Multipartite entanglement features of primordial non-Gaussianities

We discuss some entanglement features associated with cubic non-Gaussian perturbations in single-field inflationary scenarios. We adopt standard momentum-space techniques to show how multipartite entanglement arises for inflationary perturbation modes, focusing on the dynamics of the comoving curvature perturbation. In particular, we quantify entanglement generation via the recently proposed Entanglement Distance, which introduces a geometric interpretation of quantum correlations in terms of the Fubini-Study metric. In the continuum limit, we show that the Entanglement Distance arising from displacement transformations is proportional to the total number of excitations in the quantum state for cubic perturbations, thus providing an upper bound on the von Neumann entanglement entropy of any reduced state compatible with such excitations. Within the interaction picture, we further observe that the quantum correlations arising from cubic gravitational interactions are typically much larger than the standard squeezing contribution, in agreement with previous studies focusing on von Neumann entropy generation across the Hubble horizon. We further show how the inflationary parameters affect the total amount of such correlations, highlighting in particular their dependence on the inflationary energy scales and the number of e-foldings during slow-roll.