The Friedmann equations: Newtonian mechanics vs. general relativity

Abstract

In this paper, we present a heuristic derivation of the perturbed Friedmann equations based on Newtonian mechanics, offering an intuitive perspective on these cosmological relations. This approach highlights the remarkable agreement between Newtonian and relativistic descriptions within certain limits, serving both as a conceptual – and even philosophical – bridge, and as a pedagogical tool to deepen understanding of the physical principles governing the evolution of the universe. By simplifying the complex mathematical framework of general relativity, this method provides an accessible means of exploring the dynamics of the universe. It underscores how classical mechanics, when applied carefully, can offer insights that align with relativistic results in the linear approximation. This connection not only enhances our understanding of the universality of physical laws but also reinforces the idea that relativistic phenomena can often be interpreted through familiar classical analogues.