In the standard model of the Hot Big Bang, the time since
the Big Bang depends on the current value of the expansion rate
and the amount of matter in the universe. The expansion rate
is given by Hubble's constant. The amount of matter can be
measured in terms of the ratio of the mean density to the
critical density, the parameter called Omega, which governs
both the geometry of the universe
and its ultimate fate.
Look at it this way. Since the Big Bang, the universe has been
expanding, but the expansion has been slowing because of the
gravitational attraction of the matter in the universe. Since the
deceleration depends on the amount of gravity, it also depends
on the amount of matter, which we can describe in terms of the
critical density. The more matter, the more deceleration.
The current expansion then depends on the amount of deceleration.
In the case that the mean density of the universe is
exactly equal to the critical density, then we say that the
universe is "flat", and the time since the Big Bang is given
If the universe is open, then there has been less deceleration,
and the time since the Big Bang is more than 2/3 times 1/Ho.
On the other hand, if the universe is closed, then there has been
more deceleration, and the time since the Big Bang is less than that.
The WMAP satellite has revealed that the universe
is 13.7 +/- 0.2 billion years old, and that the universe is flat. We know
know the values of the cosmological parameters
to very high precision.