A Geometric Correspondence between Renormalized Vacuum Energy and Horizon Temperature in de Sitter Space

This paper investigates the structural correspondence between the macroscopic vacuum energy density and the thermal properties of the causal horizon in a dynamically expanding spacetime. Using the framework of quantum information geometry, we demonstrate that both the horizon temperature and the renormalized vacuum energy emerge from the same underlying geometric properties of the quantum state space. By synthesizing these derivations, we uncover a scaling behavior that functionally mirrors the Stefan-Boltzmann law. This framework provides a novel interpretation of macroscopic vacuum energy not as an isolated energetic artifact, but as the intrinsic geometric radiation arising fundamentally from the underlying information manifold.