Unveiling the dynamics of the universe

TL;DR

This paper introduces two pedagogical methods for explaining solutions of Einstein's equations in cosmology, aiming to aid undergraduate teaching by simplifying complex concepts through effective potential and dynamical systems.

Contribution

It presents novel, simplified approaches for teaching Einstein's equations in cosmology, making complex solutions more accessible for students.

Findings

Effective potential approach clarifies universe dynamics.

Dynamical system method offers intuitive understanding.

Applied to various cosmological models for educational purposes.

Abstract

We present two methods for describing, from a pedagogical point of view, the solutions of Einstein's equations applied to a homogeneous and isotropic universe. In the first method, we define an effective gravitational potential of the universe, and the second method makes use of the fact that we can define a dynamical system of equations. The methods are applied to different cosmological models whose properties are discussed in turn. The ultimate intention is to provide simple examples to be revised in a first Cosmology course for undergraduates.