Space-time correlations within pairs produced during inflation: A wave-packet analysis

In homogeneous universes the propagation of quantum fields gives rise to pair creation of quanta with opposite momenta. When computing expectation values of local operators, the correlations between these quanta are averaged out and no space-time structure is obtained. In this article, by an appropriate use of wave packets, we reveal the space-time structure of these correlations. We show that every pair emerges from vacuum configurations which are torn apart so as to give rise to two semiclassical currents: that carried by the particle and that of its ''partner.'' During inflation the partner's current lives behind the Hubble horizon centered around the particle. Hence any measurement performed within a Hubble patch would correspond to an uncorrelated density matrix, as for Hawking radiation. However, when inflation stops, the Hubble radius grows and eventually encompasses the partner. When this is realized the coherence is recovered within a patch. In this paper, we focus on the case of a massive field with rare pair creation events. However, our analysis also applies to cases leading to arbitrary high occupation numbers. Hence it could be applied to primordial gravitational waves and primordial density fluctuations