Paper13_Dark Energy Under B Framework

This paper develops the dark-energy block within the alpha-beta-phi framework, deriving cosmic acceleration directly from a filtered-vacuum architecture. The construction starts from the visible Lagrangian, where the geometric channel (phi) couples non-minimally to curvature and the structural channel (beta) enters the filtered potential sourced by the deep vacuum reservoir (alpha). Key Technical Highlights: Action-Based Derivation: Step-by-step variation of the visible Lagrangian to obtain modified Einstein equations, scalar equations of motion, and their homogeneous Friedmann reduction. Dynamical Evolution: In the slow-filter regime, the model reduces to a controlled one-parameter deformation of Lambda-CDM, where the energy density scales with the scale factor (a) and the effective equation of state (weff) deviates slightly from -1. Parametrization: The framework allows for a natural translation into standard CPL parameters (w0, wa), providing a bridge between theoretical predictions and observational benchmarks. Observational Integration: The study organizes current data from H(z) benchmarks, Pantheon+ SNIa, and DESI DR2 BAO into a single formal narrative. Conclusion: The result is a coherent derivation showing how dark energy emerges from the base Lagrangian and how the alpha-beta-phi structure supports a controlled late-time dynamical dark-energy sector without severing continuity with standard cosmology.