2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/187537In this paper we analyse the possibility of having homogeneous isotropic cosmological models with observers reaching $t=\infty$ in finite proper time. It is shown that just observationally-suggested dark energy models with $w\in(-5/3,-1)$ show this feature and that they are endowed with an exotic curvature singularity. Furthermore, it is shown that non-accelerated observers in these models may experience a duration of the universe as short as desired by increasing their linear momentum. A subdivision of phantom models in two families according to this behavior is suggested.6 pages, 1 figure, RevTeX4, new references and comments addedGeneral Relativity and Quantum CosmologyAstrophysicsHigh Energy Physics - Theorytext