Closed-Form Formulae for Inflation Correlators

TL;DR

This paper provides exact, closed-form formulas for inflation correlators involving massive particles, enabling precise calculations for cosmological collider models and future phenomenological research.

Contribution

It introduces a novel bootstrap method that yields exact expressions for inflation correlators with arbitrary parameters, avoiding infinite sums.

Findings

Derived closed-form expressions involving special functions

Applicable to a wide range of cosmological collider models

Facilitates future phenomenological studies and complex correlator construction

Abstract

We derive exact and closed-form expressions for a large class of two-point and three-point inflation correlators with the tree-level exchange of a single massive particle. The intermediate massive particle is allowed to have arbitrary mass, spin, chemical potential, and arbitrary nonderivative or derivative couplings to external inflaton modes. We also allow the coupling coefficients to have arbitrary complex power dependences on the conformal time. Our results feature closed-form expressions involving only familiar special functions and without any infinite sums. This is achieved by an improved bootstrap method with a suitable change of variables. Our results cover a wide range of cosmological collider models and can be directly used for future phenomenological studies. Our results can also be used as basic building blocks for constructing more complicated inflation correlators.