The description of the various geometries of the Universe (open, closed, flat) also relate to their futures.

There are two possible futures for our Universe, continual expansion (open and flat), turn-around and

collapse (closed). Note that flat is the specific case of expansion to zero velocity.

The key factor that determines which history is correct is the amount of mass/gravity for the Universe as

a whole. If there is sufficient mass, then the expansion of the Universe will be slowed to the point of

stopping, then retraction to collapse. If there is not a sufficient amount of mass, then the Universe will

expand forever without stopping. The flat Universe is one where there is exactly the balance of mass to

slow the expansion to zero, but not for collapse.

The parameter that is used to measure the mass of the Universe is the critical density, Omega. Omega is

usually expressed as the ratio of the mean density observed to that of the density in a flat Universe.

Given all the range of values for the mean density of the Universe, it is strangely close to the density of a

flat Universe. And our theories of the early Universe (see inflation) strongly suggest the value of Omega

should be exactly equal to one. If so our measurements of the density by galaxy counts or dynamics are

grossly in error and remains one of the key problems for modern astrophysics.

Cosmological Constants:

The size, age and fate of the Universe are determined by two constants:

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