Dynamical Dark Energy and the Unresolved Hubble Tension: Multi-model Constraints from DESI 2025 and Other Probes

Abstract We present a Bayesian comparative analysis of five cosmological models: ΛCDM, w CDM, w 0 w a CDM, ϕ CDM (with scalar-field dark energy), and an interacting dark energy scenario (the ξ -index model), to investigate dark energy evolution and the Hubble tension. Utilizing the latest data from the second data release of the Dark Energy Spectroscopic Instrument (Baryon Acoustic Oscillations, BAO), Pantheon+ (type Ia supernovae, SNIa), and cosmic microwave background (CMB) data (including lensing) from Planck and the Atacama Cosmology Telescope, we report three key findings. First, the Hubble constant ( H 0 ) inferred from the combined data consistently aligns with early-universe measurements across all models, indicating a persistent Hubble tension. Second, we find compelling evidence for dynamical dark energy: early-universe (CMB) constraints favor a phantom phase (with an equation-of-state parameter w < −1), while late-universe (BAO/SNIa) data prefer quintessence ( w > −1). Third, the full data set suggests a late-time interaction between dark energy and matter. Our results demonstrate that dark energy evolves with cosmic time, challenging the cosmological-constant paradigm.