Entanglement entropy of $alpha$-vacua in de Sitter space

We consider the entanglement entropy of a free massive scalar field in the one parameter family of $alpha$-vacua in de Sitter space by using a method developed by Maldacena and Pimentel. An $alpha$-vacuum can be thought of as a state filled with particles from the point of view of the Bunch-Davies vacuum. Of all the $alpha$-vacua we find that the entanglement entropy takes the minimal value in the Bunch-Davies solution. We also calculate the asymptotic value of the Renyi entropy and find that it increases as $alpha$ increases. We argue these feature stem from pair condensation within the non-trivial $alpha$-vacua where the pairs have an intrinsic quantum correlation.