On virialization with dark energy

We review the inclusion of dark energy in the formalism of spherical collapse, and the virialization of a two-component system, made of matter and dark energy. We compare two approaches in previous studies. The first assumes that only the matter component virializes, e. g. as in the case of a classic cosmological constant. The second approach allows the full system to virialize as a whole. We show that the two approaches give fundamentally different results for the final state of the system. This might be a signature discriminating between the classic cosmological constant which cannot virialize and a dynamical dark energy mimicking a cosmological constant. This signature is independent of the measured value of the equation of state. An additional issue which we address is energy non-conservation of the system, which originates from the homogeneity assumption for the dark energy. We propose a way to take this energy loss into account.