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

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