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

TL;DR

This paper demonstrates that under zero spatial curvature, the Finsler-Randers cosmological model and the DGP braneworld model have identical Hubble expansion, showing a form of cosmological equivalence despite their different geometrical origins.

Contribution

It establishes a cosmological equivalence between Finsler-Randers and DGP models for cosmic expansion and compares their growth of matter perturbations.

Findings

Finsler-Randers and DGP models share the same Hubble expansion under zero curvature.

The growth index for Finsler-Randers is approximately 9/14, slightly lower than DGP's 11/16.

The growth factor differs by about 0.1-2% between the two models.

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.