Do cyclic models of the universe

[_heretic]

I have a question as to the actual nature of cyclic models of the universe (e.g. Roger Penrose's Conformal Cyclic Cosmology or the Ekpyrotic universe) - essentially where the universe has no beginning or end it simply goes through cycles eternally in both time directions. So in these situations would the entire history of the universe be considered to be mathematically an countably infinite or uncountably infinite as a set? That is, would each cycle (e.g. big bang to big crunch) be classed as an element of a countably infinite set or an uncountably infinite one?

Furthermore, if the set of these cycles was countably infinite would that mean that each cycle (i.e one in which there is an Earth and this post of the Physics Forums) could only ever occur **once** in the entire history of the universe. (?) Or would it mean that each cycle could have identical "looking" cycles later on. i.e at time N1 we encounter cycle A in which there is an Earth with this post on the Physics Forums, and later, at time N2 we encounter cycle B in which there is a situation functionally the same as in cycle A: Identical planet with identical post on identical network which, for all intents and purposes, is then the same as cycle A (?)

Thanks in advance!

 

[_heretic]

Anyone?

 

[twofish-quant]

So in these situations would the entire history of the universe be considered to be mathematically an countably infinite or uncountably infinite as a set? That is, would each cycle (e.g. big bang to big crunch) be classed as an element of a countably infinite set or an uncountably infinite one?

Countably infinite since you can map everything to integers.

Furthermore, if the set of these cycles was countably infinite would that mean that each cycle (i.e one in which there is an Earth and this post of the Physics Forums) could only ever occur **once** in the entire history of the universe. (?) Or would it mean that each cycle could have identical "looking" cycles later on. i.e at time N1 we encounter cycle A in which there is an Earth with this post on the Physics Forums, and later, at time N2 we encounter cycle B in which there is a situation functionally the same as in cycle A: Identical planet with identical post on identical network which, for all intents and purposes, is then the same as cycle A (?)

It's called Poincaire recurrence, but if you have the universe a situation in which you have countably infinite universes in a non-infinite phase space (i.e. you have infinite universes but the number of possible universes is finite) then mathematically things will repeat.

Yes this does lead to weird things which bothers people.

 

[_heretic]

Thanks for the info twofish-quant Just to clarify though, in terms of universe cycles what would the phase space be likely measuring? e.g. Possible energies at the big bang?