Cosmological Parameters

Cosmological parameter results

Description

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 #planck2013-p11.

Production process

Parameter chains are produced using CosmoMC, a sampling package available from [1]. This includes the sample analysis package GetDist, and the scripts for managing and analysing the full grid or runs. Chain products provided here have had burn in removed. Some results with additional data are produced by importance sampling.

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. We had some issues producing reliable results from the minimizer used to produce the best fits, so in some cases the quoted fits may be significantly improved.

Related products

Results of the parameter exploration runs should be reproducible using CosmoMC with the Planck likelihood code.

Parameter Tables

These list paramter constraints for each considered model and data combination separately

• PDF tables with 68% limits File:Grid limit68.pdf
• PDF tables with 95% limits File:Grid limit95.pdf

There are also summary comparison tables, showing how constraints for selected models vary with data used to constrain them:

• Comparison tables with 68% limits File:Comparetables limit68.pdf
• Comparison tables with 95% limits File:Comparetables limit95.pdf

Parameter Chains

We provide the full chains and getdist outputs for our parameter results.

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The download contains a hierarchy of directories, with each separate chain in a separate directory. The structure for the directories is

base_AAA_BBB/XXX_YYY_.../

where AAA and BBB are any additional parameters that are variend in addition to the six parameters of the baseline model. XXX, YYY, etc encode the data combinations used. The parameter tags are defined in #planck2013-p11. Data combination tags are as follows (see the parameters paper for full description and references):

Tag	Data
planck	high-L Planck temperature (CamSpec, 50 <= l <= 2500)
lowl	low-L: Planck temperature (2 <= l <= 49)
lensing	Planck lensing power spectrum reconstruction
lowLike	low-L WMAP 9 polarization
tauprior	A Gaussian prior on the optical depth, tau = 0.09 +- 0.013
BAO	Baryon oscillation data from DR7, DR9 and and 6DF
SNLS	Supernova data from the Supernova Legacy Survey
Union2	Supernova data from the Union compilation
HST	Hubble parameter constraint from HST (Riess et al)
WMAP	The full WMAP (temperature and polarization) 9 year data

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.

base_AAA_BBB_XXX_YYY.ext

where ext describes the type of file

Tag	Data
.txt	parameter chain file with burn in removed
.minimum	Best-fit parameter values, -log likelihoods and chi-square
.bestfit_cl	The best-fit temperature and polarization power spectra and lensing potential (see below)
.inputparams	Input parameters used when generating the chain
.minimum.inputparams	Input parameters used when generating the best fit
.ranges	prior ranges assumed for each parameter

In addition each directory contains any importances sampled outputs with additional data. These have names of the form

base_AAA_BBB_XXX_YYY_post_ZZZ.ext

where ZZZ is the data likelihood that is added by importance sampling.

In addition to the main ouputs, each directory contains a dist subdirectory, containing results of chain analysis. File names follow the above convntions, with the following extensions

Tag	Data
.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

Data likelihoods are either included when running the chains, or by importance sampling. Data combinations that are added by importance sampling appear at the end of the list, following the {\tt post{\textunderscore}} tag. WMAP9 chains are run from the WMAP9 likelihood code with the same baseline assumptions as \textit{Planck}, and hence may different slightly from those available on Lambda (e.g. the baseline model has non-zero neutrino mass). Note that the best fits are merely examples of parameter combinations that fit the data well, due to parameter degeneracies there may be other combinations of parameters that fit the data nearly equally well.

Beneath each table is the minus log Likelihood $\chi^2_{\rm eff}$ for each best fit model, and also the contributions coming from each separate part of the likelihood. The $R-1$ value is also given, which measures the convergence of the sampling chains, with small values being better converged. The sampling uncertainty on quoted mean values are typically of order $R-1$ in units of the standard deviation.

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References

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1. References

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