In search of an observational quantum signature of the primordial
  perturbations in slow-roll and ultra slow-roll inflation
  In the standard inflationary paradigm, cosmological density perturbations are
generated as quantum fluctuations in the early Universe, but then undergo a
quantum-to-classical transition. A key role in this transition is played by
squeezing of the quantum state, which is a result of the strong suppression of
the decaying mode component of the perturbations. Motivated by ever improving
measurements of the cosmological perturbations, we ask whether there are
scenarios where this decaying mode is nevertheless still observable in the late
Universe, ideally leading to a ``smoking gun'' signature of the quantum nature
of the perturbations. We address this question by evolving the quantum state of
the perturbations from inflation into the post-inflationary Universe. After
recovering the standard result that in slow-roll (SR) inflation the decaying
mode is indeed hopelessly suppressed by the time the perturbations are observed
(by $\sim 115$ orders of magnitude), we turn to ultra slow-roll (USR)
inflation, a scenario in which the usual decaying mode actually grows on
super-horizon scales. Despite this drastic difference in the behavior of the
mode functions, we find also in USR that the late-Universe decaying mode
amplitude is dramatically suppressed, in fact by the same $\sim 115$ orders of
magnitude. We finally explain that this large suppression is a general result
that holds beyond the SR and USR scenarios considered and follows from a
modified version of Heisenberg's uncertainty principle and the observed
amplitude of the primordial power spectrum. The classical behavior of the
perturbations is thus closely related to the classical behavior of macroscopic
objects drawing an analogy with the position of a massive particle, the
curvature perturbations today have an enormous effective mass of order $m_{\rm
pl}^2/H_0^2 \sim 10^{120}$, making them highly classical.
