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

Abstract

We perform a detailed comparison between the Finsler-Randers cosmological model and the Dvali, Gabadadze and Porrati braneworld model. If we assume that the spatial curvature is strictly equal to zero then we prove the following interesting proposition: {\it 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 ${\gamma }_{FR}\simeq 9/14$ which is somewhat lower than that of DGP gravity (${\gamma }_{DGP}\simeq 11/16$) implying that the growth factor of the Finsler-Randers model is slightly different ($\sim 0.1-2$) from the one provided by the DGP gravity model.

Comments: 6 pages, 2 figures, accepted for publication in Phys. Rev. D. (typos corrected, published version)