Kaniadakis Holographic Dark Energy with Particle Horizon as IR Cutoff

We construct a holographic dark-energy model using Kaniadakis entropy with the particle horizon as the infrared cutoff, consistently modifying both the holographic density and the Friedmann background. In standard Einstein gravity, noninteracting particle-horizon holographic dark energy (HDE) does not produce the sufficiently negative pressure required for late-time accelerated expansion. We show that the Kaniadakis deformation changes this behavior while the particle horizon is retained. For the representative parameter choice $K=1.90\times {10}^{-36}$, with ${\mathrm{\Omega }}_{\mathrm{D}\mathrm{E}0}=0.7$ and $c^2=0.64$, the deceleration parameter changes sign at $z\simeq 0.585$ in the noninteracting case. Including the interaction strengths $b^2=0.03$ and $0.06$ changes the transition only slightly, giving $z\simeq 0.586$ and $0.589$, respectively. Thus, for the parameter set considered here, the interaction does not generate the acceleration; rather, the transition is already present in the noninteracting Kaniadakis model and the interaction produces only a small shift in its timing. We derive the autonomous evolution equations, the effective dark-energy equation of state, and the deceleration parameter. The adiabatic squared sound speed is also examined as a diagnostic of the effective-fluid stability, while statefinder variables are used to characterize deviations from $\mathrm{\Lambda }$CDM. Finally, we verify that the $K\to 0$ limit continuously recovers standard Einstein-gravity particle-horizon HDE, for which the noninteracting model remains decelerating.