Summary: Dark energy recently began to dominate in the Universe, making its expansion accelerating. If dark energy is assumed to originate from a quintessence field, we have obtained consistent cosmological solutions to the Friedmann equations for an accelerating universe which can be interpreted as compactified Lorentzian wormholes; we shown that then, unlike asymptotically de Sitter spaces, there should be no event horizons placed at finite distances in the future, in the spacetimes described by these FRW solutions, even for constant quintessence equations of state predicting acceleration. It is argued that it is the existence of signals travelling backward in time that prevents event horizons to occur at finite distances in the future in these space-times. We have also solved the Friedmann equations for different regimes that preceded our present accelerating era and are predicted by quintessence tracking models. As an alternative proposal to the tracked description, we further suggest a new cosmological scenario where the entire evolution of the Universe prior to the present accelerating expansion occurred in a Euclidean regime with imaginary time, and the primordial inflation is viewed as an artifact originating from Lorentzian causality underlying all current physical instruments and hence the results they provide and their interpretation. By recourse to the noted analogy between this cosmological scenario and the epistemological aspects of Plato’s cave myth of ancient Greek philosophy that concern geometric forms, we call the resulting universe model a Platonic universe.