Subtleties in decoherence and squeezing of cosmological perturbations

We revisit the cosmological perturbations in minimal single-field inflation, focusing on subtleties arising from total time derivatives (boundary terms) in their action and the corresponding slow-roll unsuppressed phase in the wave functional. While these total derivatives do not contribute to field correlators, they can significantly influence processes related to momentum-space entanglement, including decoherence and squeezing. We also discuss the necessity of considering such terms from several perspectives: the well-defined variational principle in gravity, the integration-by-parts procedure of cosmological perturbations and the WKB limit of the Wheeler-DeWitt equation. Finally, we explore these subtleties in a proposed cosmological Bell test utilizing momentum-space entanglement, showing a possible window for Bell violation. References: 2405.07141, 2305.08071 and 2207.04435