On Internal Consistency of Holographic Dark Energy Models

Holographic dark energy (HDE) models, underlain by an effective quantum field theory (QFT) with a manifest UV/IR connection, have become a convincing candidate for the dark energy in the universe. On the other hand, the maximum number of quantum states a conventional QFT in the box of size $L$ is capable to describe, refer to those boxes which are on the brink of experiencing a sudden collapse to a black hole. Another restriction on the underlying QFT is that the UV cutoff, which cannot be chosen independently of the IR cutoff and therefore becomes a function of time in a cosmological setting, should stay the largest energy scale even in the standard cosmological epochs preceding a dark energy dominated one. We show that, irrespective of whether one deals with the saturated form of HDE or takes a certain degree of non-saturation in the past, the above restrictions cannot be met in a radiation-dominated universe, an epoch in the history of the universe which is expected to be perfectly describable within conventional QFT.