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Interacting dark energy-dark matter models have been widely analyzed in theliterature in an attempt to find traces of new physics beyond the usualcosmological ($\Lambda$CDM) models. Such a coupling between both darkcomponents is usually introduced in a phenomenological way through a flux inthe continuity equation. However, models with a Lagrangian formulation are alsopossible. A class of the latter assumes a conformal/disformal coupling thatleads to a fifth force on the dark matter component, which consequently doesnot follow the same geodesics as the other (baryonic, radiation, and darkenergy) matter sources. Here we analyze how the usual cosmologicalsingularities of the standard matter frame are seen from the dark matter one,concluding that by choosing an appropriate coupling, dark matter observers willsee no singularities but a non-beginning, non-ending universe. By consideringtwo simple phenomenological models we show that such a type of coupling can fitobservational data as well as the usual $\Lambda$CDM model.

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