BECU Γεωμετρία (Geometry): Structure Determines Galaxy Dynamics and Cosmology

Description: The BECU (Baryonic–Emergent Coupling Universe) framework presents a structure-driven geometric approach to galaxy dynamics, gravitational lensing, and cosmology. In this framework, gravitational phenomena are interpreted as a response of geometry to the spatial distribution of baryonic matter, quantified through a structural field:K = |∇ρ| / ρ. Within this formulation: Galaxy rotation curves arise naturally from a saturating geometric response. The Baryonic Tully–Fisher relation (BTFR) emerges as a structural scaling relation. Gravitational lensing is described through a separation between dynamical and lensing potentials. A unified description across galactic and cosmological scales is achieved without introducing additional matter components. A key result is the identification of an emergent structural exponent:α ≈ 1.34,which consistently reproduces observed galaxy scaling relations across large samples. The model is validated using SPARC rotation curve data and remains stable under subsampling, filtering, and parameter variation. The term “Γεωμετρία” (Geometry) is used to emphasize that the governing mechanism is the structural organization of matter, rather than additional components or modified force laws. This work provides a geometry-based interpretation of gravitational phenomena and establishes a unified framework linking galaxy dynamics, lensing, and cosmology through the structural organization of matter.