21. The figure above shows the scale factor vs time measured from the present for
Ho = 71 km/sec/Mpc and for Ωo = 0 (green), Ωo = 1 (black), and Ωo = 2 (red)
with no vacuum energy; the WMAP model with ΩM= 0.27 and ΩV = 0.73 (magenta);
and the Steady State model with ΩV = 1 (blue). The ages ofthe Universe in these
five models are 13.8, 9.2, 7.9, 13.7 and infinity Gyr. The recollapse of the Ωo = 2
model occurs when the Universe is 11 times older than it is now, and all observations
indicate Ωo < 2, so we have at least 80 billion more years before any Big Crunch.