this builds on an earlier theorem, which i haven't looked at (and probably wouldn't understand anyway) which apparently makes rigorous the intuitively attractiv

this builds on an earlier theorem, which i haven't looked at (and probably wouldn't understand anyway) which apparently makes rigorous the intuitively attractive idea that if you trace back in time something that is getting bigger then at some point you reach zero. the reason oscillating universes are caught out by this is that (apparently - this is all just my impression on a quick skim, having never understood things much and leaving astronomy - not even astrophysics - decades ago) even though they oscillate, they need to get systematically bigger to work around some problems with entropy. another model they considered is a universe that "just sits there" like a seed, forever, until (randomly) deciding to grow. and that has problems with quantum mechanics (which you can imagine - how can something be stable for an infinite amount of time?). one problem is that it's a paper that really only attacks current models. they don't prove that no other model could be thought up. you could also argue another weakness of the paper is a reliance on our notions of basic physics (quantum and statistical mechanics) holding true even in the distant past. but then, what else can you do?