Superhorizon entanglement from inflationary particle production

We investigate entanglement generation between the sub- and super-Hubble modes of inflaton fluctuations, in the context of particle production from perturbations during inflation. We consider a large-field inflationary scenario where inflation is driven by a vacuum energy symmetry breaking potential and the scalar inflaton field is nonminimally coupled to spacetime curvature. In particular, we focus on the slow-roll phase, adopting a quasi-de Sitter scale factor to properly account for the presence of perturbations and computing the pair production probability associated to the coupling between the inflaton and spacetime inhomogeneities. The interaction Lagrangian at first order is constructed from inhomogeneities induced by the inflaton dynamics, and the initial Bunch-Davies vacuum state of the field evolves under the action of such Lagrangian. In this framework, we quantify the total amount of entanglement via the von Neumann entropy of the reduced density operator for superhorizon modes, tracing out sub-Hubble degrees of freedom. We then compare these outcomes with entanglement production for quadratic chaotic inflation and for a small-field quadratic hilltop scenario, preserving field-curvature coupling in both cases and pointing out the main differences between large and small-field approaches. We show that the amount of entanglement entropy arising from such geometric production grows rapidly in slow-roll regime and that it is typically higher in large-field scenarios. We also discuss our outcomes in light of recent findings for the squeezing entropy of cosmological perturbations and cubic nonlinearities in de Sitter space.