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In the standard inflationary paradigm, cosmological density perturbations aregenerated as quantum fluctuations in the early Universe, but then undergo aquantum-to-classical transition. A key role in this transition is played bysqueezing of the quantum state, which is a result of the strong suppression ofthe decaying mode component of the perturbations. Motivated by ever improvingmeasurements of the cosmological perturbations, we ask whether there arescenarios where this decaying mode is nevertheless still observable in the lateUniverse, ideally leading to a ``smoking gun'' signature of the quantum natureof the perturbations. We address this question by evolving the quantum state ofthe perturbations from inflation into the post-inflationary Universe. Afterrecovering the standard result that in slow-roll (SR) inflation the decayingmode 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 onsuper-horizon scales. Despite this drastic difference in the behavior of themode functions, we find also in USR that the late-Universe decaying modeamplitude is dramatically suppressed, in fact by the same $\sim 115$ orders ofmagnitude. We finally explain that this large suppression is a general resultthat holds beyond the SR and USR scenarios considered and follows from amodified version of Heisenberg's uncertainty principle and the observedamplitude of the primordial power spectrum. The classical behavior of theperturbations is thus closely related to the classical behavior of macroscopicobjects drawing an analogy with the position of a massive particle, thecurvature perturbations today have an enormous effective mass of order $m_{\rmpl}^2/H_0^2 \sim 10^{120}$, making them highly classical.

In search of an observational quantum signature of the primordial perturbations in slow-roll and ultra slow-roll inflation