Triangular invariants, three-point functions and particle stability on the de Sitter universe

TL;DR

This paper investigates three-point functions on the de Sitter universe using geometric and analytic methods, deriving integrals and applying results to analyze scalar particle stability in this spacetime.

Contribution

It introduces a generalized star-triangle identity on the cone and de Sitter space, advancing the understanding of three-point functions and particle stability in curved spacetime.

Findings

Derived new integral identities for three-point functions

Connected geometric and analytic approaches in de Sitter space

Provided insights into scalar particle stability on the de Sitter universe

Abstract

We study a class of three-point functions on the de Sitter universe and on the asymptotic cone. A blending of geometrical ideas and analytic methods is used to compute some remarkable integrals, on the basis of a generalized star-triangle identity living on the cone and on the complex de Sitter manifold. We discuss an application of the general results to the study of the stability of scalar particles on the Sitter universe.