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 non-equilibrium particle creation. These macroscopic processes are sufficient to neutralize the geometric divergence of the GO cutoff, as we discuss in the work.