Our current standard theory of gravity is unable to fully explain the accelerating expansion of the universe. This expansion seems to imply a repulsive force associated with gravitational interaction. We propose a 2-charge theory of gravity based on the Quantum Field Theory applied to a second rank tensor eld that allows for an attractive force between like charges and a repulsive force between opposite charges. This model could partly explain matter-antimatter asymmetry, the smallness of the cosmological constant, and the accelerating expansion of the universe. Our calculation of a lattice model with a billion points shows that the net gravitational force at any space-time point would be slightly repulsive. This new model is also consistent with the local physics described by the standard theory of gravity. Our theory may be experimentally supported by results from the ALPHA Collaboration.