  There seems to exist agreement about the fact that inflation squeezes the
quantum state of cosmological perturbations and entangles modes with
wavenumbers $\vec k$ and $-\vec k$. Paradoxically, this result has been used to
justify both the classicality as well as the quantumness of the primordial
perturbations at the end of inflation. We reexamine this question and point out
that the definition of two-mode squeezing of the modes $\vec k$ and $-\vec k$
used in previous work rests on choices that are only justified for systems with
time-independent Hamiltonians and finitely many degrees of freedom. We argue
that for quantum fields propagating on generic time-dependent
Friedmann-Lema\^itre-Robertson-Walker backgrounds, the notion of squeezed
states is subject to ambiguities, which go hand in hand with the ambiguity in
the definition of particles. In other words, we argue that the question "does
the cosmic expansion squeeze and entangle modes with wavenumbers $\vec k$ and
$-\vec k$?" contains the same ambiguity as the question "does the cosmic
expansion create particles?". When additional symmetries are present, like in
the (quasi) de Sitter-like spacetimes used in inflationary models, one can
resolve the ambiguities, and we find that the answer to the question in the
title turns out to be in the negative. We further argue that this fact does not
make the state of cosmological perturbations any less quantum, at least when
deviations from Gaussianity can be neglected.
