2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/169991We prove that the leaves of an inverse mean curvature flow provide a foliation of a future end of a cosmological spacetime $N$ under the necessary and sufficent assumptions that $N$ satisfies a future mean curvature barrier condition and a strong volume decay condition. Moreover, the flow parameter $t$ can be used to define a new physically important time function.22 pages, v2: Some minor typos corrected, will be the published versionDifferential GeometryGeneral Relativity and Quantum Cosmology35J60, 53C21, 53C44, 53C50, 58J05text