Differential equations for tree--level cosmological correlators with massive states

TL;DR

This paper develops mathematical tools to compute tree-level cosmological correlators involving massive states in de Sitter space, expressing results as series of polylogarithms using differential equations and cohomology techniques.

Contribution

It introduces a novel approach combining integration by parts, twisted cohomology, and differential equations to analyze massive correlators in cosmology.

Findings

Explicit power series expression for massive correlator

Representation of correlator terms as multiple polylogarithms

Method applicable to other cosmological correlator calculations

Abstract

We study mathematical aspects concerning two site tree-level cosmological correlators with massive internal and external states in a de Sitter universe. We employ integration by parts identities, (relative) twisted cohomology and the method of differential equations. We explicitly express the internally massive, externally conformally coupled correlator as a power series with respect to a small mass parameter, where the various terms in the series are given by multiple polylogarithms.