A comprehensive numerical study on four categories of holographic dark energy models

Holographic dark energy (HDE), which arises from a theoretical attempt to apply the holographic principle (HP) to the dark energy (DE) problem, has attracted significant attention over the past two decades. We perform a comprehensive numerical study on HDE models that can be classified into four categories: 1) HDE models with other characteristic length scale, 2) HDE models with extended Hubble scale, 3) HDE models with dark sector interaction, 4) HDE models with modified black hole entropy. For theoretical models, we select seven representative models, including the original HDE (OHDE) model, Ricci HDE (RDE) model, generalized Ricci HDE (GRDE) model, interacting HDE (IHDE1 and IHDE2) models, Tsallis HDE (THDE) model, and Barrow HDE (BHDE) model. For cosmological data, we use the Baryon Acoustic Oscillation (BAO) data from the Dark Energy Spectroscopic Instrument (DESI) 2024 measurements, the Cosmic Microwave Background (CMB) distance priors data from the Planck 2018, and the type Ia supernovae (SNe) data from the PantheonPlus compilation. Using $\chi^2$ statistic and Bayesian evidence, we compare these HDE models with current observational data. It is found that: 1) The $\Lambda$CDM remains the most competitive model, while the RDE model is ruled out. 2) HDE models with dark sector interaction perform the worst across the four categories, indicating that the interaction term is not favored under the framework of HDE. 3) The other three categories show comparable performance. The OHDE model performs better in the BAO+CMB dataset, and the HDE models with modified black hole entropy perform better in the BAO+CMB+SN dataset. 4) HDE models with the future event horizon exhibit significant discrepancies in parameter space across datasets. The BAO+CMB dataset favors a phantom-like HDE, whereas the BAO+CMB+SN leads to an equation of state (EoS) much closer to the cosmological constant.