With the repeating universe theory does it mean just the universe repeats itself or does time and specific events repeat as well?
In Nature, events repeat with respect to time. Vice versa, the existence of overall-compounded-reciprocal time cycle that is almost periodic is not ruled out. .
Broad Cycles in Nature that are (almost) periodic with respect to our
Earth's progressive time:
Integration of micro-mass-Disintegration-of macro-mas-Integration.
So, I see Big Bang - Universal Apocalypse-Big Bang Cycle of period
exceeding (20 + 20) 40 billion years.