This is a cut and paste:
The universe's fate is intimately connected to its shape which, in turn, depends on a single number, Omega: the ratio of the average mass density of the universe to the critical value required to just maintain equilibrium.
An open universe, corresponding to omega less than one, will expand forever. Matter will spread thinner and thinner. Galaxies will exhaust their gas supply for forming new stars, and old stars will eventually burn out, leaving only dust and dead stars. The universe will become quite dark and, as the temperature of the universe will approaches absolute zero, quite cold. The universe will not end, exactly, just peter out in a Big Chill.
The expansion of a closed universe, with an Omega greater than one, will slow down until it reaches a maximum size, when it begins its inward collapse. Like a video of the Big Bang and expansion run backward, the universe will become denser and hotter until it ends in an infinitely hot, infinitely dense Big Crunch--perhaps providing the seed for another Big Bang.
If Omega equals 1 exactly, then cosmic expansion will coast to a halt infinitely far into the future. The universe will not end in a Big Crunch nor expand into an infinite Big Chill, but will remain at equilibrium.
This last case is consistent with the inflation hypothesis, and also commands the most observational support. Not to mention the fact that, for most of us, it's an emotionally appealing scenario. Even though the universe's fate lies billions of years in the future, it's the only one we have.
http://archive.ncsa.uiuc.edu/Cyberia/Cosmos/CosmosFate.html
Also look here:
http://www.sciencedaily.com/releases/2004/07/040728090338.htm