Cosmological parameters and MC chains
The cosmological parameter results explore a variety of cosmological models with combinations of Planck and other data. We provide results from MCMC exploration chains, as well as best fits, and sets of parameter tables. Definitions, conventions and reference are contained in Planck-2013-XVIPlanck-2015-A15.
Parameter chains are produced using CosmoMC, a sampling package available here. This includes the sample analysis package (and GUI) GetDist, and the scripts for managing, analysing, and plotting results from the full grid or runs. Chain products provided here have had burn in removed. Some results with additional data are produced by importance sampling.
Note that the baseline model includes one massive neutrino (0.06eV). Grid outputs include WMAP 9 results for consistent assumptions.
Caveats and known issues
- Confidence intervals are derived from the MCMC samples, and assume the input likelihoods are exactly correct, so there is no quantification for systematic errors other than via the covariance, foreground and beam error models assumed in the likelihood codes.
- Non-linear lensing modelling uses Halofit; for some extended models and CMB lensing only analyses, tails of the chains may be away from the domain of validity.
- The CAMB version used for most results is Dec 2014; the Jan 2015 version is used for lensing-only models with neutrinos, and only differs in the neutrino corrections to the Halofit model.
- There is evidence of temperature-polarization leakage that may affect results including high-L polarization, use caution in the interpretation of results including polarization
- Alternative CamSpec likelihood results in the tables are generated using a slightly older CosmoMC version, with fewer derived parameters and a slightly different BBN predictions for the helium abundance.
Results of the parameter exploration runs should be reproducible using CosmoMC with the Planck likelihood code.
These list parameter constraints for each considered model and data combination separately. For the baseline likelihood see
- PDF tables with 68% limits File:Baseline params table 2015 limit68.pdf
- PDF tables with 95% limits File:Baseline params table 2015 limit95.pdf
There are also larger files including alternative CamSpec and DetSet likelihood results, along with shifts in parameters compared to baseline in units of the baseline error:
- PDF tables with 68% limits File:Params table 2015 limit68.pdf
- PDF tables with 95% limits File:Params table 2015 limit95.pdf
|plikHM||baseline high-L Planck power spectra (plik cross half-mission, 30 <= l <= 2508)|
|plikDS||high-L Planck power spectra (plik cross detsets, 30 <= l <= 2508)|
|CamSpecHM||high-L Planck power spectra (CamSpec cross half-mission, 30 <= l <= 2500)|
|CamSpecDS||high-L Planck power spectra (CamSpec cross detsets, 30 <= l <= 2500)|
|lowl||low-L: Planck temperature only (2 <= l <= 29)|
|lowTEB||low-L temperature and LFI polarization (2 <= l <= 29)|
|lowEB||low-L LFI polarization only (2 <= l <= 29)|
|WMAPTEB||low-L temperature, and LFI+WMAP polarization (2 <= l <= 29)|
|lensing||Planck lensing power spectrum reconstruction|
|lensingonly||Planck lensing power spectrum reconstruction only; T,E fixed to best-fit spectrum + priors|
|BKP||The Bicep-Keck-Planck fiducial B mode likelihood|
|zre6p5||A hard prior z_re > 6.5|
|tau07||A Gaussian prior on the optical depth, tau = 0.07 +- 0.02|
|reion||A hard prior z_re > 6.5, combined with Gaussian prior z_re = 7 +- 1|
|BAO||Baryon oscillation data from DR11LOWZ, DR11CMASS, MGS and 6DF|
|JLA||Supernova data from the SDSS-II/SNLS3 Joint Light-curve Analysis|
|H070p6||Hubble parameter constraint, H_0 = 70.6 +- 3.3|
|theta||theta_MC fixed to 1.0408|
|WLonlyHeymans||Conservative cut of the CFHTLenS weak lensing data + priors|
|WMAP||The full WMAP (temperature and polarization) 9 year data|
The high-L Planck likelihoods have TT, TE, EE variants from each spectrum alone, plus the TTTEEE joint constraint.
Tags used to identify the model parameters that are varied are described in File:Parameter tag definitions 2015.pdf.
