A preferred ground state for the scalar field in de Sitter space

TL;DR

This paper explores the Sorkin-Johnston vacuum in de Sitter space, showing it aligns with the Euclidean state for certain fields and dimensions, and validates its properties through causal set simulations.

Contribution

It applies the SJ vacuum proposal to de Sitter space, deriving two-point functions and demonstrating its relation to known vacua across different dimensions and patches.

Findings

SJ vacuum coincides with Euclidean/Bunch-Davies state for heavy fields in even dimensions

Derived two-point functions for global and Poincaré patches in various dimensions

Causal set simulations confirm the continuum behavior of the SJ two-point function

Abstract

We investigate a recent proposal for a distinguished vacuum state of a free scalar quantum field in an arbitrarily curved spacetime, known as the Sorkin-Johnston (SJ) vacuum, by applying it to de Sitter space. We derive the associated two-point functions on both the global and Poincar\'e (cosmological) patches in general d+1 dimensions. In all cases where it is defined, the SJ vacuum belongs to the family of de Sitter invariant alpha-vacua. We obtain different states depending on the spacetime dimension, mass of the scalar field, and whether the state is evaluated on the global or Poincar\'e patch. We find that the SJ vacuum agrees with the Euclidean/Bunch-Davies state for heavy ("principal series") fields on the global patch in even spacetime dimensions. We also compute the SJ vacuum on a causal set corresponding to a causal diamond in 1+1 dimensional de Sitter space. Our simulations show that the mean of the SJ two-point function on the causal set agrees well with its expected continuum counterpart.