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 within standard cosmologies and apply our analysis to minimally coupled quintessence. We also check past results for early dark energy parametrizations.