Baryon Acoustic Oscillations — 2D Sound Horizon

This 2D companion simulation independently integrates the same real cosmology as the 3D Baryon Acoustic Oscillation model — the Friedmann equation for the scale factor a(t), the radiation-pressure sound speed c_s(a), and the comoving sound-horizon integral r_s(t) = ∫ c_s/a dt — but steps them forward directly in cosmic time rather than reading a precomputed table, so the running horizon value on screen is the literal partial integral at each instant. A circular wavefront grows outward from a point seed in the photon-baryon plasma, slowing as the baryon load R(t) grows, then freezes the moment recombination decouples photons from baryons at z ≈ 1090 — reproducing the ≈144 Mpc comoving Baryon Acoustic Oscillation scale. Live plots of c_s(t), R(t) and the running r_s(t) integral track the physics alongside the animation.