Vacuum state in de Sitter spacetime with static charts

TL;DR

This paper analyzes the Bunch-Davies vacuum in de Sitter spacetime with static charts, revealing its global mode structure and entanglement properties, which are important for understanding vacuum fluctuations and nonlocality.

Contribution

It provides a detailed construction of positive-frequency modes in static charts and clarifies the global structure of the Bunch-Davies vacuum in de Sitter space.

Findings

Modes are expressed as superpositions of conformally-flat chart modes.

The Bunch-Davies vacuum is shown to be an entangled state across static charts.

Results aid in studying thermal and nonlocal properties of vacuum fluctuations.

Abstract

We study the free massive scalar field in de Sitter spacetime with static charts. In particular, we find positive-frequency modes for the Bunch-Davies vacuum state natural to the static charts as superpositions of the well-known positive-frequency modes in the conformally-flat chart. We discuss in detail how these modes are defined globally in the two static charts and the region in their future. The global structure of these solutions leads to the well-known description of the Bunch-Davies vacuum state as an entangled state. Our results are expected to be useful not only for studying the thermal properties in the vacuum fluctuations in de Sitter spacetime but also for understanding the nonlocal properties of the vacuum state.