A diagrammatic approach to the spectrum of cosmological perturbations

TL;DR

This paper introduces a diagrammatic method to compute the spectrum of quantum fluctuations from inflation, simplifying the process with visual rules and algebraic steps, applicable after multiple background transitions.

Contribution

It presents a novel diagrammatic approach that allows for straightforward calculation of the inflationary perturbation spectrum across various background transitions.

Findings

Spectrum can be fully determined using the proposed graphical rules.

Method simplifies calculations of quantum fluctuations after multiple transitions.

Provides a systematic way to analyze inflationary perturbations.

Abstract

We compute the spectral distribution of the quantum fluctuations of the vacuum, amplified by inflation, after an arbitrary number of background transitions. Using a graphic representation of the process we find that the final spectrum can be completely determined trough a synthetic set of working rules, and a list of simple algebraic computations.