Before recombination the universe is an opaque, nearly-uniform plasma of photons, electrons and baryons (protons + He nuclei), tightly coupled by Thomson scattering. A primordial density perturbation launches a spherical sound wave in this photon-baryon fluid — the same physics as a sound wave in air, but the "gas" is relativistic radiation pressure resisting gravitational collapse.
Friedmann eq: H(a) = H0·√(Ω_r/a⁴ + Ω_m/a³)
Sound speed: c_s(a) = c / √(3·(1 + R_b(a))), R_b(a) = (3Ω_b)/(4Ω_γ)·a
Sound horizon: r_s(a) = ∫₀ᵃ c_s(a′) / (a′² H(a′)) da′ (comoving)
R_b is the baryon-to-photon momentum-density ratio — more baryons weigh the fluid down and slow the wave, exactly like a denser medium slows a sound wave in air. At recombination (z ≈ 1090, when the plasma has cooled enough for electrons to bind to nuclei) the photons decouple: Thomson scattering stops, the fluid stops behaving as a pressure-supported gas, and the sound wave freezes at a fixed comoving radius r_s ≈ 144 Mpc — the sound horizon at last scattering.
That frozen shell leaves a permanent, faint overdensity of baryons at a fixed comoving distance from every initial seed. Billions of years later, galaxies preferentially form where matter was already denser — so galaxy pairs separated by ≈144 Mpc are slightly more common than any other separation. This is the Baryon Acoustic Oscillation (BAO) "standard ruler," independently measured in the CMB's angular power spectrum and in the large-scale clustering of galaxies (SDSS, DES, eBOSS), and used to map the expansion history of the universe.
Once decoupled, the photons themselves keep travelling — not at the sound speed, but at the full speed of light c — so the outer "photon shell" in this simulation (the light you would see today as the CMB) pulls steadily ahead of the frozen baryon shell, tracing the comoving particle horizon ∫ c/(a′² H(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; lowering it does the opposite — a real, testable prediction later confirmed by Planck.
- This model fixes the decoupling redshift and ignores helium and neutrino decoupling for tractability — the qualitative mechanism and the ≈144 Mpc scale are physically accurate.