Modified Spacetime Geometry as an Alternative to Dark Matter in Macro- and Microworlds

This paper proposes a novel geometric framework of spacetime that eliminates the necessity of introducing hypothetical Dark Matter on galactic scales. By introducing a modified metric tensor that incorporates spacetime discreteness at the Planck scale and the dynamics of a scalar field, we derive altered gravitational field equations. It is demonstrated that the effects conventionally attributed to hidden mass can emerge naturally as a geometric consequence of non-local interactions between microworld points and the Hubble expansion.