We propose worldsheet formulae for correlators of the massive non-linear sigma model (NLSM), scalar Dirac-Born-Infeld (DBI), and special Galileon (sGal) theories in de Sitter momentum space in terms of the recently proposed cosmological scattering equations constructed from conformal generators in the future boundary. The four-point integrands are constructed from simple building blocks and we propose a generalised double copy which maps the NLSM correlator to the DBI and sGal correlators, including mass deformations and curvature corrections. Finally, we compute the soft limits of these correlators and find that they can also be written in terms of boundary conformal generators acting on contact diagrams.
Armstrong, C., Gomez, H., Jusinskas, R. L., Lipstein, A., & Mei, J. (2022). Effective field theories and cosmological scattering equations. Journal of High Energy Physics, 2022(8), Article 54. https://doi.org/10.1007/jhep08%282022%29054