Clarifying spherical collapse in coupled dark energy cosmologies
  The spherical collapse model is often used to follow the evolution of
overdensities into the nonlinear regime. We describe the correct approach to be
used in coupled dark energy cosmologies, where a fifth force, different from
gravity and mediated by the dark energy scalar field, influences the collapse.
We reformulate the spherical collapse description by deriving it directly from
the set of nonlinear hydrodynamical Navier Stokes equations. By comparing with
the corresponding relativistic equations, we show how the fifth force should be
taken into account within the spherical collapse picture and clarify the
problems arising when an inhomogeneous scalar field is considered within a
spherical collapse picture. We then apply our method to the case of coupled
quintessence, where the fifth force acts among cold dark matter particles, and
to growing neutrino quintessence, where the fifth force acts between neutrinos.
Furthermore, we review this method when applied to standard cosmologies and
apply our analysis to minimally coupled quintessence and check past results for
early dark energy parametrizations.
