Eternal vs singular observers in interacting dark energy-dark matter models

Abstract: Interacting dark energy-dark matter models have been widely analyzed in the literature in an attempt to find traces of new physics beyond the usual cosmological ($\Lambda$CDM) models. Such a coupling between both dark components is usually introduced in a phenomenological way through a flux in the continuity equation. However, models with a Lagrangian formulation are also possible. A class of the latter assumes a conformal/disformal coupling that leads to a fifth force on the dark matter component, which consequently does not follow the same geodesics as the other (baryonic, radiation, and dark energy) matter sources. Here we analyze how the usual cosmological singularities of the standard matter frame are seen from the dark matter one, concluding that by choosing an appropriate coupling, dark matter observers will see no singularities but a non-beginning, non-ending universe. By considering two simple phenomenological models we show that such a type of coupling can fit observational data as well as the usual $\Lambda$CDM model.