Cosmological equivalence between the Finsler-Randers space-time and the DGP gravity model

We perform a detailed comparison between the Finsler-Randers cosmological model and the Dvali, Gabadadze, and Porrati (DGP) braneworld model. If we assume that the spatial curvature is strictly equal to zero then we prove the following interesting proposition: despite the fact that the current cosmological models have a completely different geometrical origin, they share exactly the same Hubble expansion. This implies that the Finsler-Randers model is cosmologically equivalent with that of the DGP model as far as the cosmic expansion is concerned. At the perturbative level we find that the Finsler-Randers growth index of matter perturbations is γFR9/14, which is somewhat lower than that of DGP gravity (γDGP11/16), implying that the growth factor of the Finsler-Randers model is slightly different (~0.1--2%) from the one provided by the DGP gravity model.