Non-locality effect on the entanglement entropy in deSitter

We investigate the effect of infrared non-locality on the entanglement between two causally separated open-charts in the deSitter space-time. Inspired by the work of Maldacena and Pimentel who gave a precise methodology for the computation of the long-range entanglement for the local massive scalar field theory on deSitter space-time, we aim to investigate the change in behaviour of this long-range entanglement due to the presence of infrared non-locality in the theory. By considering a nonlocal scalar field theory where the non-locality becomes important in the infrared, we follow the footsteps of Maldacena and Pimentel to compute the entanglement entropy of the free non-local scalar field theory in the Bunch-Davies vacuum. It is found that the presence of infrared non-locality will have strong effect on the long-range entanglement. In some case it is noted that if the strength of non-locality is large then it will tend to decrease the long-range entanglement in the infrared. We also consider the behaviour of R\'enyi entropy, where a strong role of non-locality on the entropy is noticed.