Cosmological Scattering Equations

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 ${\varphi }^4$ 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.

arXiv commentv3. minor changes, accepted to PRL

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• Selected Topics in Analytic Conformal Bootstrap: A Guided Journey
• Helical Inflation Correlators: Partial Mellin-Barnes and Bootstrap Equations
• Bootstrapping Large Graviton non-Gaussianities
• Bootstrapping One-Loop Inflation Correlators with the Spectral Decomposition
• From Amplitudes to Contact Cosmological Correlators
• Closed-Form Formulae for Inflation Correlators
• Cosmological Scattering Equations at Tree-level and One-loop
• Analytical evaluation of cosmological correlation functions
• Towards Color-Kinematics Duality in Generic Spacetimes
• Graviton scattering in self-dual radiative space-times
• New recursions for tree-level correlators in (Anti) de Sitter space
• A handbook of holographic 4-point functions
• Continuous Spectrum on Cosmological Collider
• On Holography in General Background and the Boundary Effective Action from AdS to dS
• Effective Field Theories and Cosmological Scattering Equations
• Enhanced Soft Limits in de Sitter Space
• A Scattering Amplitude for Massive Particles in AdS
• Soft theorems for boosts and other time symmetries
• Flat-space structure of gluon and graviton in AdS