de Sitter corrections to supertranslation Ward identity and soft graviton theorem

TL;DR

This paper investigates how de Sitter space modifies the soft graviton theorem and supertranslation Ward identity, revealing perturbative corrections in the small cosmological constant limit and connecting asymptotic symmetries with scattering amplitudes.

Contribution

It derives the first perturbative corrections to the Weinberg soft graviton theorem and supertranslation Ward identity in de Sitter space, extending flat space results.

Findings

Perturbative corrections to the soft graviton theorem in de Sitter space.

Modified supertranslation Ward identity consistent with de Sitter geometry.

Reduction of the Ward identity to flat space soft theorem in the small cosmological constant limit.

Abstract

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.