One of the major challenges with "Big Bounce" that media coverage of it tends to overlook is that it is not entirely clear how the previous universe, which is presumably high entropy if it's supposed to be like ours, becomes the low entropy feedstock for the next universe. There's still a "And Here There Be Magic" step there.

I'm not saying there's no solution; indeed, this is the sort of thing where the problem is that the profusion of proposed solutions is exactly the thing that shows there's a problem there. I think people tend to intuitively think that "lots and lots of possible solutions" is somehow better than "no solutions at all" but they're actually nearly the same thing.

Based on the theory of gravity in the article it's actually, "Archimedes Principle all the way down."

https://en.wikipedia.org/wiki/Archimedes%27_principle

You’d have to explain how the steadily increasing entropy in our universe would revert to a low-entropy state again.