Unphysical properties in a class of interacting dark energy models

Models with non-gravitational interactions between the dark matter and dark energy components are an alternative to the standard cosmological scenario. These models are characterized by an interaction term, and a frequently used parameterization is $Q = 3\xi H \rho_{x}$, where $H$ is the Hubble parameter and $\rho_{x}$ is the dark energy density. Although current observations support such a model for negative values of the interaction parameter $\xi$, we show here that this interval of values of $\xi$ leads the model to predict a violation of the Weak Energy Condition (WEC) for the dark matter density, regardless of the value of the equation-of-state parameter of the dark energy component. This violation is accompanied by unphysical instabilities of matter perturbations.