Cosmological cutting rules for Bogoliubov initial states: any mass and spin

TL;DR

This paper extends cosmological cutting rules derived from the optical theorem to include fields of any mass and spin, broadening their applicability in cosmological perturbation theory.

Contribution

It generalizes Bogoliubov initial state cutting rules to encompass fields of arbitrary mass and spin, providing new propagator identities and discontinuity relations.

Findings

Generalized cutting rules to any mass and spin fields.

Defined modified propagator identities and discontinuities.

Addressed convergence issues of time integrals in the complex plane.

Abstract

The cosmological optical theorem and the cutting rules are well-known consequences of unitary time evolution in cosmology. The earlier works showed that assuming a Bunch-Davies initial state, one can derive equations relating a wavefunction diagram with a given number of internal lines to a sum of diagrams with fewer internal lines. In particular, it can relate a loop diagram to a sum of tree-level diagrams. Recently these relations were generalised to a set of excited initial states known as Bogoliubov states and they were shown to have non-trivial consequences for n-point contact and 4-point exchange diagrams. This analysis restricted the field content to massless and conformally coupled scalar fields. In this paper, we take the final step of generalising these "Bogoliubov cutting rules" to fields of any mass and spin. We define modified propagator identities and corresponding "Discontinuities" which automatically generalise the earlier relations to fields of any mass and spin. Finally, we discuss issues concerning the far past convergence of time integrals in the complex plane.