Abstract:
We study a class of shear-free, homogeneous but anisotropic cosmological
models with imperfect matter sources in the context of f (R) gravity. We show that
the anisotropic stresses are related to the electric part of the Weyl tensor in such a
way that they balance each other. We also show that within the class of orthogonal
f (R) models, small perturbations of shear are damped, and that the electric part of
the Weyl tensor and the anisotropic stress tensor decay with the expansion as well
as the heat flux of the curvature fluid. Specializing in locally rotationally symmetric
spacetimes in orthonormal frames, we examine the late-time behaviour of the de Sitter
universe in f (R) gravity. For the Starobinsky model of f (R), we study the evolutionary
behavior of the Universe by numerically integrating the Friedmann equation, where
the initial conditions for the expansion, acceleration and jerk parameters are taken
from observational data.
