de Sitter corrections to supertranslation Ward identity and soft graviton theorem

We study the tree-level scattering of massless scalars followed by an emission of a soft graviton in the small compact region inside the static patch in de Sitter space. We derive in the small cosmological constant limit the perturbative corrections to the Weinberg soft graviton theorem. Exploiting the remarkable relationship between asymptotic symmetries and soft theorems in flat space, we derive perturbative corrections to the supertranslation Ward identity. We further show that the derived supertranslation Ward identity reduces to the perturbative soft graviton theorem for the same choice of the supertranslation parameter as in flat space.