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Dynamics of the anisotropic Kantowsky-Sachs geometries in $R^n$ gravity

We construct general anisotropic cosmological scenarios governed by an $f(R)$ gravitational sector. Focusing then on Kantowski-Sachs geometries in the case of $R^n$-gravity, and modelling the matter content as a perfect fluid, we perform a detailed phase-space analysis. We find that at late times the universe can result to a state of accelerating expansion, and additionally, for a particular $n$-range ($2<n<3$) it exhibits phantom behavior. Furthermore, isotropization has been achieved independently of the initial anisotropy degree, showing in a natural way why the observable universe is so homogeneous and isotropic, without relying on a cosmic no-hair theorem. Moreover, contracting solutions have also a large probability to be the late-time states of the universe. Finally, we can also obtain the realization of the cosmological bounce and turnaround, as well as of cyclic cosmology. These features indicate that anisotropic geometries in modified gravitational frameworks present radically different cosmological behaviors comparing to the simple isotropic scenarios.