Cosmological Scattering Equations at Tree-level and One-loop

Understand

We recently proposed a formula for tree-level $n$-point correlators of massive $\phi^4$ theory in de Sitter momentum space which consists of an integral over $n$ punctures on the Riemann sphere and differential operators in the future boundary dubbed the cosmological scattering equations.

• This formula was explicitly checked up to six points via a map to Witten diagrams using the global residue theorem.
• In this work we provide further details of these calculations and present an alternative formulation based on a double cover of the Riemann sphere.
• This framework can be used to derive simple graphical rules for evaluating the integrals more efficiently.