Observations restrict the parameter space of holographic dark energy (HDE) so that a turning point in the Hubble parameter H(z) is inevitable. Concretely, cosmic microwave background, baryon acoustic oscillations and type Ia supernovae (SNE) data put the turning point in the future, but removing SNE results in an observational turning point at positive redshift. From the perspective of theory, not only does the turning point violate the null energy condition, but as we argue, it may be interpreted as an evolution of the Hubble constant H ₀ with redshift, which is at odds with the very FLRW framework within which data has been analysed. Tellingly, neither of these are problems for the flat ΛCDM model, and a direct comparison of fits further disfavours HDE relative to flat ΛCDM.

观测限制了全息暗能量 (HDE) 的参数空间，因此哈勃参数H ( z )的转折点是不可避免的。具体而言，宇宙微波背景、重子声波振荡和 Ia 型超新星 (SNE) 数据将转折点置于未来，但去除 SNE 导致观测转折点为正红移。从理论的角度来看，转折点不仅违反了零能量条件，而且正如我们所争论的，它可以解释为哈勃常数H ₀的演化红移，这与分析数据的 FLRW 框架不一致。很明显，对于平坦的 ΛCDM 模型来说，这些都不是问题，并且拟合的直接比较进一步不利于 HDE 相对于平坦的 ΛCDM。