|Age of the Universe|
So given our three parameters, H0, OmegaM, and OmegaL, we can solve for the expansion age and future fate of the universe. We can also solve for something called the "lookback" time. Remember that when we look out in space we are also looking back in time, since the light from distant objects takes time to get to us. So we see distant galaxies as they were when the universe was young.
If we know the three cosmological parameters, we can determine the age of the universe at any given redshift we observe. Or, since we also can calculate the current age of the universe, we can solve for the "lookback time" -- ie how far back in time we are looking.
How is this useful for us? One basic constraint on all cosmological models is that the Universe should not be younger than the objects in it. For example, in our galaxy we estimate that the globular clusters have an age of 11-15 billion years (Gyr). This means that a cosmology which gives a universe age of 9 Gyr won't work. Other constraints come from distant galaxies at higher redshift. For example, an elliptical galaxy named LBDS 53W091 has been discovered at a redshift of z=1.55, and based on its spectrum it has been estimated to be 1.5-3 Gyr old. This means that at a redshift of 1.55, the universe had to be at least that old. We may be able to reject certain cosmologies based on this simple observation.