Vacuum states and theSmatrix in dS/CFT

Abstract

We propose a definition of dS/CFT correlation functions by equating them to S-matrix elements for scattering particles from ${\mathcal{I}}^{-}$ to ${\mathcal{I}}^{+}.$ In planar coordinates, which cover half of de Sitter space, we consider instead the S vector obtained by specifying a fixed state on the horizon. We construct the one-parameter family of de Sitter invariant vacuum states for a massive scalar field in these coordinates, and show that the vacuum obtained by analytic continuation from the sphere has no particles on the past horizon. We use this formalism to provide evidence that the one-parameter family of vacua corresponds to marginal deformations of the CFT by computing a three-point function.