A Study of a Modified Equation of State In (2+1)-Dimensional Holographic Cosmology

Abstract

Objectives: This study examines the validity of the cosmic holographic principle in closed (2+1)-dimensional FRW models using a modified equation of state p=ωρ+Λ with Λ=αρ. It aims to determine whether such modifications can ensure holographic compliance. Ultimately, the work highlights how spatial curvature and global topology critically influence the applicability of holographic bounds.

Methods: Using a modified equation of state p=ωρ+Λ, with Λ=αρ, we investigate a closed (2+1)-dimensional FRW cosmological model under the Susskind-Fischler holographic principle. We compare the results with flat and open models, highlighting the influence of topology and spatial curvature, to determine whether this density-dependent term is consistent with holographic bounds for closed geometries.

Results: Consistent with (3+1)-dimensional results, our analysis demonstrates that cosmic holographic bounds are satisfied by flat and open (2+1)-dimensional FRW universes. Even with a density-dependent cosmological constant (Λ = αρ), closed geometries defy these limits. This persistent violation identifies closed models from flat or open ones, indicating that holographic validity is determined by spatial curvature and global topology rather than matter content or parameterization.

Conclusion: Our analysis demonstrates that, even in the presence of a density-dependent cosmological constant, the cosmic holographic principle fails in closed geometries but is valid for flat and open (2+1)-dimensional FRW universes. This persistent violation shows that holographic applicability is determined by global topology and spatial curvature rather than by content or parameterization. The findings highlight the inherent limitations imposed by topological closure, thereby reaffirming the essential function of geometry in holographic descriptions.