Global Properties of Vacuum States in de Sitter Space

TL;DR

This paper investigates the global properties of vacuum states in de Sitter space, demonstrating their purity, mixing properties, and the necessity of the Gibbons-Hawking temperature, using algebraic quantum field theory methods.

Contribution

It establishes that vacuum states in de Sitter space possess the Reeh-Schlieder property, are pure and weakly mixing, and confirms the temperature must match the Gibbons-Hawking temperature, revealing their algebraic structure.

Findings

Vacuum states have the Reeh-Schlieder property.

Vacuum states are pure and weakly mixing.

Gibbons-Hawking temperature is necessary for these states.

Abstract

Starting from the assumption that vacuum states in de Sitter space look for any geodesic observer like equilibrium states with some a priori arbitrary temperature, an analysis of their global properties is carried out in the algebraic framework of local quantum physics. It is shown that these states have the Reeh-Schlieder property and that any primary vacuum state is also pure and weakly mixing. Moreover, the geodesic temperature of vacuum states has to be equal to the Gibbons-Hawking temperature and this fact is closely related to the existence of a discrete PCT-like symmetry. It is also shown that the global algebras of observables in vacuum sectors have the same structure as their counterparts in Minkowski space theories.