this review (god’s equations?) by john leslie of new books by roger penrose and stephen hawking/leonard mlodinow, deals with penrose’s theory of cosmic cycles:

 “…infinite time doesn’t look infinite to photons, “particles of light” without mass (more technically, without “rest-mass”). To a photon, traversing an infinite distance seems to take no time at all. Particles possessing mass are tiny “clocks”. The photon isn’t. It doesn’t “tick”. And, immense ages after all black holes have evaporated entirely through the process discovered by Hawking, the universe may contain nothing that could act as a clock. Particles possessing mass may one and all have become massless very, very gradually. Well, in Einstein’s world clocks are crucial to measuring distances. If eventually there were no clocks, just any distance could readily be traversed. Not only could the universe stop getting older and older; it could actually lose its vastness. This would allow things to carry over smoothly into a new Bang.”

leslie also discusses hawking and mlodinow’s ideas about the many-branched universe:

All branches are equally real, for despite appearances superpositions never collapse. They instead grow to include whomever observes them; any observer develops seemingly incompatible properties. In a complex sense, the observer splits or branches. Well, scientists in the “quantum cosmology” community mostly accept this. However, they would typically reject the book’s idea that all branching depends on observations. Suppose your double, your “other half” with seemingly incompatible properties, inhabits a universe-branch where a cat is alive. In your branch a double of the cat is dead. Looking to see which branch you inhabited needn’t, most of them would say, be what killed that cat.
The book’s ideas about creating the past render matters worse. “Observations you make on a system in the present affect its past.” This is proved, the authors say, by “delayed choice experiments” where any question to be asked experimentally is decided at a late moment. Yet couldn’t you instead claim that past events merely looked as if they’d taken particular forms, or else that they took them, but only in a universe-branch into which the experimental decision helped to place you? Either way, nothing ever reacts to a choice which hasn’t yet been made.

in limiting our consideration only to dimensions which are known, however, we must all be missing a few tricks (not that i think theories should be built on unknown dimensions…).