Dynamical systems methods and statender diagnostic of interacting vacuum energy models

We study three interacting dark energy models within the framework of four-dimensional General Relativity and a spatially flat Universe. In particular, we first consider two vacuum models where dark energy interacts with dark matter, while relativistic matter as well as baryons are treated as non-interacting fluid components. Secondly, we investigate a third model where the gravitational coupling is assumed to be a slowly-varying function of the Hubble rate and dark energy and dark matter interact as well. We compute the statefinders parameters versus red-shift as well as the critical points and their nature applying dynamical systems methods. In the case of only an interaction term, our main findings indicate that (i) significant differences between the models are observed as we increase the strength of the interaction term, and (ii) all the models present an unique attractor corresponding to acceleration. On the other hand, when we allow for a variable gravitational coupling, we find that (i) the deviation from the concordance model depends of both the strength of gravitational coupling parameter and the interaction term, and (ii) there is an unique attractor corresponding to acceleration.