Shear dynamics in Bianchi I cosmologies with Rn-gravity

We give the equations governing the shear evolution in Bianchi spacetimes for general f ( R) theories of gravity. We consider the case of R-n-gravity and perform a detailed analysis of the dynamics in Bianchi I cosmologies which exhibit local rotational symmetry. We find exact solutions and study their behaviour and stability in terms of the values of the parameter n. In particular, we found a set of cosmic histories in which the universe is initially isotropic, then develops shear anisotropies which approach a constant value.