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: $\mathrm{\Lambda }$CDM, $w$CDM, $w_0{w}_a$CDM, $\phi$CDM (with scalar-field dark energy), and an interacting dark energy scenario (the $\xi$-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 $\mathit{\text{Planck}}$ and the Atacama Cosmology Telescope (ACT), 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 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.