KLT-Like Behaviour of Inflationary Graviton Correlators

TL;DR

This work extends the spinor-helicity method to inflationary four-point graviton correlators and derives a KLT-like relation that mirrors flat-space gravity=gauge^2 structure only in part. By computing graviton exchange diagrams within the in-in formalism and dissecting the tensor contributions, the authors identify cross, square, and anomalous terms, highlighting additional de Sitter-specific pieces absent in flat spacetime. The analysis of collinear, squeezed, and collapsed limits clarifies how these terms behave and relate to lower-point correlators, providing insights into when and how a complete KLT-like factorization might emerge. The results point to rich, new structures in inflationary amplitudes and set the stage for future work on higher-point functions, other inflationary models, and symmetry-based constraints such as conformal invariance.

Abstract

We use the spinor helicity formalism to study KLT-like relations for the inflationary graviton four-point correlation function. New features are observed in this correlation function compared to the graviton scattering amplitude in flat spacetime. After obtaining the general momentum dependence, collinear, squeezed and collapsed limits are considered to further study the features of the correlation function, and the relation to the corresponding flat space scattering amplitude.

Figures (3)

• Figure 1: $\left\langle 1^{+}2^{+}3^{+}4^{+}\right\rangle _{s}$
• Figure 2: Momentum configurations in different limits
• Figure 3: Factorization of correlation function in collapsed limit into two correlation functions in squeezed limit