Constraints of dynamical dark energy models from different observational datasets

The measurements of baryon acoustic oscillation by the Dark Energy Spectroscopic Instrument Data Release 2 indicate that dark energy may be dynamical with a time-varying equation of state. This has challenged the core assumptions of the $\Lambda$CDM model and aroused widespread discussion. Existing work has achieved fruitful results in the dark energy models, exploring various parameterization forms, but it lacks systematic parameter constraints based on the latest dataset combinations. We use $\Lambda$CDM as a baseline model and carry out rigorous statistical constraints on key cosmological parameters for seven representative parameterization models. The Planck PR4 and DESI DR2 observations are incorporated into our study. We use four datasets: CMB+BAO+PantheonPlus, CMB+BAO+DES-Y5, CMB+BAO+Union3, and CMB+BAO(without LRG1 and LRG2)+DES-Y5. Our results may not effectively alleviate ${H}_{0}$ tension, but may relatively reduce ${\sigma }_{8}$ tension. By comparing the Akaike Information Criterion and the Bayesian evidence obtained for each model, we demonstrate that the linear Chevallier-Polarski-Linder parameterization is not the optimal choice in all cases. The Logarithmic model shows the best fitting performance among three different SNIa samples. However, with CMB+BAO(without LRG1 and LRG2)+DES-Y5, Jassal-Bagla-Padmanabhan and Chevallier-Polarski-Linder models gain more obvious preference. All two-parameter dynamical dark energy models perform most prominently in the CMB+BAO+DES-Y5 dataset, with the Logarithmic model providing strong evidence to support dynamical dark energy.