Conformal extension of the Bunch-Davies state across the de Sitter boundary

TL;DR

This paper explores the extension of the Bunch-Davies state across the de Sitter boundary using Vasy's asymptotic data, providing a formula for solution reconstruction and establishing the equivalence of the Hadamard and Bunch-Davies states.

Contribution

It introduces a conformal extension framework for the Bunch-Davies state and derives a reconstruction formula from asymptotic data in de Sitter space.

Findings

Hadamard state from conformal infinity matches Bunch-Davies state

Derived a short-hand formula for solution reconstruction

Established the equivalence of states across the boundary

Abstract

In the setting of the massive Klein-Gordon equation on de Sitter space, we discuss Vasy's asymptotic data at conformal infinity in terms of plane waves. In particular, we derive a short-hand formula for reconstructing solutions from their asymptotic data. Furthermore, we show that the natural Hadamard state induced from future (or past) conformal infinity coincides with the Bunch-Davies state.