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ΛCDM Graphical History

Graphical Parameter Comparisons

Standard ΛCDM requires only 6 independent parameters to completely specify the cosmological model. The specific set of six parameters used to define the cosmological model is somewhat open to choice. Within the context of fitting a ΛCDM model to a CMB power spectrum, the six selected key parameters are primarily chosen to avoid degeneracies and thus speed convergence of the model fit to the data (Kosowsky et al. 2002). Other interesting parameters providing additional physical insight may be derived from the model once the defining six parameters have been set.

We have chosen to focus initially on a mixed set of independent and derived parameters, based on their intrinsic importance in ΛCDM and/or the availability of multiple datasets that provide valuable independent cross-checks. We include the scalar power law index ns, the age of the Universe t0, the optical depth to reionization τ, and four parameters related to matter content. These four are the physical baryon density Ωbh2, the physical CDM density Ωch2, the matter density Ωm, and the fluctuation amplitude σ8. The Ω parameters are defined as the ratio of the present day mean density of each component χ to the critical density: by definition ΣχΩχ = 1. Neglecting smaller order terms, Ωc + Ωb + ΩΛ ≈ 1, and Ωm ≈ Ωc + Ωb. The reduced Hubble constant, h, is defined as H0/100, where H0 is the present-day Hubble parameter. Other parameters may be included in future updates to this text.

Sources in the literature for values of these selected parameters determined between the years 1996 and 2016 are shown in the Data References Table. It would be a formidable task to include all results from all experiments and every paper. Therefore, results presented here are representative, and there are multiple caveats associated with those choices. For example, we do not guarantee that the datapoints are statistically independent of each other, although the choice of data sources is motivated to some extent by a wish to include independent determinations. There also has been no attempt to estimate what fraction of the parameter uncertainties are due to cosmic variance, although this should clearly be a consideration.

We discuss the individual parameters in pages that follow, and include an accompanying graphical history for each. Vertical gray lines shown in the graphical histories are weighted averages of the WMAP and Planck data points rather than the entire sample. This is done as a visual aid, rather than a statement that this is the current best value: the WMAP and Planck data values serve as a common thread in each of the plots. In a few cases, liberties were taken in the quoting of asymmetric error bars from published results as symmetric error bars on the plots. For illustrative purposes, the differences are negligible. Quoted uncertainties are 68% confidence limits.

Data references Table

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