  Loop quantum cosmology predicts that, in simple models, the big bang
singularity of classical general relativity is replaced by a quantum bounce.
Because of the extreme physical conditions near the bounce, a natural question
is whether the universe can retain, 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
some cosmic amnesia as has been recently suggested? Here we show that this
issue can be answered unambiguously at least within an exactly solvable model,
derived from a small simplification of loop quantum cosmology, for which there
is full analytical control on the quantum theory. We show that if there exists
a semiclassical state at late times on one side, peaked around a pair of
canonically conjugate variables, then there are very strong bounds on the
fluctuations on the other side of the bounce, implying semi-classicality. For
such a model universe which grows to a size of 1 megaparsec, at late times, the
change in relative fluctuations of the only non-trivial observable of the model
across the bounce is less than $10^{-56}$ (becoming smaller for universes which
grow larger). The universe maintains (an almost) total recall.
