[Stone Mountain]

3) just the right amount of matter so that the expansion slows at an ever decreasing rate that approaches (but never reaches) zero. This results in a non-cyclic universe with a finite, bound volume.

Good point - I forgot about option 3. The way I see it, though, is that there would have to be just enough volume to keep things relatively consistent or at least cyclic - in a cycle of slightly expanding and contracting as the ratio of the matter in the universe keeps changing with respect to the size of the universe. It seems to me that if expansion is constantly slowing, at some point in the future, it will hit zero - of course this would be on the scale of billions of years... At that point, it seems to me that the universe would eventually start to contract - the logic being that if there is enough matter in the universe to slow the expansion, the expansion will eventually stop or at least stop expanding at any significant rate. At that point, since the amount of matter in the universe should still be constant (conservation of mass), wouldn't that imply that the existing matter in the universe would act on the universe and reverse the process and start it contracting?

[jwalsh07]

In order to offer a hypothesis on whether or not the universe will cease expanding, the guy doing the hypothesizing first has to know what causes the expansion and the nature of that force. To my knowledge, blue collar knowledge, nobody has those answers though it is posited that dark energy drives the expansion. What are the properties of dark energy? Your guess is as good as mine.

[Gandalf_The_Gray]

It seems to me that if expansion is constantly slowing, at some point in the future, it will hit zero... At that point, it seems to me that the universe would eventually start to contract...

Tell you what, go get some graph paper and a calculator. Pick some random numbers to plug into this equation as "X" and plot the result. You'll see what I mean after a few numbers.

Y = 1/X

Anything divided by zero is infinity by definition so try some numbers that are very small like 0.0000001 and then try some that are very large like 1,000,000.

The graph of "Y" is said to be asymptotically approaching zero as "X" approaches infinity. That is every time you double "X", "Y" is cut in half but it only goes to zero when "X" equals infinity. To further confuse the issue "Y" also is asymptotically approaching infinity as "X" goes to zero. The graph of the function is said to have two asymptotes at Y=0 and X=0.

Regards,
GtG