.6$ nG when we consider a maximally helical field. For nearly scaleinvariant PMFs we obtain $B_{1\,\mathrm{Mpc}}<2.1$ nG and $B_{1\,\mathrm{Mpc}}<0.7$ nG if the impact of PMFs on the ionization history of the Universe is included in the analysis. From the analysis of magneticallyinduced nonGaussianity we obtain three different values, corresponding to three applied methods, all below 5 nG. The constraint from the magneticallyinduced passivetensor bispectrum is $B_{1\,\mathrm{Mpc}}< 2.8$ nG. A search for preferred directions in the magneticallyinduced passive bispectrum yields $B_{1\,\mathrm{Mpc}}< 4.5$ nG, whereas the the compensatedscalar bispectrum gives $B_{1\,\mathrm{Mpc}}< 3$ 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 $B_{1\,\mathrm{Mpc}}< 1380$ nG. In our final analysis, we consider the harmonicspace correlations produced by Alfv\'en 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 data.  [Show abstract] [Hide abstract]
ABSTRACT: We present the most significant measurement of the cosmic microwave background (CMB) lensing potential to date (at a level of 40 sigma), using temperature and polarization data from the Planck 2015 fullmission release. Using a polarizationonly estimator we detect lensing at a significance of 5 sigma. We crosscheck 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 bestfitting LCDM model based on the Planck temperature and polarization power spectra. Using the lensing likelihood alone we obtain a percentlevel measurement of the parameter combination Sigma_8 Omega_m^{0.25} = 0.591+0.021. We combine our determination of the lensing potential with the Emode polarization also measured by Planck to generate an estimate of the lensing Bmode. We show that this lensing Bmode estimate is correlated with the Bmodes observed directly by Planck at the expected level and with a statistical significance of 10 sigma, confirming Planck's sensitivity to this known sky signal. We also correlate our lensing potential estimate with the largescale temperature anisotropies, detecting a crosscorrelation at the 3 sigma level, as expected due to dark energy in the concordance LCDM model.  [Show abstract] [Hide abstract]
ABSTRACT: This paper describes the mapmaking procedure applied to Planck LFI (Low Frequency Instrument) data. The mapmaking step takes as input the calibrated timelines and pointing information. The main products are sky maps of $I,Q$, and $U$ Stokes components. For the first time, we present polarization maps at LFI frequencies. The mapmaking algorithm is based on a destriping technique, enhanced with a noise prior. The Galactic region is masked to reduce errors arising from bandpass mismatch and high signal gradients. We apply hornuniform radiometer weights to reduce effects of beam shape mismatch. The algorithm is the same as used for the 2013 release, apart from small changes in parameter settings. We validate the procedure through simulations. Special emphasis is put on the control of systematics, which is particularly important for accurate polarization analysis. We also produce lowresolution versions of the maps, and corresponding noise covariance matrices. These serve as input in later analysis steps and parameter estimation. The noise covariance matrices are validated through noise Monte Carlo simulations. The residual noise in the map products is characterized through analysis of halfring maps, noise covariance matrices, and simulations.  [Show abstract] [Hide abstract]
ABSTRACT: Planck has mapped the microwave sky in nine frequency bands between 30 and 857 GHz in temperature and seven bands between 30 and 353 GHz in polarization. In this paper we consider the problem of diffuse astrophysical component separation, and process these maps within a Bayesian framework to derive a consistent set of fullsky astrophysical component maps. For the temperature analysis, we combine the Planck observations with the 9year WMAP sky maps and the Haslam et al. 408 MHz map to derive a joint model of CMB, synchrotron, freefree, spinning dust, CO, line emission in the 94 and 100 GHz channels, and thermal dust emission. Fullsky maps are provided with angular resolutions varying between 7.5 arcmin and 1 deg. Global parameters (monopoles, dipoles, relative calibration, and bandpass errors) are fitted jointly with the sky model, and bestfit values are tabulated. For polarization, the model includes CMB, synchrotron, and thermal dust emission. These models provide excellent fits to the observed data, with rms temperature residuals smaller than 4 uK over 93% of the sky for all Planck frequencies up to 353 GHz, and fractional errors smaller than 1% in the remaining 7% of the sky. The main limitations of the temperature model at the lower frequencies are degeneracies among the spinning dust, freefree, and synchrotron components; additional observations from external lowfrequency experiments will be essential to break these. The main limitations of the temperature model at the higher frequencies are uncertainties in the 545 and 857 GHz calibration and zeropoints. For polarization, the main outstanding issues are instrumental systematics in the 100353 GHz bands on large angular scales in the form of temperaturetopolarization leakage, uncertainties in the analogtodigital conversion, and very long time constant corrections, all of which are expected to improve in the near future. 
