Intermediate homogenization of the Universe and the problem of
  gravitational entropy
  This paper studies intermediate homogenization of inhomogeneous cosmological
models. It shows that spherically symmetric models, regardless of the equation
of state, can undergo intermediate homogenization, i.e. a model can approach a
homogeneous and isotropic state (which acts as a saddle point) from a
relatively wide range of initial inhomogeneous conditions. The homogenization
is not permanent - just temporary. Eventually the model evolves toward a future
inhomogeneous state. We also looked at the problem of the gravitational
entropy. All definitions of entropy that we checked give decreasing
gravitational entropy during the homogenization process. Thus, we should either
accept that gravitational entropy can decrease or try to define it in other
ways than just via density gradients, as these decrease during homogenization.
