Perturbative soft graviton theorems in de Sitter spacetime
Divyesh N. Solanki, Pratik Chattopadhyay, Srijit Bhattacharjee
TL;DR
This work investigates soft graviton theorems in a de Sitter background by performing a perturbative expansion in the small cosmological constant (large $l$) and focusing on tree-level processes in the static patch. The authors develop a curved-space LSZ formalism, solve for scalar and graviton modes up to $\mathcal{O}(l^{-2})$, and compute the $n\to n+1$ graviton-scalar amplitudes in the soft limit, identifying leading, subleading, and sub-subleading corrections to the flat-space Weinberg soft factor. They find that the leading correction is non-universal and mode-dependent, while the subleading and sub-subleading corrections are universal, gauge-invariant, and can be written in terms of angular-momentum generators $J^{\beta\gamma}$ and derivatives with respect to hard momenta. A careful analysis including a diagram with a soft graviton attached to an internal line shows extra contributions that survive at subleading order, reinforcing the structure controlled by symmetry-like operators, and the results establish a curved-space IR extension of the flat-space soft graviton theorem with potential connections to asymptotic charges and memory in de Sitter settings.
Abstract
We consider soft graviton scattering for a theory where Einstein's gravity is minimally coupled to a scalar field in the presence of a cosmological constant, i.e. in a background de Sitter space. Employing a perturbative expansion in a small cosmological constant, we compute leading, subleading and sub-subleading corrections to Weinberg's soft graviton amplitude for the tree-level scatterings in the static patch of de Sitter space. We observe similar universal features of the soft graviton amplitude as found in [JHEP10(2023)055] for the soft photons.