On the holographic domain-wall/cosmology correspondence and scalar one-point functions

We review the construction of holography for cosmologies with an emphasis on asymptotically de Sitter cosmologies. We do this by composition of the AdS/CFT correspondence and domain-wall/cosmology (DW/C) correspondence with the novel added benefit of keeping track of the DW/C marker $\eta$. This allows us to build explicitly the holographic dual of the DW/C correspondence. We then test this framework on a toy model: the GPPZ flow. We find the scalar one-point function for this flow to be invariant under the domain-wall/cosmology correspondence. Moreover, our construction seems to agree with previous literature on holography for cosmologies.