The Bayesian view of DESI DR2: Evidence and tension in a combined analysis with CMB and supernovae across cosmological models

Abstract

We apply the unimpeded framework to perform a fully Bayesian reanalysis of the DESI DR2 data, using nested sampling with PolyChord to compute evidences for $Λ$CDM and seven extensions across combinations of DESI DR1/DR2, Planck CMB, supernovae (Pantheon+, Union3, DES-SN5YR, DES-Dovekie), and DES-Y1 weak lensing. The Bayesian Ockham's razor penalises extended models, yielding weaker or opposite preferences compared to $Δχ^2$-based analyses. For DESI DR2 BAO combined with Planck CMB alone, the DESI collaboration's $3.1σ$ frequentist preference for $w_0w_a$CDM is eliminated entirely: we obtain ${\ln B = -0.57{\scriptstyle\pm0.26}}$, modestly favouring $Λ$CDM. Adding the corrected DES-Dovekie supernova calibration maintains this concordance (${\ln B = -0.01{\scriptstyle\pm0.27}}$). However, when the original DES-SN5YR calibration is included instead, the DESI collaboration's $4.2σ$ result survives the Bayesian Ockham penalty as a $3.07{\scriptstyle\pm0.10}\,σ$ preference (${\ln B = +3.32{\scriptstyle\pm0.27}}$). That this signal persists despite the Ockham penalty makes the role of tension quantification essential: our analysis traced the preference to the DES-SN5YR calibration error, which introduced a $2.95{\scriptstyle\pm 0.04}\,σ$ conflict with DESI DR2 within $Λ$CDM -- a tension that stands out from the grid -- reduced to $1.96{\scriptstyle\pm 0.04}\,σ$ once the calibration was corrected. With the calibration corrected, the Bayesian evidence for dynamical dark energy vanishes.

Figures (15)

• Figure 1: Visual summary of the Bayesian versus frequentist model comparison for the base model $\Lambda$CDM against 7 extension models using individual datasets, corresponding to \ref{['tab:desi_comparison']}.
• Figure 2: Visual summary of the Bayesian versus frequentist model comparison for the base model $\Lambda$CDM against 7 extension models using pairwise and triplet combinations, corresponding to \ref{['tab:desi_comparison']}.
• Figure 3: Monte Carlo validation of the frequentist test statistic $q = \chi^2_{\Lambda\mathrm{CDM}} - \chi^2_{\mathrm{CPL}}$ for DESI DR2 BAO alone. The empirical distribution under the $\Lambda$CDM null hypothesis (histogram) falls between the $\chi^2$ distributions for $k=1$ and $k=2$ degrees of freedom. Wilks' theorem overestimates the $p$-value: for $q_{\mathrm{obs}} \approx 4.7$, $p_{\mathrm{MC}} = 0.066$ versus $p_{\chi^2(2)} = 0.093$.
• Figure 4: Log-posterior probabilities, $\log \text{P}(\mathcal{M}_i|D)$, for eight cosmological models tested against individual datasets. Higher probabilities (more evidence) are indicated by bluer shades. Models (columns) are arranged in ascending order by their constraining power ($\mathcal{D}_{\text{KL}}$ values) from Planck with CMB lensing, providing a consistent ordering across all model comparison figures. While various datasets show mild preferences for different model extensions, $\Lambda$CDM remains consistently well-supported. Model comparison is valid only along each row. The normalisation factor, $\log\left(\sum_j \mathcal{Z}_j\right)$, is provided in the final column.
• Figure 5: Model comparison results for paired dataset combinations, presented in the same format as \ref{['fig:model_comp_single']}.