A Geometric Theory of Cosmic Expansion: A Finite Universe with Dynamic Boundary Conditions

We propose a geometric framework for cosmology by modeling the universe as a finite 3-dimensional hypersurface embedded in a static 4D bulk. Dynamic boundary interactions generate curvature gradients, quantified by a boundary tensor, which replaces dark energy in the Einstein equations. The theory resolves the Hubble tension via a radial Hubble parameter, predicts CMB quadrupole alignment, and matches large-scale structure observations. Derived from first principles, it eliminates singularities, satisfies energy conditions, and recovers general relativity as the boundary radius as R reaches infinity.Numerical solutions validate cosmic acceleration and observational consistency with lambda CDM.