Planck 2013 results. XVI. Cosmological parameters
TL;DR: In this paper, the authors present the first cosmological results based on Planck measurements of the cosmic microwave background (CMB) temperature and lensing-potential power spectra, which are extremely well described by the standard spatially-flat six-parameter ΛCDM cosmology with a power-law spectrum of adiabatic scalar perturbations.
Abstract: 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 ≳ 40) are extremely well described by the standard spatially-flat six-parameter ΛCDM 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 θ∗ = (1.04147 ± 0.00062) × 10-2, Ωbh2 = 0.02205 ± 0.00028, Ωch2 = 0.1199 ± 0.0027, and ns = 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, H0 = (67.3 ± 1.2) km s-1 Mpc-1, and a high value of the matter density parameter, Ωm = 0.315 ± 0.017. These values are in tension with recent direct measurements of H0 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 ΛCDM 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 ΛCDM cosmology. The deviation of the scalar spectral index from unity isinsensitive to the addition of tensor modes and to changes in the matter content of the Universe. We find an upper limit of r0.002< 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 Neff = 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 Neff = 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 ΛCDM 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 ≲ l ≲ 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.
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TL;DR: In this article, the authors present a cosmological analysis based on full-mission Planck observations of temperature and polarization anisotropies of the cosmic microwave background (CMB) radiation.
Abstract: This paper presents cosmological results based on full-mission Planck observations of temperature and polarization anisotropies of the cosmic microwave background (CMB) radiation. Our results are in very good agreement with the 2013 analysis of the Planck nominal-mission temperature data, but with increased precision. The temperature and polarization power spectra are consistent with the standard spatially-flat 6-parameter ΛCDM cosmology with a power-law spectrum of adiabatic scalar perturbations (denoted “base ΛCDM” in this paper). From the Planck temperature data combined with Planck lensing, for this cosmology we find a Hubble constant, H0 = (67.8 ± 0.9) km s-1Mpc-1, a matter density parameter Ωm = 0.308 ± 0.012, and a tilted scalar spectral index with ns = 0.968 ± 0.006, consistent with the 2013 analysis. Note that in this abstract we quote 68% confidence limits on measured parameters and 95% upper limits on other parameters. We present the first results of polarization measurements with the Low Frequency Instrument at large angular scales. Combined with the Planck temperature and lensing data, these measurements give a reionization optical depth of τ = 0.066 ± 0.016, corresponding to a reionization redshift of . These results are consistent with those from WMAP polarization measurements cleaned for dust emission using 353-GHz polarization maps from the High Frequency Instrument. We find no evidence for any departure from base ΛCDM in the neutrino sector of the theory; for example, combining Planck observations with other astrophysical data we find Neff = 3.15 ± 0.23 for the effective number of relativistic degrees of freedom, consistent with the value Neff = 3.046 of the Standard Model of particle physics. The sum of neutrino masses is constrained to ∑ mν < 0.23 eV. The spatial curvature of our Universe is found to be very close to zero, with | ΩK | < 0.005. Adding a tensor component as a single-parameter extension to base ΛCDM we find an upper limit on the tensor-to-scalar ratio of r0.002< 0.11, consistent with the Planck 2013 results and consistent with the B-mode polarization constraints from a joint analysis of BICEP2, Keck Array, and Planck (BKP) data. Adding the BKP B-mode data to our analysis leads to a tighter constraint of r0.002 < 0.09 and disfavours inflationarymodels with a V(φ) ∝ φ2 potential. The addition of Planck polarization data leads to strong constraints on deviations from a purely adiabatic spectrum of fluctuations. We find no evidence for any contribution from isocurvature perturbations or from cosmic defects. Combining Planck data with other astrophysical data, including Type Ia supernovae, the equation of state of dark energy is constrained to w = −1.006 ± 0.045, consistent with the expected value for a cosmological constant. The standard big bang nucleosynthesis predictions for the helium and deuterium abundances for the best-fit Planck base ΛCDM cosmology are in excellent agreement with observations. We also constraints on annihilating dark matter and on possible deviations from the standard recombination history. In neither case do we find no evidence for new physics. The Planck results for base ΛCDM are in good agreement with baryon acoustic oscillation data and with the JLA sample of Type Ia supernovae. However, as in the 2013 analysis, the amplitude of the fluctuation spectrum is found to be higher than inferred from some analyses of rich cluster counts and weak gravitational lensing. We show that these tensions cannot easily be resolved with simple modifications of the base ΛCDM cosmology. Apart from these tensions, the base ΛCDM cosmology provides an excellent description of the Planck CMB observations and many other astrophysical data sets.
