Perturbative corrections to soft photon theorems for massless scalar QED in de Sitter spacetime
Pratik Chattopadhyay
TL;DR
This work extends soft photon theorems to massless scalar QED in $d$-dimensional de Sitter space by deriving massless scalar modes and a corresponding propagator in a small-curvature expansion, then formulating a curved-space LSZ reduction for photon emission. Using a tree-level scattering picture localized to the static patch and a double scaling limit with $\delta=\omega\ell$, the authors compute perturbative corrections to the leading and sub-leading soft-photon factors, revealing curvature-induced terms proportional to $(d-4)$ and to $\lambda=(d-2)(d-4)/4$ that modify the flat-space coefficients. They demonstrate that these corrections reduce to the flat-space results as $\ell\to\infty$ and that the massless limit agrees with prior analyses in the massive-scalar case, suggesting a universal structure for soft factors across scalar masses. The results illuminate how de Sitter geometry perturbs infrared behavior and point toward connections with asymptotic symmetries in the static patch and potential loop-level extensions.
Abstract
The perturbative corrections to soft photon theorems with massive scalars in de Sitter spacetime were computed in [JHEP10(2023)055]. However, the massless limit of the scalar modes is ill-defined in their work. It therefore is ambiguous to take the massless limit of the soft factors. In this paper, we derive the massless scalar modes in $d$-dimensional de Sitter spacetime and use it to compute the perturbative corrections to the leading and sub-leading soft photon theorems. Our framework corresponds to tree level scattering of massless scalars followed by an emission of a soft photon in a compact region of the static patch of de Sitter. We show that our results are consistent with [JHEP10(2023)055] in the massless limit and we comment on the universality of our results.