Analytic Phase Constraints at the de Sitter Horizon and Infrared Vacuum Energy

Title: Analytic Phase Constraints at the de Sitter Horizon and Infrared Vacuum EnergyAuthor: S. Hadi Mahdavi MortazaviSummary:This research develops a novel semiclassical framework that links the analytic structure of de Sitter scalar modes to the origin of vacuum energy (Dark Energy). By focusing on the branch-cut structure of Hankel functions at the cosmological horizon, the author proposes that the horizon acts as a physical "phase-rectifier." This mechanism enforces a causal constraint on infrared modes, leading to an effective vacuum energy component that scales as ρ ~ H² MPl², consistent with holographic dark energy models.Key Highlights:- Analytic Continuity & Causality: Provides a microscopic derivation of horizon-induced phase locking based on Hankel function analyticity.- Observational Correlation: Establishes a direct predictive link between primordial CMB power spectrum anomalies (non-Bunch–Davies features) and the current late-time vacuum energy density.- Theoretical Framework: Formulates the horizon response through a bilocal quadratic constraint and provides an equivalent Bogoliubov/entangled vacuum representation.- Phenomenology: Compares findings with recent DESI 2024 data, interacting dark energy models, and open-quantum-system approaches.Subject Areas:Theoretical Physics, Semiclassical Gravity, Cosmology, de Sitter Space, Quantum Field Theory in Curved Spacetime, Dark Energy, Casuality.