Cosmological Application of Geometric Unification: Galactic Rotation Curves and Accelerated Expansion from Torsion-Gauge Field Coupling

We present a cosmological application of the geometric unification framework developed in (1),where spacetime torsion is dynamically coupled to Standard Model gauge fields through a funda-mental algebraic constraint. This application provides a unified geometric explanation for three keyastrophysical phenomena: (1) flat galactic rotation curves without additional dark matter particles,(2) the accelerated expansion of the Universe without cosmological constant, and (3) the origin anddiversity of galactic structures including spiral arms and thin disks. The mechanism involves theformation of chiral condensates in curved spacetime with torsion, leading to effective potentials thatmodify gravitational dynamics on galactic scales while naturally generating observed morphologies.All parameters are determined from first principles of the fundamental theory. We derive the modi-fied Friedmann equations from the geometric constraint, solve for galactic rotation profiles, explainspiral structure formation and galactic planarity, and demonstrate consistency with observationaldata from SPARC galaxies and Planck satellite. The model predicts testable signatures in CMBpolarization, gravitational lensing statistics, and detailed galactic structure properties, providingcomprehensive observational tests of the geometric unification framework.