Cosmological Scattering Equations

TL;DR

This paper introduces a worldsheet formula for calculating tree-level correlation functions of a scalar field in de Sitter space, connecting cosmological models with scattering equations and flat space limits.

Contribution

It presents a novel worldsheet formula for cosmological correlators that generalizes scattering equations to de Sitter space and reduces to known flat space amplitudes.

Findings

Reproduces Witten diagram expansion at four and six points.

Supports on mass-deformed scattering equations in momentum space.

Reduces to CHY formula in flat space limit.

Abstract

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 $\phi^4$ 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.