Can the late dark energy parameterization reconcile the Hubble tension?

In this study, we constructed ten dark energy models to test whether they can reconcile the Hubble tension and how much it is affected by parameterization. To establish a fair test, the models are diverse, encompassing fractional, logarithmic, exponential, and inverse exponential forms as well as several non-parameterized models. The dataset we used includes the NPIPE pipeline of cosmic microwave background (CMB) power-spectrum data from Planck2020, Pantheon+ samples from Supernovae Type Ia, and baryon acoustic oscillations. The MCMC calculations imply dark energy transferring from w < -1 to w > -1 for the four parameterized dark energy models. However, these models cannot adequately reconcile the Hubble tension. Notably, we found that phantom-like dark energy with w < -1 can achieve the greatest reduction in the Hubble tension to 0.1808 sigma . However, AIC analysis indicates that this alleviation is at the cost of high AIC. We also investigated the effect of constructions on the derivative of the equation of state , cosmic density parameter, CMB power spectrum C-TT , and matter spectra P(k). We also found that the Hubble tension may be related to the reionization process.