Expansion of the Universe

Interactive visualization of the Friedmann equation for introductory astrophysics.

Overview

expansion_universe.py solves the Friedmann equation and displays two animated panels:

Left panel	Right panel
Scale factor a(t) vs cosmic time	Comoving galaxy grid expanding in physical coordinates

A red dot sweeps along the a(t) curve while galaxies (arranged in concentric rings around a gold central observer) expand or contract in real time.

Physics

The script solves the Friedmann equation as a second-order ODE in units where H_0 = 1:

(adot)^2 = Omega_r / a^2 + Omega_m / a + Omega_k + Omega_Lambda * a^2
  addot  = -Omega_r / a^3 - Omega_m / (2 a^2) + Omega_Lambda * a

where Omega_k = 1 - Omega_m - Omega_r - Omega_Lambda determines the spatial curvature.

Controls

• Three sliders: Omega_m (matter), Omega_r (radiation), Omega_Lambda (dark energy)
• Four preset buttons: LCDM, Einstein-de Sitter, Open, Closed
• Click on either panel to pause/resume the animation
• Info box displays Omega_k, universe classification (Open/Flat/Closed), and age in units of H_0^{-1}

Presets

Preset	Omega_m	Omega_r	Omega_Lambda	Behavior
LCDM	0.31	0.00	0.69	Accelerating expansion (our universe)
Einstein-de Sitter	1.00	0.00	0.00	Decelerating, flat, matter-only
Open	0.30	0.00	0.00	Expands forever, negatively curved
Closed	4.00	0.00	0.00	Expands then recollapses (Big Crunch)

Requirements

• Python 3.9+
• numpy, scipy, matplotlib

pip install numpy scipy matplotlib

Running

python expansion_universe.py

Testing

pip install pytest pytest-cov
pytest test_friedmann_physics.py test_visualization.py -v

50 tests validate physics correctness (analytic cosmological solutions, Friedmann constraint, power-law exponents) and visualization integrity (figure structure, sliders, buttons, galaxy grid geometry, animation scaling).

CI runs automatically via GitHub Actions on push and pull request.

Author

R. T. Fisher