Quantifying concordance of correlated cosmological data sets

TL;DR

The paper develops concordance and discordance estimators for correlated cosmological data within a Gaussian Linear Model, complemented by exact non-Gaussian (MCMC) approaches. It contrasts data-split and parameter-split strategies for incorporating correlations and derives optimal parameter-shift and goodness-of-fit statistics, including their exact or approximate distributions under Gaussian and non-Gaussian regimes. Using Pantheon SN data calibrated by Riess H0, it shows overall agreement with ΛCDM, finds no significant internal tensions above ~1%, and demonstrates that non-Gaussianities and data correlations can materially affect statistical conclusions, especially in high-redshift splits. The work provides a practical, cross-checked toolkit for robust internal consistency tests that will be valuable for current and future precision cosmology surveys.

Abstract

We develop estimators of agreement and disagreement between correlated cosmological data sets. These account for data correlations when computing the significance of both tensions and excess confirmation while remaining statistically optimal. We discuss and thoroughly characterize different approaches commenting on the ones that have the best behavior in practical applications. We complement the calculation of their statistical distribution within the Gaussian model with one estimator that takes non-Gaussianities fully into account. To illustrate the use of our techniques, we apply these estimators to supernovae measurements of the distance-redshift relation, absolutely calibrated by the local distance ladder. The suite of best estimators that we discuss finds results that are in excellent agreement between estimators and find no indications of significant internal inconsistencies in this data set above the $1\%$ probability threshold. This shows the robustness of local determinations of the Hubble constant to features in the distance-redshift relation.

Figures (11)

• Figure 1: The joint marginalized posterior of the full Pantheon SN data set compared to the results obtained neglecting the correlation between the $z>z_{\rm cut}$ and $z<z_{\rm cut}$ SN measurements for the two SN splits that we consider, in panels a) and b) respectively. The filled contour corresponds to the 68% C.L. region while the continuous contour shows the 95% C.L. region.
• Figure 2: The GLM joint marginalized posterior parameter distribution for SN data splits and parameter splits. Different panels show different SN redshift cuts. The filled contour corresponds to the 68% C.L. region while the continuous contour shows the 95% C.L. region.
• Figure 3: The comparison of the GLM and MCMC joint marginalized posterior parameter distribution for SN parameter splits. Different panels show different SN redshift cuts. The filled contour corresponds to the 68% C.L. region while the continuous contour shows the 95% C.L. region.
• Figure 4: The comparison of the MCMC joint marginalized posterior parameter distribution for the full SN data set and the low redshift end of the $z_{\rm cut}=0.7$ split. The filled contour corresponds to the 68% C.L. region while the continuous contour shows the 95% C.L. region.
• Figure 5: The joint posterior of parameter split parameter differences for the two SN split that we consider. The filled contour corresponds to the 68% C.L. region while the continuous contour shows the 95% C.L. region. The dashed lines represent the position of zero shift while the dashed contour shows the probability level that intersects zero, as reported in Tab. \ref{['Tab:MCMCParamSplitParamShiftresults']}.