Anisotropic Bianchi type-III model in Palatini f ( R ) $f (R)$ gravity

Abstract

We derive exact solutions for anisotropic Bianchi type-III cosmological model in the Palatini formalism of $f (R)$ gravity using Dynamical System Approach. For the $f (R)$ of the form $f(R) =R-\beta /R^{n} $ and $f(R) =R+\alpha R^{m} $ , we have found the fixed points describing the radiation-dominated, matter dominated and de Sitter evolution periods. Fixed points have also been found which have non-vanishing shear playing a very significant role in describing the anisotropy present in the early universe. In addition, we have also found that the spatial curvature affect isotropisation of this cosmological model.