10,728 citations
Max Planck Society1, Yale University2, Space Telescope Science Institute3, Harvard University4, University of Colorado Boulder5, Columbia University6, University of Toronto7, Argonne National Laboratory8, Ohio State University9, European Southern Observatory10, Aix-Marseille University11, ETH Zurich12, California Institute of Technology13, New York University14, Louisiana State University15, Australian National University16, Cornell University17, University College London18, Goddard Space Flight Center19, Leibniz Institute for Astrophysics Potsdam20
TL;DR: Astropy as discussed by the authors is a Python package for astronomy-related functionality, including support for domain-specific file formats such as flexible image transport system (FITS) files, Virtual Observatory (VO) tables, common ASCII table formats, unit and physical quantity conversions, physical constants specific to astronomy, celestial coordinate and time transformations, world coordinate system (WCS) support, generalized containers for representing gridded as well as tabular data, and a framework for cosmological transformations and conversions.
Abstract: We present the first public version (v02) of the open-source and community-developed Python package, Astropy This package provides core astronomy-related functionality to the community, including support for domain-specific file formats such as flexible image transport system (FITS) files, Virtual Observatory (VO) tables, and common ASCII table formats, unit and physical quantity conversions, physical constants specific to astronomy, celestial coordinate and time transformations, world coordinate system (WCS) support, generalized containers for representing gridded as well as tabular data, and a framework for cosmological transformations and conversions Significant functionality is under activedevelopment, such as a model fitting framework, VO client and server tools, and aperture and point spread function (PSF) photometry tools The core development team is actively making additions and enhancements to the current code base, and we encourage anyone interested to participate in the development of future Astropy versions
9,720 citations
TL;DR: In this article, the authors present cosmological parameter results from the full-mission Planck measurements of the cosmic microwave background (CMB) anisotropies, combining information from the temperature and polarization maps and the lensing reconstruction.
Abstract: 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 manyparameters,withresidualmodellinguncertaintiesestimatedtoaffectthemonlyatthe05σlevelWefindgoodconsistencywiththestandard spatially-flat6-parameter ΛCDMcosmologyhavingapower-lawspectrumofadiabaticscalarperturbations(denoted“base ΛCDM”inthispaper), from polarization, temperature, and lensing, separately and in combination A combined analysis gives dark matter density Ωch2 = 0120±0001, baryon density Ωbh2 = 00224±00001, scalar spectral index ns = 0965±0004, and optical depth τ = 0054±0007 (in this abstract we quote 68% confidence regions on measured parameters and 95% on upper limits) The angular acoustic scale is measured to 003% precision, with 100θ∗ = 10411±00003Theseresultsareonlyweaklydependentonthecosmologicalmodelandremainstable,withsomewhatincreasederrors, in many commonly considered extensions Assuming the base-ΛCDM cosmology, the inferred (model-dependent) late-Universe parameters are: HubbleconstantH0 = (674±05)kms−1Mpc−1;matterdensityparameterΩm = 0315±0007;andmatterfluctuationamplitudeσ8 = 0811±0006 We find no compelling evidence for extensions to the base-ΛCDM model Combining with baryon acoustic oscillation (BAO) measurements (and consideringsingle-parameterextensions)weconstraintheeffectiveextrarelativisticdegreesoffreedomtobe Neff = 299±017,inagreementwith the Standard Model prediction Neff = 3046, and find that the neutrino mass is tightly constrained toPmν < 012 eV The CMB spectra continue to prefer higher lensing amplitudesthan predicted in base ΛCDM at over 2σ, which pulls some parameters that affect thelensing amplitude away from the ΛCDM model; however, this is not supported by the lensing reconstruction or (in models that also change the background geometry) BAOdataThejointconstraintwithBAOmeasurementsonspatialcurvatureisconsistentwithaflatuniverse, ΩK = 0001±0002Alsocombining with Type Ia supernovae (SNe), the dark-energy equation of state parameter is measured to be w0 = −103±003, 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 r0002 < 006 Standard big-bang nucleosynthesis predictions for the helium and deuterium abundances for the base-ΛCDM cosmology are in excellent agreement with observations The Planck base-ΛCDM 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, 36σ, 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
4,688 citations
TL;DR: In this article, the authors report on the implications for cosmic inflation of the 2018 Release of the Planck CMB anisotropy measurements, which are fully consistent with the two previous Planck cosmological releases, but have smaller uncertainties thanks to improvements in the characterization of polarization at low and high multipoles.
