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

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 Poincaré (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 α-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 Poincaré 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.

Waves in the Witten Bubble of Nothing and the Hawking Wormhole

“…A fundamental result of this paper is the explicit expression of the solutions established in part 5, that shows the dynamics of the fields is mainly governed by that of the scalar fields in dS 3 : the waves propagating on the Witten space-time are represented by a Kaluza-Klein tower, i.e. a sum of waves on dS 3 . We perform the complete spectral analysis of the self-adjoint operator L. If Φ(λ, .)…”

“…We shall see that ρ = R does not locate a boundary, but a surface of minimal area, the bubble of nothing, that is just the 3-dimensional De Sitter space-time dS 3 : ds…”

“…Therefore M is foliated by the two-parameter family of submanifolds defined by x = Cst., ψ = Cst., of De Sitter spacetimes dS 3 . In this section, we establish several analytic expressions of the scalar field as a superposition of Klein-Gordon waves on the 2+1-dimensional De Sitter spacetime…”

“…that is just the Klein-Gordon equation with mass √ λ = √ λ k on the De Sitter space-time dS 3 , and the energy of u is the sum of the energies of u k : (V.11)…”

“…In particular the set B = {| ξ ξ ξ | 2 −τ 2 = R 2 } is not a boundary but a surface of minimal area isometric with the 2+1-dimensional de Sitter space dS 3 …”