Multipartite entanglement features of primordial non-gaussianities

TL;DR

This study identifies multipartite entanglement features in single-field inflation driven by cubic non-Gaussian gravitational interactions. It develops the Entanglement Distance (ED), a geometric measure based on the Fubini-Study metric, to quantify quantum correlations among inflationary perturbation modes in momentum space. The analysis shows that, in the perturbative regime, the ED associated with cubic interactions is proportional to the total number of excitations and provides an upper bound on the von Neumann entropy of any reduced perturbation state, with cubic contributions typically dominating over standard squeezing. The results highlight the sensitivity of these quantum correlations to the inflationary energy scale and duration (H_I and N), and discuss generalizations to continuous-variable multipartite entanglement and potential observational implications for the quantum-to-classical transition of cosmological perturbations.

Abstract

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.

Figures (1)

• Figure 1: Number density $n(k)$ as a function of the comoving wavenumber $k$, assuming slight variations in the total number of inflationary e-foldings $N$. We select $k \lesssim a(\tau_f) H_I$, further setting $H_I= 4 \times 10^{13}$ GeV and $N-N_*=10$, in agreement with Planck data.