Abstract: We report on the implications for cosmic inflation of the 2018 Release of the Planck CMB anisotropy measurements. The results are fully consistent with 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 $n_\mathrm{s}=0.9649\pm 0.0042$ at 68% CL and show no evidence for a scale dependence of $n_\mathrm{s}.$ Spatial flatness is confirmed at a precision of 0.4% at 95% CL with the combination with BAO data. The Planck 95% CL upper limit on the tensor-to-scalar ratio, $r_{0.002}<0.10$, is further tightened by combining with the BICEP2/Keck Array BK15 data to obtain $r_{0.002}<0.056$. In the framework of single-field inflationary models with Einstein gravity, these results imply that: (a) slow-roll models with a concave potential, $V" (\phi) < 0,$ are increasingly favoured by the data; and (b) two different methods for reconstructing the inflaton potential find no evidence for dynamics beyond slow roll. Non-parametric reconstructions of the primordial power spectrum consistently confirm a pure power law. A complementary analysis also finds no evidence for theoretically motivated parameterized features in the Planck power spectrum, a result further strengthened for certain oscillatory models by a new combined analysis that includes Planck bispectrum data. The new Planck polarization data provide a stringent test of the adiabaticity of the initial conditions. The polarization data also provide improved constraints on inflationary models that predict a small statistically anisotropic quadrupolar modulation of the primordial fluctuations. However, the polarization data do not confirm physical models for a scale-dependent dipolar modulation.
3,438 citations
TL;DR: In this paper, the authors used the Wide Field Camera 3 (WFC3) on the Hubble Space Telescope (HST) to reduce the uncertainty in the local value of the Hubble constant from 3.3% to 2.4%.
Abstract: We use the Wide Field Camera 3 (WFC3) on the Hubble Space Telescope (HST) to reduce the uncertainty in the local value of the Hubble constant from 3.3% to 2.4%. The bulk of this improvement comes from new near-infrared (NIR) observations of Cepheid variables in 11 host galaxies of recent type Ia supernovae (SNe Ia), more than doubling the sample of reliable SNe Ia having a Cepheid-calibrated distance to a total of 19, these in turn leverage the magnitude-redshift relation based on ∼300 SNe Ia at z < 0.15. All 19 hosts as well as the megamaser system NGC 4258 have been observed with WFC3 in the optical and NIR, thus nullifying cross-instrument zeropoint errors in the relative distance estimates from Cepheids. Other noteworthy improvements include a 33% reduction in the systematic uncertainty in the maser distance to NGC 4258, a larger sample of Cepheids in the Large Magellanic Cloud (LMC), a more robust distance to the LMC based on late-type detached eclipsing binaries (DEBs), HST observations of Cepheids in M31, and new HST-based trigonometric parallaxes for Milky Way (MW) Cepheids. We consider four geometric distance calibrations of Cepheids: (i) megamasers in NGC 4258, (ii) 8 DEBs in the LMC, (iii) 15 MW Cepheids with parallaxes measured with HST/FGS, HST/WFC3 spatial scanning and/or Hipparcos, and (iv) 2 DEBs in M31. The Hubble constant from each is 72.25 ± 2.51, 72.04 ± 2.67, 76.18 ± 2.37, and 74.50 ± 3.27 km s(−)(1) Mpc(−)(1), respectively. Our best estimate of H (0) = 73.24 ± 1.74 km s(−)(1) Mpc(−)(1) combines the anchors NGC 4258, MW, and LMC, yielding a 2.4% determination (all quoted uncertainties include fully propagated statistical and systematic components). This value is 3.4σ higher than 66.93 ± 0.62 km s(−)(1) Mpc(−)(1) predicted by ΛCDM with 3 neutrino flavors having a mass of 0.06 eV and the new Planck data, but the discrepancy reduces to 2.1σ relative to the prediction of 69.3 ± 0.7 km s(−)(1) Mpc(−)(1) based on the comparably precise combination of WMAP+ACT+SPT+BAO observations, suggesting that systematic uncertainties in CMB radiation measurements may play a role in the tension. If we take the conflict between Planck high-redshift measurements and our local determination of H (0) at face value, one plausible explanation could involve an additional source of dark radiation in the early universe in the range of ΔN (eff) ≈ 0.4–1. We anticipate further significant improvements in H (0) from upcoming parallax measurements of long-period MW Cepheids.
2,228 citations
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University of California, Berkeley1, Lawrence Berkeley National Laboratory2, Instituto Superior Técnico3, Pierre-and-Marie-Curie University4, Stockholm University5, European Southern Observatory6, Collège de France7, University of Cambridge8, University of Barcelona9, Yale University10, Space Telescope Science Institute11, European Space Agency12, University of New South Wales13
TL;DR: In this paper, the mass density, Omega_M, and cosmological-constant energy density of the universe were measured using the analysis of 42 Type Ia supernovae discovered by the Supernova Cosmology project.
