Is an infinite universe compatible with cyclic models?

[TheHeraclitus]

TL;DR Summary

If space is flat and infinite are cyclic models possible? The answer seems intuitively no but I wonder if it's correct.

Cyclic models for reference.
I will take simple Big Bounce as an example of what I have in mind.
In Big Bounce there periods of expansion and periods of contraction which result in a never-ending series of Big Bangs. However if Universe is infinite in extent this would require infinite amount of matter would have to contract into one point but that seems impossible.

 

[PeroK]

The big bounce implies that quantum things cause the bounce while the universe still has finite density. That could happen everywhere in a spacially infinite universe - in the same way that a big bang can.