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

Abstract

Introducing an additional symmetry (δ symmetry) in the Einstein-Hilbert action, we obtain a gravitational field model (δ gravity) based on two symmetric tensors, g_μv and ̃g_μv where an effective metric, given by g_μv = g_μv + ̃g_μv must be defined to describe the trajectories of massless particles. In previous papers, a truncated versions of δ gravity applied to cosmology was presented, where the δ 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 δ gravity, introducing a new kind of matter fields (δ matter) in order to preserve the δ 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 δ matter. Additionally, δ matter gives us an excellent candidate for Dark Matter.