Evidence of dynamical dark energy found via the DESI DR2 Lymanα 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+$, DES-Dovekie, and Union3), and the cosmic microwave background CamSpec likelihood. We consider several dark-energy parameterizations such as chevallier–polarski–linder , logarithmic, exponential, jassal–bagla–padmanabhan, barboza–alcaniz, and generalized emergent dark energy, as well as the wCDM model and non-flat extensions of the standard ΛCDM and wCDM models. Using the Metropolis-Hastings MCMC algorithm, we constrain the cosmological parameters of each model and compute the Bayesian evidence using the publicly available code to assess the performance of each model relative to ΛCDM. Our results show that the non-flat extensions remain consistent with spatial flatness, with Ω_k ≈ 0 for all dataset combinations. Further, all dark-energy parameterizations predict w_0 > -1, w_a < 0, and w_0 + w_a < -1, which favor a dynamical dark-energy scenario of the Quintom-B type. We also find a moderate preference for dynamical dark-energy models relative to the standard ΛCDM scenario, reaching up to sim3.10σ for the Lyα + CMB + Galaxy BAO dataset. When DESI DR2 Lyα measurements are combined with different SNe Ia samples and the CMB, the deviations decrease and remain typically below sim2σ, corresponding only to inconclusive preference relative to ΛCDM. However, this level of evidence is not statistically decisive, and it remains too early to rule out the ΛCDM model. Finally, the Bayes factor in logarithmic space (łn B_ MCEvidence ij ) shows that model preference relative to ΛCDM depends strongly on the dataset combination. For Lyα + CMB + Galaxy BAO, wCDM and owCDM show moderate evidence, while most other models provide weak or inconclusive evidence. With Pantheon^+ or DES-Dovekie, o$wCDM shows strong evidence, whereas other models show moderate evidence.