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.