  We present a model of the gravitational field based on two symmetric tensors.
Gravity is affected by the new field, but outside matter the predictions of the
model coincide exactly with general relativity, so all classical tests are
satisfied. We find that massive particles do not follow a geodesic while
massless particles trajectories are null geodesics of an effective metric. We
study the Cosmological case, where we get an accelerated expansion of the
universe without dark energy. We also introduce the possibility to explain dark
matter with $\tilde{\delta}$ gravity.
