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

We apply the $\mathtt{\text{unimpeded}}$ framework to perform a fully Bayesian reanalysis of the DESI DR2 data, using nested sampling with $\mathtt{\text{PolyChord}}$ to compute evidences for $\mathrm{\Lambda }$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 $\mathrm{\Delta }{\chi }^2$-based analyses. For DESI DR2 BAO combined with Planck CMB alone, the DESI collaboration’s $3.1\sigma$ frequentist preference for $w_0{w}_a$CDM is eliminated entirely: we obtain $\ln B=-0.57\pm 0.26$, modestly favouring $\mathrm{\Lambda }$CDM. Adding DES-Dovekie, the recalibration of DES-SN5YR, maintains this concordance ($\ln B=-0.30\pm 0.19$). However, when the earlier DES-SN5YR calibration is included instead, the DESI collaboration’s $4.2\sigma$ result survives the Bayesian Ockham penalty as a $3.07\pm 0.10,\sigma$ preference ($\ln B=+3.32\pm 0.27$). That this signal persists despite the Ockham penalty makes the role of tension quantification essential: our analysis traced the preference to the earlier DES-SN5YR calibration, which introduced a $2.95\pm 0.04,\sigma$ conflict with DESI DR2 within $\mathrm{\Lambda }$CDM – a tension that stands out from the grid – reduced to $1.96\pm 0.04,\sigma$ with the DES-Dovekie recalibration. With DES-Dovekie, the Bayesian evidence for dynamical dark energy vanishes.