Future Boundary Conditions in De Sitter Space

TL;DR

The paper proposes a novel Dirichlet-type future boundary condition for asymptotically de Sitter spacetimes with an eternal observatory, arguing that acausal boundary data do not manifest in observable measurements within the observatory and that the bulk geometry can be fixed from boundary data on the observatory. Through explicit linearized analyses in dS$_3$ and dS$_4$, it demonstrates that boundary demons in the causally disconnected region can destructively interfere with slow-falling modes to yield purely fast-falling behavior at $I^+$ for both scalars and gravitons. It then constructs bulk-to-bulk two-point functions under these boundary conditions and shows they are not realizable as Wightman functions in any dS-invariant vacuum, but they coincide with the double analytic continuation of AdS correlators and possess Hadamard short-distance structure with antipodal singularities. The work highlights a potential bridge between dS holography and AdS intuition, suggesting a path toward a holographic description of de Sitter physics via boundary data on the observatory and its $I^+$ boundary.

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.