Ultimate fate of the various FRW models. Note, with a cosmological constant one cannot associate the future simply with the geometry (open or closed).
Similar plot. the diagonal lines are labeled with ages in units of the Hubble time (the concordance model is the red dot with age just under the Hubble time.
Repeat plot of the time evolving FRW models: a(t)
Figure from Open University text "Galaxies and Cosmology"