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.
