  The abundance and distribution of collapsed objects such as galaxy clusters
will become an important tool to investigate the nature of dark energy and dark
matter. Number counts of very massive objects are sensitive not only to the
equation of state of dark energy, which parametrizes the smooth component of
its pressure, but also to the sound speed of dark energy as well, which
determines the amount of pressure in inhomogeneous and collapsed structures.
Since the evolution of these structures must be followed well into the
nonlinear regime, and a fully relativistic framework for this regime does not
exist yet, we compare two approximate schemes: the widely used spherical
collapse model, and the pseudo-Newtonian approach. We show that both
approximation schemes convey identical equations for the density contrast, when
the pressure perturbation of dark energy is parametrized in terms of an
effective sound speed. We also make a comparison of these approximate
approaches to general relativity in the linearized regime, which lends some
support to the approximations.