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ABSTRACT: We study the implications of Planck data for models of dark energy (DE) and modified gravity (MG), beyond the cosmological constant scenario. We start with cases where the DE only directly affects the background evolution, considering Taylor expansions of the equation of state, 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. 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 kessence, f(R) theories and coupled DE. In addition to the latest Planck data, for our main analyses we use baryonic acoustic oscillations, typeIa supernovae and local measurements of the Hubble constant. We further show the impact of measurements of the cosmological perturbations, such as redshiftspace 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 are in agreement with LCDM. When testing models that also change perturbations (even when the background is fixed to LCDM), some tensions appear in a few scenarios: the maximum one found is \sim 2 sigma for Planck TT+lowP when parameterizing observables related to the gravitational potentials with a chosen time dependence; the tension increases to at most 3 sigma when external data sets are included. It however disappears when including CMB lensing. 
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ABSTRACT: We present results based on fullmission Planck observations of temperature and polarization anisotropies of the CMB. These data are consistent with the sixparameter inflationary LCDM cosmology. From the Planck temperature and lensing data, for this cosmology we find a Hubble constant, H0= (67.8 +/ 0.9) km/s/Mpc, a matter density parameter Omega_m = 0.308 +/ 0.012 and a scalar spectral index with n_s = 0.968 +/ 0.006. (We quote 68% errors on measured parameters and 95% limits on other parameters.) Combined with Planck temperature and lensing data, Planck LFI polarization measurements lead to a reionization optical depth of tau = 0.066 +/ 0.016. Combining Planck with other astrophysical data we find N_ eff = 3.15 +/ 0.23 for the effective number of relativistic degrees of freedom and the sum of neutrino masses is constrained to < 0.23 eV. Spatial curvature is found to be Omega_K < 0.005. For LCDM we find a limit on the tensortoscalar ratio of r <0.11 consistent with the Bmode constraints from an analysis of BICEP2, Keck Array, and Planck (BKP) data. Adding the BKP data leads to a tighter constraint of r < 0.09. We find no evidence for isocurvature perturbations or cosmic defects. The equation of state of dark energy is constrained to w = 1.006 +/ 0.045. Standard big bang nucleosynthesis predictions for the Planck LCDM cosmology are in excellent agreement with observations. We investigate annihilating dark matter and deviations from standard recombination, finding no evidence for new physics. The Planck results for base LCDM are in agreement with BAO data and with the JLA SNe sample. However the amplitude of the fluctuations is found to be higher than inferred from rich cluster counts and weak gravitational lensing. Apart from these tensions, the base LCDM cosmology provides an excellent description of the Planck CMB observations and many other astrophysical data sets.  [Show abstract] [Hide abstract]
ABSTRACT: Fullsky CMB maps from the 2015 Planck release allow us to detect departures from global isotropy on the largest scales. We present the first searches using CMB polarization for correlations induced by a nontrivial topology with a fundamental domain intersecting, or nearly intersecting, the last scattering surface (at comoving distance $\chi_{rec}$). We specialize to flat spaces with toroidal and slab topologies, finding that explicit searches for the latter are sensitive to other topologies with antipodal symmetry. These searches yield no detection of a compact topology at a scale below the diameter of the last scattering surface. The limits on the radius $R_i$ of the largest sphere inscribed in the topological domain (at loglikelihoodratio $\Delta\ln{L}>5$ relative to a simplyconnected flat Planck bestfit model) are $R_i>0.97\chi_{rec}$ for the cubic torus and $R_i>0.56\chi_{rec}$ for the slab. The limit for the cubic torus from the matchedcircles search is numerically equivalent, $R_i>0.97\chi_{rec}$ (99% CL) from polarisation data alone. We also perform a Bayesian search for a Bianchi VII$_h$ geometry. In the nonphysical setting where the Bianchi cosmology is decoupled from the standard cosmology, Planck temperature data favour the inclusion of a Bianchi component. However, the cosmological parameters generating this pattern are in strong disagreement with those found from CMB anisotropy data alone. Fitting the induced polarization pattern for this model to Planck data requires an amplitude of $0.1\pm0.04$ compared to +1 if the model were to be correct. In the physical setting where the Bianchi parameters are fit simultaneously with the standard cosmological parameters, we find no evidence for a Bianchi VII$_h$ cosmology and constrain the vorticity of such models to $(\omega/H)_0<7.6\times10^{10}$ (95% CL). [Abridged]
Publication Stats
6k  Citations  
458.01  Total Impact Points  
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Institutions

19892015

University of California, Santa Barbara
 Department of Physics
Santa Barbara, California, United States


19922006

University of California, Berkeley
 Department of Physics
Berkeley, California, United States


1991

University of Oxford
Oxford, England, United Kingdom
