Cosmological Scattering Equations

We propose a worldsheet formula for tree-level correlation functions describing a scalar field with arbitrary mass and quartic self-interaction in de Sitter space, which is a simple model for inflationary cosmology. The correlation functions are located on the future boundary of the spacetime and are Fourier-transformed to momentum space. Our formula is supported on mass-deformed scattering equations involving conformal generators in momentum space and reduces to the CHY formula for ${\varphi }^4$ amplitudes in the flat space limit. Using the global residue theorem, we verify that it reproduces the Witten diagram expansion at four and six points, and sketch the extension to $n$ points.