De Sitter corrections to supertranslation Ward identity and soft graviton theorem

TL;DR

This work analyzes tree-level scattering of massless scalars with soft graviton emission in a small-region de Sitter static patch, deriving perturbative corrections to the Weinberg soft graviton theorem in the large-$l$ (small cosmological constant) limit. By exploiting the link between soft theorems and asymptotic symmetries, the authors obtain perturbative corrections to the supertranslation Ward identity and show that the perturbative soft graviton theorem is recovered from the corresponding Ward identity for a flat-space choice of the supertranslation parameter. The results establish a universal structure for de Sitter corrections up to $\mathcal{O}(l^{-2})$ that reduces to flat-space results as $\delta = \omega l \to \infty$, and they clarify how de Sitter curvature feeds into both soft factors and charge definitions. The work contributes to the infrared understanding of gravity in near-flat de Sitter spaces and opens questions about deriving these charges from near-horizon asymptotic symmetries and about extensions to Cachazo-Strominger soft theorems.

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.

Figures (2)

• Figure 1: The Penrose diagram of the de Sitter space. The scattering processes are confined to the compact region depicted in gray inside the static patch.
• Figure 2: Scattering of massless scalars with momenta $p_i$, emitting a graviton with momentum $k$.