The Holographic Origin of Future Singularities and the Role of Spatial Curvature in Cosmic Expansion

We investigate the fundamental cosmological implications of holographic dark energy using the Granda‐Oliveros (GO) infrared cutoff, spatial curvature, and generalized entropies. We demonstrate that the GO cutoff establishes a geometric origin for phantom acceleration, inevitably leading to a big rip singularity without requiring exotic matter. Incorporating spatial curvature reveals that topology acts as a quantitative catalyst; positive curvature accelerates the singularity in closed universes, but cannot alter its fundamental behavior. Furthermore, we show that Kaniadakis generalized entropy modifications are structurally insufficient to prevent this finite‐time divergence. To successfully soften the big rip and yield an asymptotic little rip, it is necessary (as first alternative) to integrate irreversible thermodynamical mechanisms, such as nonequilibrium particle creation. These macroscopic processes are sufficient to neutralize the geometric divergence of the GO cutoff, as we discuss in the work.