On DESI's DR2 exclusion of $Λ$CDM

The DESI collaboration, combining their Baryon Acoustic Oscillation (BAO) data with cosmic microwave background (CMB) anisotropy and supernovae data, have found significant indication against the $Λ$CDM cosmology. This can also be interpreted as the significance of the detection of the $w_a$ parameter that measures variation of the dark energy equation of state. DESI’s DR2 article quotes exclusion of $Λ$CDM for combinations of BAO and CMB data with each of three different and overlapping supernovae compilations (at 2.8-sigma for Pantheon+, 3.8-sigma for Union3, and 4.2-sigma for DESY5). We show that one can neither choose amongst nor average over these three different significances. We demonstrate how a principled statistical combination yields a combined exclusion significance of 3.1-sigma. Further we argue that, faced with these competing significances, the most secure inference from the DESI DR2 results is the 3.1-sigma level exclusion of $Λ$CDM obtained from combining DESI+CMB alone, omitting supernovae.

💡 Research Summary

The paper critically re‑examines the claim made in the DESI second data release (DR2) that the standard ΛCDM cosmology is excluded at high significance when Baryon Acoustic Oscillation (BAO) data are combined with Cosmic Microwave Background (CMB) measurements and one of three supernova (SN) compilations. The DESI collaboration reports three different exclusion levels – 2.8 σ for Pantheon+, 3.8 σ for Union3, and 4.2 σ for DESY5 – and presents these as independent confirmations of evolving dark energy, parameterised by the Chevallier‑Polarski‑Linder (CPL) form (w(a)=w_{0}+w_{a}(1-a)).

The authors argue that these three numbers cannot be treated as independent measurements because the SN data sets heavily overlap (many of the same supernovae appear in more than one compilation) and, more importantly, they are analysed with different pipelines (different light‑curve fitters, hierarchical Bayesian frameworks, etc.). Consequently, the usual product of likelihoods that would strengthen a combined constraint is statistically invalid. Instead, when the same underlying data are processed by multiple methods, the correct operation is to average the resulting posterior probability distributions, assigning equal weight to each analysis in the absence of a priori reasons to prefer one over the others.

Mathematically, they write the combined posterior as
(p_{\rm combined}(\theta)=\frac{1}{3}\sum_{i=1}^{3}p_i(\theta))
and show that the probability mass lying beyond the ΛCDM point is dominated by the weakest of the three results. Using the complementary error function they derive a simple expression for the combined significance:
(\sigma_{\rm combined}= \sqrt{2},\mathrm{Erfc}^{-1}!\bigl