A Modified Equation Of State In (2+1)-Dimensional Holographic Cosmology

Abstract: We investigate the cosmic holographic principle (Susskind-Fischler) in a closed (2+1)-dimensional Friedmann-Robertson-Walker model using a modified equation of state , where . While the holographic principle holds for flat and open (2+1)-dimensional universes - mirroring (3+1)-dimensional results - we find it systematically fails for closed (2+1)-dimensional geometries. This failure persists even with equation-of-state adjustments ( ), demonstrating that spatial curvature fundamentally disrupts holographic constraints. Our results show that the holographic principle remains valid for flat and open universes across dimensions, but closed (2+1)-dimensional configurations violate holographic bounds regardless of matter content or cosmological constant parameterization. This establishes spacetime curvature as a critical factor determining holographic validity, with topological closure creating inherent limitations. The findings align with broader holographic studies, confirming that spatial topology governs a universe's ability to satisfy holographic constraints. Specifically, while (2+1)-dimensional flat and open FRW universes comply with holography, closed counterparts cannot meet these requirements, highlighting a fundamental difference in how cosmological models interact with holographic bounds based on their geometric structure