Watching Discovery Channel show about various pre-universe theories. Glad to see the idea of an effect without a cause is rapidly being abandoned.
Here's an idea that intrigues me, touched on by one of the guest geniuses (don't remember his name).

Suppose the universe continues to disperse for umpteen bajillion years until finally the last bit of matter dissolves and there's nothing left but energy spread out over, what to us, would seem an unimaginably immense volume. However, without stuff, the concept of volume and distance and size becomes moot. But a quantum amount of energy would still be a quantum amount of energy. With no matter to provide relative distance relationships or density, the universe suddenly becomes an infinitely dense point of energy, not by shrinking in the sense we know it, but by the fact that there is nothing but energy, with nothing in between one quantum amount and the next. It hates that (apparently). The laws of physics are essentially reset, like dropping zeros from an over inflated currency, and inflation or big bang or whatever your view of the mechanics of how a universe goes from very small to very large, begins again.

Oddly enough, that makes perfect sense to me.

Allow me to expand (pun intended)

It's probably already got a name, but I'm going to call it Inflatable Photon Theory. The loss of the last bit of matter triggers a sudden chain reaction of expansion in the lonely photons. Something about the manner in which this takes place causes neutrinos (or something) to precipitate into bits of matter and a new universe is born.

Some other points to ponder (giving you guys a head start on actually doing the work). There would have to be some critical ratio of photons to not photons. As long as there remains even the tiniest bit of matter, with a specific number of photons in it, the size of the photon is set. Once that's gone, the photon's only reference is the amount of energy that defines it. Now they're all the same size, as far as they know, and as far as they can tell, they're squished together like sardines. This environment triggers....okay, work that bit out for me.

It actually works well with the computer like model of the universe, since it's more intuitive from a standpoint of an equation working itself out than from a fixed physical perspective.

It's been interesting to see the cycling universe hypotheses come back into some sort of mainstream.

Personally, I don't get how any cycling universe hypotheses at all square with the concept of an accelerating universe. I've actually seen someone posit the idea that although the universe is cycling, this is the last cycle, because we have tipped over into acceleration.

Having this universe 'turn into a singularity no matter what the size' is an interesting idea. Matter dissolving seems unlikely - we still haven't encountered a single instance of proton decay - but perhaps... there are ways around that? (?)

(I've often wondered in Narlikar's "Machian mass" case where m α t², could there be a limit? Can matter get 'too old'?)

I don't know. I don't find it particularly satisfying, but perhaps we should take note of what they might be counting for evidence of cycling universes. I'm sorry I haven't been keeping up on that; it's been a slow news decade :)

I like the currency analogy. Ha, the Italian lira model of the universe :)

So have you (or any of youse guys) read Endless Universe by Steinhardt and Turok? I admit that it hasn't been on my radar, but now that I read their Q&A, it sounds like the sort of thing into which one should poke one's nose.

I prefer a cyclic universe for the simple reason that my poor brain finds a one-off universe more difficult to digest.  If you care to look at it, I presented a speculative idea called the inverted universe that combines expansion and contraction as part of a cyclic universe.
http://youtu.be/Iqv-cygKSnU
I hope it can contribute something to the discussion.  What I didn't mention is that the simultaneous expansion and contraction might account for dark energy (the universe is torn asunder so to speak), and the eventual collapse of the universe into the mother of all black holes is the ultimate reset in which all information is lost, including entropy, so that a subsequent universe starts with the same entropy as the previous one.
It's all speculative, except for the fact that I have no math and physics skills to back up my assertions -that's the only thing that is proven.

Also, galaxies are supposed to move further and further apart in an expanding universe, but many galaxies and even clusters of galaxies have been observed to intersect.  That would tally with the notion that the universe is contracting.  I have not found any article explaining why galaxies collide.  Is that some huge turbulence?

I had a quick look-see at the video, and I think you've got the way Big Bang Theory - even in cyclic versions - a bit wrong. The "expanding shell" is not a normal 3D explosion, it's a "spacetime" explosion. That actually means that it is supposed to behave as a hypersphere. There isn't supposed to be an outer concentrated shell of anything - if anything, it's supposed to be super smooth but still somehow form matter out of that.

As an aside, I see the supernova light curve evidence weakening a bit with some papers that are essentially painting parts of the observations as possible Malmquist issues (that is to say, the further out we go, the more biased to energetic events or bright objects the observations seem, and they might not be representative because of that - I'll have to look up the two relevant papers on supernovas of which I'm thinking), and I'm wondering whether that was really the only driver behind dark energy (apart from needing another adjustable parameter so that the universe is actually older than the oldest stars in it :)