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

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.