MG11 
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Shear dynamics in Bianchi I cosmologies with $R^n$-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 {\it 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 dissipate at late times to a constant value $\sigma_0$.