Evidence for the dynamical dark energy with evolving Hubble constant

Hubble constant tension, together with the recent indications of dynamical dark energy proposed from the Dark Energy Spectroscopic Instrument (DESI) baryon acoustic oscillation (BAO) measurements, poses significant challenges to the standard cosmological model. We investigate the possible redshift evolution of dark energy and the Hubble constant through a data-driven approach, and assess whether such evolution can alleviate the Hubble constant tension. We perform a model-independent reconstruction of the dark-energy equation of state $w(z)$, jointly with an evolving Hubble constant $H_0(z)$. The analysis combines the DESI DR2 BAO dataset with multiple Type Ia supernova samples and evaluates the statistical preference for the reconstructed model using Bayesian evidence. The reconstructed $w(z)$ varies with redshift and exhibits two potential phantom crossings at $z\sim0.5$ and $z\sim1.5$. Meanwhile, $H_0$ decreases continually from local to high redshift, alleviating the Hubble constant tension effectively. The joint $w(z)$-$H_0(z)$ model is favored over the $w$CDM ($\Lambda$CDM) framework, with a logarithmic Bayes factor $\ln \boldsymbol{\mathcal B}= 5.04~(8.53)$. The results remain stable under different prior choices and dataset combinations. Our data-driven reconstructions suggest redshift evolution in both $w(z)$ and $H_0(z)$, offering a potential route to mitigate the Hubble constant tension. Future BAO measurements from Euclid and next-generation CMB experiments will provide critical tests of these results and bring deeper insights into the nature of dark energy and the evolution of cosmic expansion.