According to the cyclical model of universe does the universe repeat itself?
Answers
I think the term "repeating universe theory" could have several different interpretations.
Let us look at an couple of possibilities.
Suppose the nature of the universe is such that it will stop expanding and eventually experience a "big crunch".
Suppose further that such a "big crunch" will be automatically followed by another "big bang" with the same amount of matter/energy, etc. We could call that a "repeating universe theory", but perhaps there's something more...
If such a cycle is inevitable then there are some theories that we might attach to it:
(1) The theory that the following "big bang" will of necessity be identical to that which started this cycle, and will result in exactly the same sequence of events. Such a theory is almost certainly false.
(2) The theory that there are a large but finite number of possible initial configurations for a "big bang" in such a recurring cycle, so if an infinite number of "big bang" - "big crunch" cycles occur then at least one configuration will repeat. OK so far, but does the initial configuration determine all following events? - probably not.
(3) Like (2), but since the length of a "big bang" - "big crunch" cycle is finite, then if spacetime is quantised, there are a finite number of possible states through which the universe goes during a cycle. So there is a ridiculously huge but finite number of possible cycles. So in an infinite number of cycles, at least one possible sequence will repeat.