Finsler-Randers cosmology: dynamical analysis and growth of matter perturbations

We study for the first time the dynamical properties and the growth index of linear matter perturbations of the Finsler-Randers (FR) cosmological model, for which we consider that the cosmic fluid contains matter, radiation and a scalar field. Initially, for various FR scenarios we implement a critical point analysis and we find solutions which provide cosmic acceleration and under certain circumstances we can have de Sitter points as stable late-time attractors. Then we derive the growth index of matter fluctuations in various Finsler- Randers cosmologies. Considering cold dark matter and neglecting the scalar field component from the perturbation analysis we find that the asymptotic value of the growth index is gamma(infinity) (FR) approximate to 9/16, which is close to that of the concordance. cosmology, gamma(Lambda) approximate to 6/11. In this context, we show that the current FR model provides the same Hubble expansion with that of the Dvali, Gabadadze and Porrati (DGP) gravity model. However, the two models can be distinguished at the perturbation level since the growth index of the FR model is similar to 18.2% lower than that of the the DPG gravity gamma(DGP) approximate to 11/16. If we allow pressure in the matter fluid then we obtain gamma(infinity) (FR) approximate to 9(1+wm)(1+2wm)/2[ 8+3wm(5+3wm)], where wm is the matter equation of state parameter. Finally, we extend the growth index analysis by using the scalar field and we find that the evolution of the growth index in FR cosmologies is affected by the presence of scalar field.