Abstract: We report measurements of the mass density, Omega_M, and
cosmological-constant energy density, Omega_Lambda, of the universe based on
the analysis of 42 Type Ia supernovae discovered by the Supernova Cosmology
Project. The magnitude-redshift data for these SNe, at redshifts between 0.18
and 0.83, are fit jointly with a set of SNe from the Calan/Tololo Supernova
Survey, at redshifts below 0.1, to yield values for the cosmological
parameters. All SN peak magnitudes are standardized using a SN Ia lightcurve
width-luminosity relation. The measurement yields a joint probability
distribution of the cosmological parameters that is approximated by the
relation 0.8 Omega_M - 0.6 Omega_Lambda ~= -0.2 +/- 0.1 in the region of
interest (Omega_M <~ 1.5). For a flat (Omega_M + Omega_Lambda = 1) cosmology we
find Omega_M = 0.28{+0.09,-0.08} (1 sigma statistical) {+0.05,-0.04}
(identified systematics). The data are strongly inconsistent with a Lambda = 0
flat cosmology, the simplest inflationary universe model. An open, Lambda = 0
cosmology also does not fit the data well: the data indicate that the
cosmological constant is non-zero and positive, with a confidence of P(Lambda >
0) = 99%, including the identified systematic uncertainties. The best-fit age
of the universe relative to the Hubble time is t_0 = 14.9{+1.4,-1.1} (0.63/h)
Gyr for a flat cosmology. The size of our sample allows us to perform a variety
of statistical tests to check for possible systematic errors and biases. We
find no significant differences in either the host reddening distribution or
Malmquist bias between the low-redshift Calan/Tololo sample and our
high-redshift sample. The conclusions are robust whether or not a
width-luminosity relation is used to standardize the SN peak magnitudes.
16,838 citations
TL;DR: In this article, the authors used spectral and photometric observations of 10 Type Ia supernovae (SNe Ia) in the redshift range 0.16 " z " 0.62.
Abstract: We present spectral and photometric observations of 10 Type Ia supernovae (SNe Ia) in the redshift range 0.16 " z " 0.62. The luminosity distances of these objects are determined by methods that employ relations between SN Ia luminosity and light curve shape. Combined with previous data from our High-z Supernova Search Team and recent results by Riess et al., this expanded set of 16 high-redshift supernovae and a set of 34 nearby supernovae are used to place constraints on the following cosmo- logical parameters: the Hubble constant the mass density the cosmological constant (i.e., the (H 0 ), () M ), vacuum energy density, the deceleration parameter and the dynamical age of the universe ) " ), (q 0 ), ) M \ 1) methods. We estimate the dynamical age of the universe to be 14.2 ^ 1.7 Gyr including systematic uncer- tainties in the current Cepheid distance scale. We estimate the likely e†ect of several sources of system- atic error, including progenitor and metallicity evolution, extinction, sample selection bias, local perturbations in the expansion rate, gravitational lensing, and sample contamination. Presently, none of these e†ects appear to reconcile the data with and ) " \ 0 q 0 " 0.
16,674 citations
TL;DR: In this paper, the authors present observations of 10 type Ia supernovae (SNe Ia) between 0.16 0 and 4.0 sigma confidence levels, for two fitting methods respectively.
Abstract: We present observations of 10 type Ia supernovae (SNe Ia) between 0.16 0) and a current acceleration of the expansion (i.e., q_0 0, the spectroscopically confirmed SNe Ia are consistent with q_0 0 at the 3.0 sigma and 4.0 sigma confidence levels, for two fitting methods respectively. Fixing a ``minimal'' mass density, Omega_M=0.2, results in the weakest detection, Omega_Lambda>0 at the 3.0 sigma confidence level. For a flat-Universe prior (Omega_M+Omega_Lambda=1), the spectroscopically confirmed SNe Ia require Omega_Lambda >0 at 7 sigma and 9 sigma level for the two fitting methods. A Universe closed by ordinary matter (i.e., Omega_M=1) is ruled out at the 7 sigma to 8 sigma level. We estimate the size of systematic errors, including evolution, extinction, sample selection bias, local flows, gravitational lensing, and sample contamination. Presently, none of these effects reconciles the data with Omega_Lambda=0 and q_0 > 0.
