A Critique of Holographic Dark Energy

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 (CMB), baryon acoustic oscillations (BAO) 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 (NEC), 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 $\Lambda$CDM model, and a direct comparison of fits further disfavours HDE relative to flat $\Lambda$CDM.