The statement in the above caught my eye. As far as I can tell, Steinhardt's cyclic universe collapses to the extent that all massive bodies cease to exist. In fact, once the temperature of the universe rises above the Higgs temperature, which is just above the electro-weak energy level, mass as we know it ceases to exist, at least according to the Standard Theory.
So what happens is something like the big bang. The universe comes rushing in. Dark Energy diminuishes because it is proportional to the amount of space in the universe, so physicists seem to think, and mass with its gravity takes over. The universe is heading for a massive black hole when its temperature rises above Higgs, the mass disappears and the universe bounces.
What I have not been able to figure out from Steinhardt's work is how close does the universe get to the singularity of the big bang. We know that it gets within 300,000 years because of COBE data. It must get to the electro-weak force era for mass to disappear just beyond that energy level. But then the universe continues to coast or implode. So I cannot determine if it gets to within a few minutes or hours of the singularity. But after that it re-expands just like a Big Bang according to Steinhardt.
For example, it could get to the energy level where matter and anti-matter can co-exist. Steinhadt to my knowledge has not addressed these questions. If someone knows where he has, I would very much like the reference.