Origin of holographic dark energy models

We investigate the origin of holographic dark energy models which were recently proposed to explain the dark energy-dominated universe. For this purpose, we introduce the spacetime foam uncertainty of $\delta l \ge l_{\rm p}^{\alpha}l^{\alpha-1}$. It was argued that the case of $\alpha=2/3$ could describe the dark energy with infinite statistics, while the case of $\alpha=1/2$ can describe the ordinary matter with Bose-Fermi statistics. However, two cases may lead to the holographic energy density if the latter recovers from the geometric mean of UV and IR scales. Hence the dark energy with infinite statistics based on the entropy bound is not an ingredient for deriving the holographic dark energy model. Furthermore, it is shown that the agegraphic dark energy models are the holographic dark energy model with different IR length scales.