This is a 2D companion to the "Supernova Light-Curve Time Dilation" 3D sim, built around a genuinely different mechanic: instead of watching two flashing supernovae, it reproduces the real 1998 discovery method (Perlmutter/Riess/Schmidt) — plot distance modulus μ against redshift z for many standard candles and see which cosmological model actually fits.
Comoving distance: D_C(z) = (c/H₀) ∫₀ᶻ dz′/E(z′)
E(z′) = √(Ωm(1+z′)³ + ΩΛ) (flat: Ωm+ΩΛ=1)
Luminosity distance: D_L(z) = (1+z)·D_C(z)
Distance modulus: μ(z) = 5·log₁₀(D_L / 1 Mpc) + 25
Tired light (naive): μ_tired(z) = 5·log₁₀(D_C / 1 Mpc) + 25 (no (1+z) dimming factors)
60 synthetic Type Ia supernovae are generated once from the true cosmology (Ωm=0.30, ΩΛ=0.70, H₀=70) plus realistic ±0.15 mag intrinsic scatter, then held fixed while you search for the model that explains them. Dragging Ωm down from 1.0 (a matter-only universe, the default assumption before 1998) toward ≈0.3 should make the running χ² drop sharply — reproducing, in miniature, the actual evidence for dark energy. The mini chart on the left sweeps χ² across all Ωm values at your current H₀ and marks where the true minimum sits.
The tired-light overlay reuses the same distance ladder but omits both (1+z) dimming factors — one from each photon losing energy, one from photons arriving less often — that a genuinely expanding metric predicts. Real light-curve-width surveys (Leibundgut 1996; Goldhaber 2001; Blondin 2008) ruled this out: at these redshifts it fits far worse (a much larger χ²) than expanding-space ΛCDM.
Click any data point in the diagram to see that supernova's own light curve — rest-frame vs. observed, stretched by the same (1+z) factor as its redshift, computed live rather than looked up from a table.