arXiv2026
We systematically investigate four cosmological models within a parameterized framework that allows for a redshift dependence of \(H_0\): three phenomenological models (\(αΛ\)CDM, \(αw\)CDM, and \(αw_0w_a\)CDM), and the $J$CDM model motivated by big bang quantum cosmology. Using cosmic microwave background (CMB) data, baryon acoustic oscillations (BAO), cosmic chronometer (CC) measurements of the Hubble parameter, and three Type Ia supernova samples (PantheonPlus, DESY5, and Union3), we perform Markov chain Monte Carlo (MCMC) analyses to obtain posterior distributions of the model parameters. We also perform separate analyses using early-time and late-time data to assess how each observational epoch affects the model constraints. For the three phenomenological models, the parameter \(α\) describing the redshift evolution of \(H_0\) is consistent with zero within \(2σ\). The Hubble constant inferred from the \(αΛ\)CDM model is consistent with CMB results, while the $J$CDM model yields a larger Hubble constant but is strongly disfavored by model comparison criteria. Using the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC) for model comparison, we find that the standard \(Λ\)CDM model remains the most favored by the data. Among the four models, the \(αw_0w_a\)CDM model shows a marginal AIC advantage ($\rm ΔAIC \sim$ -2 to -13). However, this preference does not translate into a reduction of the Hubble tension, which is consistent with existing studies supporting dynamical dark energy. Moreover, none of the models can simultaneously satisfy both the early- and late-time constraints, and the combined datasets alone are insufficient to conclusively determine whether these parametrizations can resolve the tension.