Cosmological cutting rules for Bogoliubov initial states

TL;DR

This paper extends the cosmological optical theorem and cutting rules from the Bunch-Davies initial state to more general Bogoliubov initial states, providing new methods to compute wavefunction coefficients in cosmology.

Contribution

It generalizes the cosmological optical theorem to Bogoliubov initial states, including parity-odd interactions, and offers a prescription for calculating wavefunction coefficients from Bunch-Davies states.

Findings

Confirmed the generalized cutting rules in explicit examples.

Preserved scale invariance by adiabatically turning on interactions.

Provided a method to compute Bogoliubov wavefunction coefficients from Bunch-Davies coefficients.

Abstract

The field theoretic wavefunction in cosmological spacetimes has received much attention as a fundamental object underlying the generation of primordial perturbations in our universe. Assuming an initial Bunch-Davies state, unitary time evolution implies an infinite set of cutting rules for the wavefunction to all orders in perturbation theory, collectively known as the cosmological optical theorem. In this work, we generalise these results to the case of Bogoliubov initial states, accounting for both parity-even and parity-odd interactions. We confirm our findings in a few explicit examples, assuming IR-finite interactions. In these examples, we preserve scale invariance by adiabatically turning on interactions in the infinite past rather than imposing a Bogoliubov state at some finite initial time. Finally, we give a prescription for computing Bogoliubov wavefunction coefficients from the corresponding Bunch-Davies coefficients for both n-point contact and four-point exchange diagrams.