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

We present a Bayesian comparative analysis of five cosmological models: ΛCDM, wCDM, w₀wₐCDM, ϕCDM (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 Dark Energy Spectroscopic Instrument (DESI) DR2 (Baryon Acoustic Oscillations, BAO), Pantheon+ (Type Ia Supernovae, SNIa), and Cosmic Microwave Background (CMB) data (including lensing) from Planck and the Atacama Cosmology Telescope (ACT), we report three key findings. First, the Hubble constant (H₀) 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). Third, the full dataset 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.