Interacting dark energy: clarifying the cosmological implications and viability conditions

In this study, cosmological models are considered, where dark matter and dark energy are coupled and may exchange energy through non-gravitational interactions with one other. These interacting dark energy (IDE) models have previously been introduced to address problems with the standard $\Lambda$CDM model of cosmology (which include the coincidence problem, Hubble tension and $S_8$ discrepancy). However, conditions ensuring positive energy densities have often been overlooked. Assuming two different linear dark energy couplings, $Q = \delta H \rho_{\rm{de}}$ and $Q = \delta H \rho_{\rm{dm}}$, we find that negative energy densities are inevitable if energy flows from dark matter to dark energy (iDMDE regime) and that consequently, we should only seriously consider models where energy flows from dark energy to dark matter (iDEDM regime). To additionally ensure that these models are free from early time instabilities, we need to require that dark energy is in the `phantom' ($\omega<-1$) regime. This has the consequence that model $Q=\delta H \rho_{\rm{dm}}$ will end with a future big rip singularity, while $Q = \delta H \rho_{\rm{de}}$ may avoid this fate with the right choice of cosmological parameters.