14,295 citations
TL;DR: In this paper, the mass density, Omega_M, and cosmological-constant energy density of the universe were measured by the analysis of 42 Type Ia supernovae discovered by the Supernova Cosmology Project.
Abstract: We report measurements of the mass density, Omega_M, and cosmological-constant energy density, Omega_Lambda, of the universe based on the analysis of 42 Type Ia supernovae discovered by the Supernova Cosmology Project. The magnitude-redshift data for these SNe, at redshifts between 0.18 and 0.83, are fit jointly with a set of SNe from the Calan/Tololo Supernova Survey, at redshifts below 0.1, to yield values for the cosmological parameters. All SN peak magnitudes are standardized using a SN Ia lightcurve width-luminosity relation. The measurement yields a joint probability distribution of the cosmological parameters that is approximated by the relation 0.8 Omega_M - 0.6 Omega_Lambda ~= -0.2 +/- 0.1 in the region of interest (Omega_M 0) = 99%, including the identified systematic uncertainties. The best-fit age of the universe relative to the Hubble time is t_0 = 14.9{+1.4,-1.1} (0.63/h) Gyr for a flat cosmology. The size of our sample allows us to perform a variety of statistical tests to check for possible systematic errors and biases. We find no significant differences in either the host reddening distribution or Malmquist bias between the low-redshift Calan/Tololo sample and our high-redshift sample. The conclusions are robust whether or not a width-luminosity relation is used to standardize the SN peak magnitudes.
14,013 citations
TL;DR: The focus is on applied inference for Bayesian posterior distributions in real problems, which often tend toward normal- ity after transformations and marginalization, and the results are derived as normal-theory approximations to exact Bayesian inference, conditional on the observed simulations.
Abstract: The Gibbs sampler, the algorithm of Metropolis and similar iterative simulation methods are potentially very helpful for summarizing multivariate distributions. Used naively, however, iterative simulation can give misleading answers. Our methods are simple and generally applicable to the output of any iterative simulation; they are designed for researchers primarily interested in the science underlying the data and models they are analyzing, rather than for researchers interested in the probability theory underlying the iterative simulations themselves. Our recommended strategy is to use several independent sequences, with starting points sampled from an overdispersed distribution. At each step of the iterative simulation, we obtain, for each univariate estimand of interest, a distributional estimate and an estimate of how much sharper the distributional estimate might become if the simulations were continued indefinitely. Because our focus is on applied inference for Bayesian posterior distributions in real problems, which often tend toward normality after transformations and marginalization, we derive our results as normal-theory approximations to exact Bayesian inference, conditional on the observed simulations. The methods are illustrated on a random-effects mixture model applied to experimental measurements of reaction times of normal and schizophrenic patients.
13,884 citations
"Planck 2013 results. XVI. Cosmologi..." refers methods in this paper
...Since the pioneering work of Peebles (1968) and Zeldovich et al. (1969), which identified the main physical processes involved in recombination, there has been significant progress in numerically modelling the many relevant atomic transitions and processes that can affect the details of the recombination process (Hu et al. 1995; Seager et al. 2000; Wong et al. 2008; Hirata & Switzer 2008; Switzer & Hirata 2008; Rubino-Martin et al. 2009; Grin & Hirata 2010; Chluba & Thomas 2011; Ali-Haimoud et al. 2010; Ali-Haimoud & Hirata 2011)....
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...However, the recombination history can be computed even more rapidly by using the simple effective three-level atom model developed by Seager et al. (2000) and implemented in the recfast code8, with appropriately chosen small correction functions calibrated to the full numerical results (Wong et al. 2008; Rubino-Martin et al. 2009; Shaw & Chluba 2011)....
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...We check that the spread in the means between chains is small compared to the standard deviation, using the standard Gelman and Rubin (Gelman & Rubin 1992) criterion 12As described in Planck Collaboration XV (2013), we use spectra calculated on different masks to isolate the contribution of Galactic cirrus at each frequency, which we subtract from the 143× 143, 143× 217 and 217× 217 power spectra (i.e., the correction is applied to the power spectra, not in the map domain)....
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...We check that the spread in the means between chains is small compared to the standard deviation, using the standard Gelman and Rubin (Gelman & Rubin 1992) criterion 12As described in Planck Collaboration XV (2013), we use spectra calculated on different masks to isolate the contribution of…...
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...Although the main processes that lead to recombination at z ≈ 1090 are well understood, cosmological parameters from Planck can be sensitive to sub-percent differences in the ionization fraction xe (Hu et al. 1995; Lewis et al. 2006; Planck Collaboration: Cosmological parameters Rubino-Martin et al. 2009; Shaw & Chluba 2011)....
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