Future Boundary Conditions in De Sitter Space

TL;DR

This paper explores a novel boundary condition in de Sitter space that imposes flatness everywhere except at a point, leading to causality violations that are unobservable, and connects these conditions to anti-de Sitter space correlations.

Contribution

It introduces an unconventional future boundary condition in de Sitter space and analyzes its implications, linking it to anti-de Sitter space correlations.

Findings

Bulk two-point functions under this boundary condition are not realizable in de Sitter invariant vacua.

These functions match those obtained via double analytic continuation from anti-de Sitter space.

The boundary condition results in causality violations that are unobservable within the spacetime.

Abstract

We consider asymptotically future de Sitter spacetimes endowed with an eternal observatory. In the conventional descriptions, the conformal metric at the future boundary I^+ is deformed by the flux of gravitational radiation. We however impose an unconventional future "Dirichlet" boundary condition requiring that the conformal metric is flat everywhere except at the conformal point where the observatory arrives at I^+. This boundary condition violates conventional causality, but we argue the causality violations cannot be detected by any experiment in the observatory. We show that the bulk-to-bulk two-point functions obeying this future boundary condition are not realizable as operator correlation functions in any de Sitter invariant vacuum, but they do agree with those obtained by double analytic continuation from anti-de Sitter space.