We provide the full chains and getdist outputs for our parameter results. The entire grid of results is available from as a 3.7GB compressed file:
Where nn is the most recent update. You can also download the Bicep2/Keck/Planck (BKP) joint constraints for +r models, and smaller files containing key results in the base model only:
The download contains a hierarchy of directories, with each separate chain in a separate directory. The structure for the directories is
where AAA and BBB are any additional parameters that are varied in addition to the six parameters of the baseline model. XXX, YYY, etc encode the data combinations used. These follow the naming conventions described above under Parameter Tables. Each directory contains the main chains, 4-8 text files with one chain in each, and various other files all with names of the form
where ext describes the type of file, and the possible values or ext are
|.txt||parameter chain file with burn in removed|
|.paramnames||File that describes the parameters included in the chains|
|.inputparams||Input parameters used when generating the chain|
|.minimum||Best-fit parameter values, -log likelihoods and chi-square|
|.minimum.theory_cl||The best-fit temperature and polarization power spectra and lensing potential (see below)|
|.minimum.plik_foregrounds||The best-fit foreground model (additive component) for each data power spectrum used|
|.minimum.inputparams||Input parameters used when generating the best fit|
|.ranges||prior ranges assumed for each parameter|
In addition each directory contains any importance sampled outputs with additional data. These have names of the form
where ZZZ is the data likelihood that is added by importance sampling. Finally, each directory contains a dist subdirectory, containing results of chain analysis. File names follow the above conventions, with the following extensions
|.margestats||mean, variance and 68, 95 and 99% limits for each parameter (see below)|
|.likestats||parameters of best-fitting sample in the chain (generally different from the .minmum global best-fit)|
|.covmat||Covariance matrix for the MCMC parameters|
|.corr||Correlation matrix for the parameters|
|.converge||A summary of various convergence diagnostics|
Python scripts for reading in chains and calculating new derived parameter constraints are available as part of CosmoMC, see the readme for details . The config directory in the download includes information about the grid configuration used by the plotting and grid scripts.
The file formats are standard Jan 2015 CosmoMC outputs. CosmoMC includes python scripts for generating tables, 1D, 2D and 3D plots using the provided data, as well as a GUI for conveniently making plots from grid downloads. The formats are summarised here:
- Chain files
- Each chain file is ASCII and contains one sample on each line. Each line is of the format
- weight like param1 param2 param3 …
- Here weight is the importance weight or multiplicity count, and like is the total -log Likelihood. param1,param2, etc are the parameter values for the sample, where the numbering is defined by the position in the accompanying .paramnames files.
- Note that burn in has been removed from the cosmomc outputs, so full chains provided can be used for analysis. Importance sampled results (with _post) in the name have been thinned by a factor of 10 compared to the original chains, so the files are smaller, but this does not significantly affect the effective number of samples. Note that due to the way MCMC works, the samples in the chain outputs are not independent, but it is safe to use all the samples for estimating posterior averages.
- .margestats files
- Each row contains the marginalized constraint on individual parameters. The format is fairly self explanatory given the text description in the file, with each line of the form
- parameter mean sddev lower1 upper1 limit1 lower2 upper2 limit2 lower3 upper3 limit3
- where sddev is the standard deviation, and the limits are 1: 68%, 2: 95%, 3: 99%. The limit tags specify whether a given limit is one tail, two tail or none (if no constraint within the assumed prior boundary).
- .minimum.theory_cl files
- They contain the best-fit theoretical power spectra (without foregrounds) for each model. The columns are: , , , , , and , were in . Also is the power spectrum of the lensing deflection angle, where is the lensing potential power spectrum. Note that the lensing spectrum may not be accurate at L > 400 due to the maximum wavenumber and non-linear correction accuracy settings.
- Planck 2013 results. XVI. Cosmological parameters, Planck Collaboration, 2014, A&A, 571, A16.
- Planck 2015 results. XIII. Cosmological parameters, Planck Collaboration, 2016, A&A, 594, A13.
Cosmic Microwave background
(Planck) Low Frequency Instrument