Cosmological histories from the Friedmann equation: The universe as a particle

TL;DR

This paper presents an intuitive reformulation of the Friedmann equation, enabling easier visualization of the universe's expansion histories as a particle rolling along a track, aiding understanding for students and researchers.

Contribution

It introduces an alternative, intuitive way to write the Friedmann equation, facilitating visualization of cosmological expansion histories without new physical results.

Findings

Reformulation of the Friedmann equation as a particle on a track

Visualization of different cosmological models including static and concordance models

Enhanced pedagogical approach for understanding universe expansion

Abstract

In this note, we discuss how possible expansion histories of the universe can be inferred in a simple way, for arbitrary energy contents. No new physical results are obtained, but the goal is rather to discuss an alternative way of writing the Friedmann equation in order to facilitate an intuitive understanding of the possible solutions; for students and researchers alike. As has been noted in passing by others, this specific form of the Friedmann equation allows us to view the universal expansion as a particle rolling along a frictionless track. Specific examples depicted include the current concordance cosmological model as well as a stable static universal model.