δ Gravity, δ Matter and the Accelerated Expansion of the Universe

Introducing an additional symmetry (delta symmetry) in the Einstein-Hilbert action, we obtain a gravitational field model (delta gravity) based on two symmetric tensors, g(mu v) and (g) over tilde (mu v) where an effective metric, given by g(mu v) = g(mu v) + (g) over tilde (mu v) must be defined to describe the trajectories of massless particles. In previous papers, a truncated versions of delta gravity applied to cosmology was presented, where the delta symmetry was fixed in order to simplify the analysis of the model. The model predicts an accelerated expansion of the Universe without a cosmological constant or additional scalar fields, ending in a Big Rip. We present the full-fledged delta gravity, introducing a new kind of matter fields (delta matter) in order to preserve the delta symmetry. In this approach the prediction of the expansion of the Universe is preserved, but the value of the cosmological parameters improve greatly by the inclusion of delta matter. Additionally, delta matter gives us an excellent candidate for Dark Matter.