Kaniadakis Holographic Dark Energy: UV$-$IR Duality, Horizon Thermodynamics and Cosmological Constraints
We investigate the cosmological and thermodynamic implications of holographic dark energy derived from the Kaniadakis deformation of the Bekenstein--Hawking entropy. In a spatially flat FLRW universe, the generalized entropy generates an effective dark-energy density with an infrared correction proportional to $H^{-2}$, naturally producing an ultraviolet--infrared structure in the cosmological dynamics. Using the Hayward--Kodama formulation of apparent-horizon thermodynamics, we derive a geometric equation of state and identify Van der Waals-type criticality, characterized by an inverted first-order phase transition and an inverted swallowtail Gibbs potential. We interpret this behavior as the thermodynamic signature of a geometric phase transition of the apparent horizon rather than standard fluid coexistence. We also consider an extended model with a $\dot H$ contribution inspired by the Granda--Oliveros cutoff and show that this unconventional critical behavior persists. At the perturbative level, the same ultraviolet--infrared competition controls the effective sound speed and dark-energy response through a dimensionless coupling $A(z)$, which acts as a geometric order parameter. In the minimal model, $A(z)$ may cross zero during matter domination, marking a transition between infrared- and ultraviolet-dominated regimes, whereas the extended scenario remains ultraviolet dominated. Finally, we confront both models with cosmic chronometers, PantheonPlus Type Ia supernovae, DESI DR2 baryon acoustic oscillations, and redshift-space distortion data. Bayesian comparison with $Λ$CDM, CPL, and standard holographic dark energy strongly disfavors the minimal model. The extended model yields the best maximum-likelihood fit among those considered, but remains disfavored relative to $Λ$CDM after accounting for its larger parameter volume.