Quote:
Originally Posted by Brian W
Ok Craig, time to share some of your expertise. In the A. Guth article there is talk of 'omega' and how it needs to equal 1.
It is obviously a buzz word that I should know. What is it?
B
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Imagine a very simple Universe composed of a very large mass and a very small mass. There is a gravitational force between the masses.
Suppose the small mass is at some fixed distance and kinetic energy is supplied to the smaller mass.
There are 3 scenarios.
(1) The kinetic energy is insufficent to overcome the gravitational potential energy. The small particle initially moves away from the larger mass but eventually stops and falls back towards the larger mass.
(2) The kinetic energy equals the gravitational potential energy. The small mass will move away from the large mass but it is being slowed down. Inertia however prevents scenario (1) from occurring.
(3) The kinetic energy is greater than the potential energy and the small mass moves away from the large mass without being slowed down.
Each scenario can also be described by the density of the large mass, since the gravitational potential energy varies according to density.
For scenario (2) to occur the density of the larger mass has a particular value. This is known as the critical density.
If the actual density of the large mass is less than the critical density than (3) occurs.
If the actual density of the large mass is greater than the critical density than (1) occurs.
Omega is simply the ratio of the actual density to the critical density.
If actual density equals critical density then Omega = 1.
This principle can be applied to our Universe. Omega descibes the effect of gravity on an expanding Universe and also the geometry of the Universe.
If Omega < 1, the Universe will expand forever. An open Universe.
If Omega = 1, the Universe will expand forever (even though it is slowing down slightly). A flat Universe.
If Omega >1, the Universe will stop expanding and eventually collapse. A closed Universe.
Our Universe is flat. This has been confirmed by the variations in the Cosmic Radiation Background hence Omega = 1.
In Cosmology Omega is more complicated as it goes beyond the density of matter. It is composed of a visible matter component (as described above), a dark matter component and dark energy.
Regards
Steven