likely shape of the universe? makes it unlikely?
plz. explain.
Let's use gum for an analogy.
First take the gum and roll it out flat. It's not going to collapse back in, it's just going to keep spreading out thinner and thinner.
Now try blowing a bubble with the gum. This would be like a spherical universe. Unlike flattening the gum out the bubble eventually will reach a critical point, deflate and collapsing back in on itself. (your cycle)
The third possibility is we flatten the gum out but curve it. So it flattens more in some spots than others. This would result in those thinning areas to become to thin and create wholes, or rip apart.
This would apply to the universe as well. If everything is thinning out the matter can't interact resulting in everything eventually settling and cooling. If everything is expanding in a bubble it will eventually reach critical point where it collapses back on itself. if it's curved there will be an unequal expansion resulting in the universe ripping apart.
Now there is more to consider than that which we don't have all worked out, but from our observations of the universe compared to models of a flat, curves and spherical one it matches a flat universe the best. So we can expect everything to evenly thin out and the matter inside to settle and cool due to lack of interaction.