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

TL;DR

This paper investigates the entanglement entropy of a scalar field in various $lpha$-vacua in de Sitter space, revealing minimal entropy in the Bunch-Davies vacuum and increased entropy with larger $lpha$, linked to pair condensation.

Contribution

It provides the first detailed analysis of entanglement entropy across the family of $lpha$-vacua in de Sitter space, highlighting the unique properties of the Bunch-Davies vacuum.

Findings

Entanglement entropy is minimized in the Bunch-Davies vacuum.

As $lpha$ increases, the Re9nyi entropy asymptotically increases.

Pair condensation in $lpha$-vacua causes intrinsic quantum correlations.

Abstract

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 R\'enyi 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.