Discriminating interacting dark energy models using Statefinder diagnostic

Abstract: In the present work, we perform a comparative study of different interacting dark energy (DE) models using the Statefinder diagnostics. In particular, 17 different forms of the energy transfer rate $Q$ between DE and dark matter (DM) were focused on, belonging to the following categories: i) linear models in energy densities of DE and DM, ii) non-linear models, iii) models with a change of direction of energy transfer between DE and DM, iv) models involving derivatives of the energy densities, v) parametrized interactions through a function of the coincidence parameter $\tilde{r}$, and finally we also consider vi) two kinds of models with a self-interaction between DM, without DE. These models have been already studied in the literature and constrained with observational data available at that time. In order to discriminate between them at background level, we use the Statefinder diagnostic, based on the computation and study of the so-called Statefinder parameters $r$, $s$ in addition to the deceleration parameter $q$. We plot the evolution trajectories for the several interacting models on the $r-q$, $r-s$ planes, and we find some distinctive features and departures from $\Lambda$CDM and other DE models, as Quintessence, Chaplygin Gas, running vacuum models (RVM) and Galileon.