Subleading Chern-Simons soft factors in perturbative de Sitter

Chern-Simons perturbations introduce corrections to soft theorems for gauge theories at subleading $\mathcal{O}\left(\omega^0\right)$ order in soft momenta. We investigate these soft theorems in flat spacetime with perturbative $1/\ell^2$ de Sitter corrections. Following previous works, we define the perturbative scattering matrix in a compact region in the static patch of de Sitter. We show that Chern-Simons corrections do not mix with the $1/\ell^2$ de Sitter curvature corrections at subleading order $\mathcal{O}\left(\omega^0\right)$. Alternatively, one can say that the subleading Chern-Simons soft factors are insensitive to the de Sitter curvature at this order, indicating their topological nature at the level of amplitudes. This also suggests a universal behavior of these Chern-Simons soft factors.