This is a 2D, independently time-integrated version of the Baryon Acoustic Oscillation mechanism: before recombination the universe is an opaque plasma of photons and baryons, tightly coupled by Thomson scattering. A primordial density perturbation launches a circular sound wave in this photon-baryon fluid — real acoustic physics, driven by radiation pressure rather than gas pressure.
Friedmann: H(a) = H0·√(Ω_r/a⁴ + Ω_m/a³)
Baryon load: R(a) = (3Ω_b)/(4Ω_γ)·a
Sound speed: c_s(a) = c / √(3·(1 + R(a)))
Cosmic time: da/dt = a·H(a) (integrated directly, step by step)
Sound horizon: r_s(t) = ∫₀ᵗ c_s(t′)/a(t′) dt′ (comoving, accumulated live)
Unlike a simple lookup, this simulation steps a(t) forward through the actual Friedmann equation and accumulates the comoving sound-horizon integral in real time as the wave expands — the running value shown is the literal partial integral up to the current cosmic time, not a precomputed constant. R(a) — the baryon-to-photon momentum-density ratio — grows as the universe expands, weighing the fluid down and slowing c_s, exactly like a denser medium slows sound in air.
At recombination (z ≈ 1090) the photons decouple, Thomson scattering stops, and the integral freezes at the comoving sound horizon r_s ≈ 144 Mpc. That frozen ring leaves a faint permanent overdensity of baryons at a fixed comoving distance from the seed — later giving galaxy pairs a very slight excess probability of ≈144 Mpc separation, the BAO "standard ruler" measured in the CMB and galaxy surveys (SDSS, DES, eBOSS).
After decoupling, photons keep travelling at the full speed of light c (not c_s), so the outer "photon shell" — the light you'd see today as the CMB — pulls steadily ahead of the frozen baryon ring, tracing the comoving particle horizon ∫c/(a′²H(a′))da′.
- Redshift slider — scrubs cosmic time from deep radiation domination (z ≈ 2000) through recombination (z ≈ 1090, marked) to z ≈ 19.
- Ωb slider — raising the baryon density slows c_s and shortens the final sound horizon — a real, testable prediction later confirmed by Planck.
- The three live plots track c_s(t), the baryon load R(t), and the running r_s integral as the wave expands.
- Simplifications: fixed decoupling redshift, no helium or neutrino decoupling physics, single-fluid sound speed — the mechanism and the ≈144 Mpc scale are physically accurate to the standard order of magnitude.