Brane Induced Curvature Mass Model:A Geometric Scalar Sector for Galactic Dynamics and Cosmology

This work introduces the Brane Induced Curvature Mass (BICM) model, a minimal geometric framework where gradients of a two dimensional deformation field generate a finite range effective mass distribution. When coupled to baryons through a Helmholtz equation, the model produces a one parameter geometric halo that fits 175 SPARC rotation curves competitively with MOND and NFW profiles. The curvature induced mass naturally reduces the intrinsic scatter of the Radial Acceleration Relation from 0.24 dex to 0.15 dex, without invoking dark matter particles or a modified force law. A relativistic embedding demonstrates that the same scalar sector also yields a consistent weak lensing signal and an effective cosmological constant at large scales. Overall, the BICM model provides a unified geometric explanation for galactic dynamics, lensing behaviour, and late time cosmic acceleration.