Hi Peter,
The problem I have with cyclic cosmology is that if when one universe disappears in a big crunch and nothing is left, then there can be no relation to a subsequent big bang like universe. If a universe which creates itself out of nothing obeys the conservation law which says that what comes out of nothing must add to nothing, then there's nothing left after the big crunch to serve as seed for the next big bang universe, so there can be no physical relation between successive universes. Moreover, to speak about successive universes not only implies that they all live in a time continuum not of their own making; to assume that the new universe pops up where the previous one disappeared, would only make sense if they pop up in a pre-existing space realm not of their own making.
Like the sum of all debts and credits on Earth by definition is zero, that doesn't mean that there exists no money. However, to an alien who by definition cannot observe the planet, who cannot communicate, interact in any way with the Earth and trade with earthlings, that money has no reality to him so the value and total amount of money to him is completely indefinite: he cannot say anything about the Earth, about its state or location.
If the information as embodied in particle properties and the associated rules of behavior aka laws of physics in a self-creating universe must be the product of a trial-and-error evolution, then information only can survive, become actual information when molded into physical, material particle and tested in actual particle interactions: only that information survives which enables its carriers, readers/writers to survive. If the universe would contain only a single charged particle (among many uncharged particles) so it wouldn't be able to express its charge, then it cannot be charged itself. If charge, if any property lives within interactions between particles, if particle express and preserve their properties by interacting, by exchanging information, then 'its', particles, particle properties are as much the cause as the effect of their interactions, of forces between them. If particles only exist to each other if and for as long as they interact, exchange information, then you cannot have one without the other, nor can one be more fundamental than the other, causally precede the other.
In other words, 'its', fundamental particles (and hence the macroscopic objects they form) only exist to one another if, to the extent and for as long as they interact but don't exist, have no physical reality to an imaginary observer outside the universe who(se body particles) cannot actually, physically interact with him. The universe is that weird, unique, paradoxical 'thing' which does not exist, which has no 'exterior', no reality as a whole, as 'seen' from without, but only exists as seen from within, so the present cosmologies don't make any sense whatsoever. As I have been trying to communicate (alas, without succeeding even once) in all previous FQXi essays, the conceptual fallacy of big bang, steady state and cyclic universes is that it makes no sense to speak about the universe as a whole as conservation laws says that it cannot have a physical reality as a whole, as 'seen' from without, but only exist as seen from within. By regarding the universe as an object which has particular properties and evolves as a whole in time, these cosmologies state that the universe lives in a spacetime realm not of its own making: that it has been created by some outside interference. All these cosmologies describe fictitious universes: they represent an essentially religious view on the universe and are tales of science fiction.
Regards, Anton