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What?
A collapsing Universe is just a theory - and we're only able to account for less than 5% of the mass in the universe that math indicates that there should be for that discussion to even go anywhere. We're a long way from being able to say anything at all about that for certain.

But anyway - so it contracts and explodes again? Does it, 'though? This seems to be supposition: which is based on what?
Everything happens "mostly the same" each time? Oh really? Why should it? This seems to be presumption: which is based on what?

We "should" be reborn every time the Universe is reborn? Should we, indeed? Why is that? This looks a lot like supposition; presumption; assumption and wild conjecture.

The 3rd paragraph is just confused.

The 4th paragraph [sigh..] is irrelevant. You can't travel back in time, and if you could, you cant kill your grandfather or you wouldn't be around to be travelling back in time. Other than that it just states the obvious.

The probability discussion, blah, blah, blah - well-trodden philosophical ground, but mixed in with the themes of paragraph 4 in an attempt to support this overall position - which is largely unsupportable, as above.

Overall, this is ridiculous and is the exact problem with this whole "time-travel" discussion - bedroom theories that aren't validated by the basic science principle of structured auto-criticism, [but instead seek to self-affirm!], that aren't properly evidenced or supported with reasonable logic and that are laced with just enough half-truth of terms and concepts not fully understood to make those theories seem reasonable.

Disclaiming such terribly poor science or logic by saying it's "just for discussion" is insufficient - and insulting! Otherwise I could just post "Green eggs and ham, green eggs and ham - the Universe is a triangle- because I said so. [It's just for discussion]".

Absolute nonsense! And the reason why the Internet is a minefield.