Geometric Repulsion from Torsion-Gauge Field Coupling: A Unified Framework for Galactic Dynamics, Cosmic Acceleration, and Large-Scale Structure

We present a comprehensive derivation of geometric repulsion emerging from the fundamental cou-pling between spacetime torsion and Standard Model gauge fields, as established in the geometric uni-fication framework [1]. Starting from the primordial curvature constraint, we demonstrate that chiral condensates in curved spacetime generate a repulsive potential Φrep(r) = (β2/12)r2ω2(r). This single mechanism simultaneously explains: (i) flat galactic rotation curves without particle dark matter, fitting SPARC data with χ2/dof = 0.92 ± 0.08; (ii) cosmicacceleration with weff ≈ −1 from dynamical torsion; (iii) the Tully-Fisher relation and core radiusscaling; and (iv) the formation of large-scale structure including voids, filaments, and domain wallsthrough the interplay between gravitational attraction and geometric repulsion. All parameters arefixed from first principles: α3β3 ≈ 1.37 from QCD algebra, β ≈ 2.5 × 10−42 GeV−1 from cosmolog-ical calculation. The model makes distinctive predictions testable with upcoming surveys includingCMB-S4, Euclid, and JWST, providing a unified geometric alternative to dark matter and darkenergy that naturally incorporates large-scale structure formation.