Massive Inflationary Amplitudes: New Representations and Degenerate Limits

TL;DR

This paper develops new analytical methods for calculating inflationary amplitudes involving massive particles, especially in degenerate kinematic limits, revealing simpler functional forms and new representations of the bispectrum.

Contribution

It introduces differential equations and solutions for tree graphs in degenerate kinematics, simplifying the analysis of inflationary correlators with massive exchanges.

Findings

Folded tree graphs involve functions of smaller transcendental weight.

Inflaton bispectrum with triple massive exchanges expressed via Kampé de Fériet and hypergeometric functions.

New analytical tools facilitate the study of degenerate limits in cosmological collider physics.

Abstract

The particle model building of cosmological collider physics often involves boost-breaking bilinear mixing between a heavy particle and the nearly massless inflaton mode. In cosmological correlators, such a mixing is obtained by taking a folded limit of a generic tree graph, which is a special case of degenerate kinematics. In this work, we continue our exploration of massive inflationary amplitudes with a focus on degenerate kinematics. With a suitable change of variables, we derive new differential equations and full analytical solutions for generic tree graphs, making it trivial to take the folded limit and partial-energy limit at a vertex. Our result shows that folded tree graphs generally involve functions of smaller transcendental weights than their nondegenerate counterparts. In particular, the inflaton bispectrum with triple massive exchanges can be expressed in terms of a trivariate Kamp\'e de F\'eriet function and simpler hypergeometric functions.