You must include DE, just as BBT must include it but perhaps in many different forms. A few years ago, an author listed by name about 24 DE theories. Being theories, they must include testable claims, so some may have fallen by the wayside, but more may have arisen.
Yes, though when you compress everything will extreme fusion take place if the contraction rate doesn't match the former expansion rate? The BBT expansion rate was such that there wasn't enough time for anything but H and He to form, ignoring the tiny trace amounts of deuterium, etc. Since it's metaphysics, there is certainly room to allow this but do we know enough to use our knowledge of everything (DM and DE) to produce models that favor it? I doubt we are there yet.
Agreed, at least as an idea. But I kinda hope you do a thread on what the term "hypothetical" means within the realm of science. Philosophy likes to use to boost favor for one idea over another. A scientific hypothesis must be objective-based and make a testable prediction. It's like a sub-theory. But, yes, the Cyclical idea is deemed possible by a number of scientists, no doubt.
But can you explain just how that recycling would work to restore things as they were? Certain labs can simulate the early physics of BBT, so if you hand them the ashes of a match, can they recycle it somehow. Would they even try? We both know the answer.
I love the expression from my thermo prof that he had as a footnote in his thermo book, "Heat won't flow from a cooler to a hotter, you can try if you like but you far better notter." Compressing a cool universe will make it hotter but it won't lift energy up to the top shelf where it once was. It can lift it up to a higher shelf but likely never back to the top. H.D. will never be the same.
But there are physicists who will argue that the 2nd law may not apply to the Universe as a whole. It's hard to get it into a lab where we can play with it.
Perhaps quantum foam and other issues off some sort of supercharge to kick the old back to the original new. But this should come at a price as well unless we accept free lunches from bizarre ideas. Is that enough metaphors?
Ok, but I will be delighted to go to Sweden for your prize when you can demonstrate that the overall negative entropy of the universe can be made to decrease even a tiny amount with some special process. Those that suggest they can do this are likely just using word salads and hand-waving, but without solid and verifiable test.
Yes, if an infinite number of cycles is required. But, like a bouncing ball that never returns to its original height, many cycles might be possible until it can no longer perform as necessary. But this too is supposition and it assumes we keep applying the 2nd law, which might not be a requirement, but the logic of it is hard to escape.
Yes, I respect your aversion to t=0. I have my own suppositional take based on all the fine-tunning discoveries and personal experiences, but my view, if addressed in depth, would be seen as religious, which must, in fairness for any scientific website, but limited in presentation.