The spherical collapse model and cluster formation beyond the $\Lambda$
  cosmology: Indications for a clustered dark energy?
  We generalize the small scale dynamics of the universe by taking into account
models with an equation of state which evolves with time, and provide a
complete formulation of the cluster virialization attempting to address the
nonlinear regime of structure formation. In the context of the current dark
energy models, we find that galaxy clusters appear to form at z\sim 1-2, in
agreement with previous studies. Also, we investigate thoroughly the evolution
of spherical matter perturbations, as the latter decouple from the background
expansion and start to ``turn around'' and finally collapse. Within this
framework, we find that the concentration parameter depends on the choice of
the considered dark energy (homogeneous or clustered). In particular, if the
distribution of the dark energy is clustered then we produce more concentrated
structures with respect to the homogeneous dark energy. Finally, comparing the
predicted concentration parameter with the observed concentration parameter,
measured for four massive galaxy clusters, we find that the scenario which
contains a pure homogeneous dark energy is unable to reproduce the data. The
situation becomes somewhat better in the case of an inhomogeneous (clustered)
dark energy.
