Geometric Stress Field: The Field Equation and Its Cosmological Implications

This work introduces the Geometric Stress Field (GSF), a covariant extension of General Relativity in which gradients of spacetime curvature generate an intrinsic geometric stress. Rather than invoking unseen matter or a cosmological constant, the framework shows how cosmic acceleration can emerge from the self-stress of geometry itself. The central idea is simple but consequential: what has been interpreted as missing matter or energy may not be missing at all, but instead encoded in the way spacetime responds to non-uniform curvature. By deriving the full gravitational field equation from a curvature-gradient action, this work reframes dark energy as a geometric phenomenon rather than a material one. This submission marks the starting point of a shift in perspective — from searching for what is absent, to understanding what has been present in spacetime all along.