Theoretical aspects of holographic dark energy

We review the theoretical aspects of holographic dark energy (HDE) in this paper. Making use of the holographic principle (HP) and the dimensional analysis, we derive the core formula of the original HDE (OHDE) model, in which the future event horizon is chosen as the characteristic length scale. Then, we describe the basic properties and the corresponding theoretical studies of the OHDE model, as well as the effect of adding dark sector interaction in the OHDE model. Moreover, we introduce all four types of HDE models that originate from HP, including (1) HDE models with the 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. Finally, we introduce the well-known Hubble tension problem, as well as the attempts to alleviate this problem under the framework of HDE. From the perspective of theory, the core formula of HDE is obtained by combining the HP and the dimensional analysis, instead of adding a DE term into the Lagrangian. Therefore, HDE remarkably differs from any other theory of DE. From the perspective of observation, HDE can fit various astronomical data well and has the potential to alleviate the Hubble tension problem. These features make HDE a very competitive dark energy scenario.