Constraints on interacting dynamical dark energy and a new test for ΛCDM model

We consider a generic description of interacting dynamical Dark Energy, characterized by an equation of state with a time dependent coefficient w(t), and which may interact with both radiation and matter. Without referring to any particular cosmological model, we find a differential equation which must be satisfied by w(t) and involving the function Q(t) which describes the interaction between Dark Energy and the other cosmological fluids. The relation we find represents a constraint for various models of interacting dynamical Dark Energy. In addition, an observable is proposed, depending on kinematic variables and on density parameters, which may serve as a new test for ΛCDM.