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We present a new kind of model, which we call δ Theories, where standard theories are modified including new fields, motivated by an additional symmetry ( δ symmetry). In previous works, we proved that δ Theories just live at one loop, so the model in a quantum level can be interesting. In the gravitational case, we have δ Gravity, based on two symmetric tensors, g μ ν and g ˜ μ ν , where quantum corrections can be controlled. In this paper, a review of the classical limit of δ Gravity in a Cosmological level will be developed, where we explain the accelerated expansion of the universe without Dark Energy and the rotation velocity of galaxies by the Dark Matter effect. Additionally, we will introduce other phenomenon with δ Gravity like the deflection of the light produced by the sun, the perihelion precession, Black Holes and the Cosmological Inflation.

δ Gravity: Dark Sector, Post-Newtonian Limit and Schwarzschild Solution