The holographic origin of future singularities and the role of spatial curvature in cosmic expansion
Miguel Cruz, Samuel Lepe, Joel Saavedra
TL;DR
This work analyzes holographic dark energy with a Granda–Oliveros cutoff in curved spacetimes, focusing on how spatial curvature and Kaniadakis entropy influence future singularities. In the standard GO setup (with curvature), the big rip arises in flat space and curvature accelerates or modulates the approach but does not remove the finite-time divergence. Introducing Kaniadakis entropy adds a $K^{2}/H^{2}$ infrared correction that creates a stable de Sitter point and drives the evolution toward a little rip, where $H$ diverges only at infinite cosmic time. Curvature then acts as a quantitative deformation, modifying the detailed expansion history but not the qualitative little-rip outcome. Altogether, the paper demonstrates that the ultimate fate of holographic cosmologies is highly sensitive to the underlying entropy-area relation, with GO predicting a big rip and the Kaniadakis deformation softening it to a de Sitter–to–little rip trajectory, consistent even in curved universes.
Abstract
In this work, we investigate the cosmological implications of holographic dark energy (HDE) when the infrared cutoff is defined through the Granda-Oliveros (GO) model and the entropy-area is generalized in the context of Kaniadakis statistics. For the GO model, we showed that a spatially flat universe inevitably evolves toward a big rip singularity. At the same time, the inclusion of spatial curvature modifies the expansion rate without removing the finite-time divergence: positive curvature speeds up the formation of the singularity, whereas negative curvature induces transitions between quintessence, de Sitter, and phantom-like regimes. When Kaniadakis entropy corrections are incorporated, the qualitative behavior changes substantially. The modified HDE density admits a stable de Sitter critical point and evolves toward a little rip singularity, in which the Hubble rate diverges only at infinite cosmic time. We further demonstrate that spatial curvature acts solely as a quantitative deformation in this scenario. Although it alters the detailed expansion history, it does not alter the little-rip character of the future singularity. Our results reveal that the asymptotic fate of holographic cosmologies is highly sensitive to the underlying entropy-area relation: the GO model robustly predicts a big rip. At the same time, its Kaniadakis deformation consistently softens the singularity into a little rip, even in curved universes.