Inflation Correlators with Multiple Massive Exchanges

TL;DR

This paper introduces a new method called family-tree decomposition that simplifies the calculation of complex inflationary correlators involving multiple massive exchanges, enabling analytical solutions in cosmological collider physics.

Contribution

It develops a simple rule using Mellin-Barnes representation to directly compute nested time integrals in inflationary correlators with multiple massive exchanges.

Findings

Derived analytical formulas for correlators with two massive exchanges.

Provided explicit examples demonstrating the rule's application.

Enabled straightforward computation of complex inflationary correlators.

Abstract

The most general tree-level boundary correlation functions of quantum fields in inflationary spacetime involve multiple exchanges of massive states in the bulk, which are technically difficult to compute due to the multi-layer nested time integrals in the Schwinger-Keldysh formalism. On the other hand, correlators with multiple massive exchanges are well motivated in cosmological collider physics, with the original quasi-single-field inflation model as a notable example. In this work, with the partial Mellin-Barnes representation, we derive a simple rule, called family-tree decomposition, for directly writing down analytical answers for arbitrary nested time integrals in terms of multi-variable hypergeometric series. We present the derivation of this rule together with many explicit examples. This result allows us to obtain analytical expressions for general tree-level inflation correlators with multiple massive exchanges. As an example, we present the full analytical results for a range of tree correlators with two massive exchanges.