Evidence of dynamical dark energy found via the DESI DR2 Lyman <i>α</i> forest

We present a comprehensive analysis of the cosmological implications of the Dark Energy Spectroscopic Instrument Data Release 2 Lyman- α forest baryon acoustic oscillation measurements, combined with complementary datasets including DESI DR2 galaxy BAO, Type Ia supernova samples (Pantheon + , DES-Dovekie, and Union3), and the cosmic microwave background CamSpec likelihood. We consider several dark-energy parameterizations such as chevallier–polarski–linder, logarithmic, exponential, jassal–bagla–padmanabhan, barboza–alcaniz, and generalized emergent dark energy, as well as the w CDM model and non-flat extensions of the standard ΛCDM and w CDM models. Using the Metropolis-Hastings MCMC algorithm, we constrain the cosmological parameters of each model and compute the Bayesian evidence using the publicly available code MCEvidence to assess the performance of each model relative to ΛCDM. Our results show that the non-flat extensions remain consistent with spatial flatness, with Ω k ≈ 0 for all dataset combinations. Further, all dark-energy parameterizations predict w 0 > −1, w a < 0, and w 0 + w a < −1, which favor a dynamical dark-energy scenario of the Quintom-B type. We also find a moderate preference for dynamical dark-energy models relative to the standard ΛCDM scenario, reaching up to ∼3.10 σ for the Ly α + CMB + Galaxy BAO dataset. When DESI DR2 Ly α measurements are combined with different SNe Ia samples and the CMB, the deviations decrease and remain typically below ∼2 σ , corresponding only to inconclusive preference relative to ΛCDM. However, this level of evidence is not statistically decisive, and it remains too early to rule out the ΛCDM model. Finally, the Bayes factor in logarithmic space (ln B ij ) shows that model preference relative to ΛCDM depends strongly on the dataset combination. For Ly α + CMB + Galaxy BAO, w CDM and o w CDM show moderate evidence, while most other models provide weak or inconclusive evidence. With Pantheon + or DES-Dovekie, o w CDM shows strong evidence, whereas other models show moderate evidence.