The age of the universe

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 exactly by:

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.

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