Emergence of classical behavior in the early universe
  We investigate three issues that have been discussed in the context of
inflation: Fading of the importance of quantum non-commutativity; the
phenomenon of quantum squeezing; and the ability to approximate the quantum
state by a distribution function on the classical phase space. In the standard
treatments, these features arise from properties of mode functions of quantum
fields in (near) de Sitter space-time. Therefore, the three notions are often
assumed to be essentially equivalent, representing different facets of the same
phenomenon. We analyze them in general Friedmann-Lemaitre- Robertson-Walker
space-times, through the lens of geometric structures on the classical phase
space. The analysis shows that: (i) inflation does not play an essential role;
classical behavior can emerge much more generally; (ii) the three notions are
conceptually distinct; classicality can emerge in one sense but not in another;
and, (iii) the third notion is realized in a surprisingly strong sense; there
is exact equality between completely general $n$-point functions in the
classical theory and those in the quantum theory, provided the quantum
operators are Weyl ordered. These features arise already for linear
cosmological perturbations by themselves: considerations such as mode-mode
coupling, decoherence, and measurement theory --although important in their own
right-- are not needed for emergence of classical behavior in any of the three
senses discussed. Generality of the results stems from the fact that they can
be traced back to geometrical structures on the classical phase space,
available in a wide class of systems. Therefore, this approach may also be
useful in other contexts.
