Anisotropic solutions in modified gravity

Anisotropic but homogeneous, shear-free cosmological models with imperfect matter sources in f(R) gravity are investigated. The relationship between the anisotropic stresses and the electric part of the Weyl tensor, as well as their evolutions in orthogonal f(R) models, is explored. The late-time behaviour of the de Sitter universe (as an example of a locally rotationally symmetric spacetimes in orthonormal frames) in f(R) gravity is examined. By taking initial conditions for the expansion, acceleration and jerk parameters from observational data, numerical integrations for the evolutionary behavior of the Universe in the Starobinsky model of f(R) have been carried out.