How does that theory account for population changes, human advances, and recorded environmental changes, ie. history. If everything stays the same, there is no change. If there is no change, then I should have had the internet, HDTV, and a cell phone at my birth. Since I did not, it must be subject to change. If it is subject to change, then you cannot repeat a prior life for infinity.
The big bang explodes, eventually creates us, then eventually gets pulled back into a giant black hole. The process repeats itself and infinite number of times.
When you start dealing with things like infinity and our knowledge of our known universe, you must also consider that infinity applies in both directions, and our known universe may be nothing more than a small molecular structure in a much greater universe, which might be a small molecular structure in a much greater universe, ad nauseam ...
Time may be a much greater determinate factor, but if infinity exist, what is time? We view time as measured against our planets rotation around our nearest star. We measure not only our own, but other organisms life span based upon how many star rotations they complete before they die.
We have a long road to travel ...