What is the future of our universe?
Like StephenG said, nobody knows for sure. But we do have confidence that the universe is expanding, and we also have confidence that the expansion is speeding up. So extrapolating from that, the future looks cold and lonely and bleak. A bit like life for the older generation!
Is the universe heading towards a Big Freeze, a Big Rip, a Big Crunch or a Big Bounce? Or is it part of an infinitely recurring cyclic model?
I'd say the Big Crunch and the Big Bounce are out. The universe didn't contract when it was small and dense. Instead it expanded, and that expansion is increasing. So it looks like we're in for a Big Freeze. However I wouldn't rule out a Big Rip of sorts. Have a look at page 5 of this paper where Milgrom mentions the strength of space. Then think of the balloon analogy, but make it a bubble-gum balloon, in vacuum.
The skin gets thinner and the balloon expands, then the skin gets even weaker, so the balloon expands even faster, and so on. Bubble-gum bubbles sometimes end badly, and there's something about this article by Phil Plait that strikes a chord.
Or is it part of an infinitely recurring cyclic model?
I don't know. I have no evidence to suggest that there's any kind of recycling going on, and I can't think of mechanism by which this might occur. I have of course read about "conformal cyclic cosmology", but I just don't buy it, along with other stuff from Penrose.
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