Quantum state of interacting primordial inhomogeneities: de-squeezing and decoherence

Abstract

We investigate how interactions affect the quantum state of scalar perturbations during inflation and the quantum correlations they may exhibit. Focusing on the case of scalar perturbations in single-field inflation, we model interactions using a Lindblad equation with a non-unitary contribution quadratic in the scalar perturbations, and of parametrisable amplitude and time dependence. We compute the quantum state of these interacting perturbations, which is fully described by its purity and squeezing parameters. First, we show that, in most of the parameter space, not only the purity but also the squeezing parameter is significantly reduced by interactions. Second, we show that this de-squeezing induced by the interactions, on top of the purity loss, causes a further suppression of quantum correlations. We thus emphasise that the quantum or classical character of the correlations exhibited by the perturbations cannot be correctly determined by computing the effect of interactions on the purity alone. Since the phenomenological framework adopted in this paper encompasses a wide class of possible interactions, our results provide general insights into the nature of decoherence processes in primordial fluctuations.