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.

💡 Research Summary

The paper investigates the late‑time cosmology of holographic dark energy (HDE) when the Granda‑Oliveiros (GO) infrared (IR) cutoff is employed, while explicitly allowing for non‑zero spatial curvature and for modifications of the horizon entropy via Kaniadakis generalized entropy. The authors first motivate the study by pointing out that recent Planck 2018 analyses hint at a closed universe (Ω_k < 0) at > 99 % confidence, a result that is in tension with local probes and that may affect the dynamics of any model that couples dark energy to geometry.

In the GO framework the dark‑energy density is taken as
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