"The quantitative description of the Universe by General Relativity requires obtaining solutions to what are termed the Einstein field equations. These are 10 equations that must be solved simultaneously; they are notoriously difficult, and only a few solutions are known. (Technically, the equations to be solved are known to mathematicians as coupled, non-linear, partial differential equations; we may take that as precise shorthand for "very difficult to solve"!)
Solutions of the Equations
Among these solutions, there are two general classes:
Static Universes
Dynamic Universes
where static universes have distance scales that are constant in time and dynamic universes are either expanding or contracting over time. It may be shown that the cosmological principle (the assumption that there are no preferred positions or directions in the Universe) is inconsistent with a static universe. That is, the cosmological principle requires that the Universe be either expanding or contracting.
The Cosmological Constant
When Einstein first realized that the solution of his equations subject to the constraints of the cosmological principle led to universes that were not static, he was dismayed..."
Gives me a great amount of respect for people who work in such abstract theory. I didn't have a grasp of this topic till that Elegant Universe special hit the TV last year ( wish TV could pump out more stuff like that). If you see the universe as either closed or open, its still mindnumbingly complex to grasp.