2DARK天文志

Abstract: 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 recall various properties of
the state after evolving unitarily through the bounce or does it suffer from
cosmic amnesia as has been recently suggested? Here we show that this issue can
be answered unambiguously by means of 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
semi-classical 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 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 $10^{-57}$ (becoming smaller for universes which grow
larger). The universe maintains (an almost) total recall.