Project — Cosmology
The equation of state of dark energy — one parameter, w, whose value determines whether the universe expands forever or eventually collapses.
An upgrade to a Hubble expansion notebook — introducing a single new parameter, w, the equation of state of dark energy. When w = −1 you recover Einstein's cosmological constant: dark energy perfectly static, never changing. When w ≠ −1 dark energy is dynamic — it evolves across cosmic history, and the Friedmann equation changes with it.
That one exponent is what DESI is trying to measure across 40 million galaxies right now. The current data favours w ≠ −1 at 3–4 sigma — not yet a discovery, but enough to take seriously. If confirmed, Einstein's cosmological constant was wrong, dark energy evolves, and new physics is required.
View on GitHub →
Where w was hiding.
The original Hubble notebook computed the expansion rate as
np.sqrt(Ω_m·(1+z)³ + Ω_Λ).
That flat Ω_Λ term with no redshift dependence was w = −1 in disguise —
dark energy assumed constant without ever saying so.
The honest version replaces it with Ω_Λ·(1+z)^(3(1+w)).
At w = −1 the exponent is zero, the term is flat, and you recover the old notebook exactly.
At any other value, dark energy evolves with redshift and cosmic history changes.
What the plots show. Plot 1 — Hubble parameter H(z) for four values of w: all lines start at 1.0 today (same universe now), then diverge at high redshift. w = −0.5 (red) gives the highest H(z) — dark energy was stronger in the past, expansion was faster. w = −1.5 (blue) gives the lowest — dark energy weaker in the past, expansion slower. Plot 2 — comoving distance vs redshift — the lines flip. Fast past expansion means photons accumulated redshift quickly, so distances are shorter. Slow past expansion means photons travelled further to accumulate the same redshift. Same observed redshift; different physical distances. That gap is what DESI is measuring.
The Big Crunch possibility. If w drives dark energy negative over time, the universe eventually stops expanding, reverses, and collapses — the Big Crunch, potentially ~20 billion years out. For two decades the assumption was forever-expansion. DESI is the first survey with the statistical power to genuinely challenge that.
Next steps: load real DESI public data, fit w directly to BAO observations, and plot the percentage difference between w = −1 and the best-fit value. One parameter. One exponent. The entire fate of the universe.