Holographic Dark Energy from Fundamental Principles to Precision Observations

Abstract

Holographic dark energy remains one of the few late universe frameworks in which the observed acceleration is tied directly to an ultraviolet and infrared consistency condition inspired by quantum gravity. The last five years have transformed the subject. The central question is no longer whether a holographic density can reproduce an accelerating background. Many constructions can do so. The decisive questions are whether the infrared prescription has a local theoretical completion, whether perturbations are stable and observationally acceptable, whether entropy deformations introduce physically meaningful freedom rather than flexible curve fitting, and whether the model survives the rapidly tightening combination of DESI baryon acoustic oscillations, supernova distances, cosmic microwave background information, cosmic chronometers, and growth measurements. This review critically synthesizes these developments with particular emphasis on the standard future event horizon model, interacting models, Barrow, Tsallis, Kaniadakis, Rényi and fractional extensions, local Ricci and Granda Oliveros cutoffs, effective field theory descriptions, nonflat cosmology, and recent data driven reconstructions. A striking empirical pattern emerges. Late time combinations can place the standard holographic parameter c close to unity or above unity, whereas the addition of cosmic microwave background information commonly drives c to values near 0.65 to 0.70 and therefore toward a phantom future. In DESI DR1 analyses the associated Bayesian evidence can strongly favor ΛCDM even when a holographic fit is acceptable in likelihood. DESI DR2 late time analyses again recover c close to unity, which sharpens rather than removes the dataset dependence. Generalized entropy models display a similarly mixed picture. Some constructions constrain deformation parameters close to their standard entropy limit, while others prefer large deformations but remain statistically disfavoured by Bayesian evidence. Structure growth calculations further show that infrared cutoff choice can determine viability. We argue that future progress requires perturbation complete models, consistent treatment of early and late universe information, explicit evidence calculations, and model comparison at the level of physically distinct cutoff and entropy prescriptions rather than broad labels. Holographic dark energy therefore remains theoretically fertile, but current observations do not yet establish it as a superior replacement for ΛCDM.