Geometric multipartite entanglement from gravitational particle production

We explore novel generation of genuine multipartite entanglement within gravitational particle production processes during inflationary stages. To this end, we focus on perturbative production mechanisms, considering a non-minimally coupled scalar inflaton field with quartic self-coupling potential and computing probability amplitudes arising from its gravitational interaction with background perturbations. The corresponding entanglement amount is quantified using the recently proposed Entanglement Distance, that provides a \emph{geometric interpretation of particle entanglement, in terms of the Fubini-Study metric}. We observe that, in the limit of negligible squeezing, the total amount of entanglement is dominated by the infrared cutoff scale, in agreement with previous studies analyzing the von Neumann entropy within bipartite scenarios. We then show that \emph{non-negligible multipartite entanglement signatures may emerge across inflation, even during the latest stages of slow-roll}, highlighting their dependence on inflationary momentum scales. Generalizations to regimes with non-negligible squeezing, cubic non-Gaussianities, additional spectator fields and possible observational signatures are also discussed.