A Sequentially-Valid Reanalysis of DESI's Dynamical Dark Energy Signal

Abstract

Surveys such as DESI release data in stages, and each release invites a fresh assessment of whether dark energy is consistent with a cosmological constant. Standard Wilks-based $\sigma$ values are interpreted as if the test were performed only once, yet revisiting the same question at DR1, DR2, DR3, and beyond inflates the chance of an apparently significant fluctuation. We reanalyse the DESI BAO evidence for dynamical dark energy using an e-process, a likelihood-ratio-based measure of evidence that remains valid under repeated looks at accumulating data: it controls the false-detection probability under continued testing across releases with no trials-factor penalty. Applied to the DESI DR1$\to$DR2 BAO sequence, the result depends strongly on which departures from $\Lambda$CDM the test is designed to detect. For a pre-specified alternative aligned with the DR2-preferred direction, the running evidence reaches $M_{DR2} = 33.97$, crossing an illustrative 5% threshold of 20. The evidence is concentrated almost entirely in the LRG2 redshift bin, and removing that bin reduces the running e-value to $M = 0.49$, mildly favouring $\Lambda$CDM. When allowing any of the seven bins to have produced the excess, the signal does not survive a look-elsewhere correction. Other physically agnostic alternatives also fail to reject $\Lambda$CDM, while a physically motivated thawing-quintessence alternative rejects more strongly than any agnostic choice. The concentration of evidence in LRG2 specifically is difficult to reconcile with a smoothly evolving equation of state. The data therefore points to a fragile, single-bin, specification-dependent signal rather than robust evidence for dynamical dark energy. We recommend that future DESI, Euclid, Roman, and LSST data releases report an anytime-valid e-process value with its test specification stated alongside conventional $\sigma$ significances.