Numerical implementation of flat FLRW models of cosmic expansion with Planck 2018 cosmological parameters

TL;DR

This paper provides a simple Python-based numerical implementation of the Friedmann equations to model the Universe's expansion in flat FLRW cosmologies, incorporating various dark energy models and serving as an educational tool.

Contribution

It introduces an explicit, modular Python code for solving the Friedmann equations with different dark energy parameters, suitable for teaching and exploring cosmological models.

Findings

Reproduces standard cosmological expansion regimes

Allows exploration of different dark energy equations of state

Provides an accessible educational simulation tool

Abstract

We present an explicit numerical implementation of the Friedmann equations to model the expansion of the Universe in spatially flat, homogeneous and isotropic Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmologies. Using cosmological parameters from the Planck 2018 results for the concordance LCDM model, we compute the evolution of the scale factor a(t) by integrating the Friedmann acceleration equation together with the continuity equation for a perfect fluid with barotropic equation of state p = w*rho. The model includes radiation, non-relativistic matter, and a dark-energy component with constant equation-of-state parameter w. An explicit Euler scheme implemented in Python is used to evolve a(t) into the past and the future, allowing exploration of the qualitative behavior of the expansion for different values of w, including the LCDM case (w = -1), phantom energy (w < -1), and values associated with domain walls and cosmic strings. The simulations qualitatively reproduce the standard radiation-, matter-, and dark-energy-dominated expansion regimes. The code is simple and modular, and is intended as a computational and pedagogical tool for undergraduate and graduate cosmology courses.