Internal robustness of growth rate data

We perform an internal robustness analysis (iR) to a compilation of the most recent $f{\sigma }_8(z)$ data, using the framework of Ref. [1]. The method analyzes combinations of subsets in the data set in a Bayesian model comparison way, potentially finding outliers, subsets of data affected by systematics or new physics. In order to validate our analysis and assess its sensitivity we performed several cross-checks, for example by removing some of the data or by adding artificially contaminated points, while we also generated mock data sets in order to estimate confidence regions of the iR. Applying this methodology, we found no anomalous behavior in the $f{\sigma }_8(z)$ data set, thus validating its internal robustness.

Figure 1

Violin plots of the internal robustness distributions, for each of the smaller subset sizes of each partition. We employed the narrow flat prior (upper panel), broad flat prior (medium panel), and Gaussian prior (lower panel). The white dots are the mean value of the internal robustness, the bold black line is the $1\sigma$ region, and the thinner black line is the $2\sigma$ region.

Figure 2

Internal robustness PDF and confidence regions from mock data based on the best fit cosmology, using each prior. They are: narrow flat prior (upper panel), broad flat prior (medium panel), and Gaussian prior (lower panel).

Figure 3

Same as Fig. 2, but the base parameters for the mock data are from Planck 2015. Priors used: narrow flat prior (upper panel), broad flat prior (medium panel), and Gaussian prior (lower panel).

Figure 4

Same as Fig. 1, but considering the “r26” data set (upper panel) and the “c1” data set (lower panel), both with a narrow flat prior.

Figure 5

Same as Fig. 2, but considering the “r26” data set (upper panel) and the “s1” data set (lower panel), both with a narrow flat prior. The mock data used to generate the confidence regions from the upper panel come from the best fit of the “r26” data set, while the ones for the lower panel are from the original data set.