Quantum bounce and cosmic recall

Loop quantum cosmology predicts that, in simple models, the big bang is replaced by a quantum bounce. A natural question is whether the universe retains, after the bounce, its memory about the previous epoch. More precisely, does the Universe retain various properties of the state after evolving unitarily through the bounce, or does it suffer from recently suggested cosmic amnesia? We show that this issue can be answered unambiguously at least within an exactly solvable model. A semiclassical state at late times on one side of the bounce, peaked on a pair of canonically conjugate variables, strongly bounds the fluctuations on the other side, implying semiclassicality. For a model universe growing to 1 megaparsec, the change in relative fluctuation across the bounce is less than 10(-56) (becoming smaller for larger universes). The universe maintains (an almost) total recall.