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 two keyastrophysical phenomena: (1) flat galactic rotation curves without additional dark matter particles,and (2) the accelerated expansion of the Universe without cosmological constant. The mechanisminvolves the formation of chiral condensates in curved spacetime with torsion, leading to effective po-tentials that modify gravitational dynamics on both galactic and cosmological scales. All parametersare determined from first principles of the fundamental theory. We derive the modified Friedmann equations from the geometric constraint, solve for galactic rotation profiles, and demonstrate con-sistency with observational data from SPARC galaxies and Planck satellite. The model predictstestable signatures in CMB polarization and gravitational lensing statistics, providing observationaltests of the geometric unification framework.