The Big Bounce theory isn't particularly new, but it's fascinating to see more recent contributions and work on it. I am happy it still is under active investigation and hasn't been disproven, as I find the idea of an endless heartbeat of the universe much more beautiful and less depressing than a Big Bang followed by heat death of the universe.
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Same. Always feels better to be part of something larger
How do these theories deal with the observation that the universe rate of expansion appears to be increasing? Wouldn’t a bounce imply that the expansion rate should decrease?
The expansion rate should decrease and eventually reverse at some point. I don't think anyone has yet defined when or why, or the theory would be considered complete. But us currently being in the phase of expansion doesn't automatically invalidate the theory I don't think. Then again, I'm not an astrophysicist.