Model Predictive Scoring Shows Specific BAO Observations (not SNIa) Drives $w_0w_a$ Tension

Abstract

The recent analyses of DESI DR2 BAO, Planck CMB and various Supernovae datasets have shown preferences for evolving dark energy at various levels of significance, under frequentist model comparison tests. However, the same analysis done with a pure Bayesian model comparison test can lead to the opposite conclusion due to the impact of $w_0w_a$ priors. In contrast to these in-sample model comparison route, we approach the problem along a third axis -- which model better predicts unseen data. We use the Expected Log Predictive Density (ELPD) metric to score the predictiveness of $\Lambda$CDM and $w_0w_a$CDM models, using the leave-one-redshift-block-out cross-validation estimator. The comparison metric $\Delta$ELPD is out-of-sample, unlike $\Delta \chi^2_{\rm MAP}$ and Bayes Factor, and insensitive to prior width, unlike the Bayes factor. Aggregated, we find modest preferences for $w_0 w_a$CDM, primarily driven by the BAO. Decomposing the $\Delta$ELPD score by redshift we find that a single BAO block, LRG2 ($z = 0.706$), supplies the entire BAO preference. Interestingly, the biggest outlier point, LRG1, contributes little to the model predictive scoring because both $\Lambda$CDM and $w_0w_a$CDM fail to predict the observation by equal amount. On the other hand, all SNIa datasets' $\Delta$ELPD scores are consistent with $0$, indicating that at an out-of-distribution predictive level, the $w_0w_a$CDM tension is entirely driven by one BAO point, not SNIa.