CMB Acoustic Oscillator: Baryon-Photon Plasma Waveform (2D)

The 3D version plots the finished CMB power spectrum from a static fitting formula. This 2D companion goes one level deeper: it numerically evolves the actual tight-coupling oscillator equation Θ(η)+Ψ = [Θ(0)+(1+R)Ψ]·cos(k·r_s(η)) for one chosen multipole ℓ, animating a single acoustic mode ringing through conformal time from the Big Bang to recombination — a breathing plasma strip shows the photon-baryon fluid compressing (red) and rarefying (blue) in real time, the waveform panel traces Θ(η)+Ψ as it oscillates, and the spectrum panel on the right builds up point by point as you scrub or auto-sweep ℓ, so the connection between "one ringing mode" and "one point on the power spectrum" is visible instead of assumed. All four cosmological parameters drive the same underlying physics as the 3D original: baryon density Ω_b shifts the oscillator's zero-point (visibly boosting compression over rarefaction), dark matter Ω_c deepens the driving potential well, and H₀ rescales the angular-diameter distance that maps ℓ to physical wavenumber k — verified numerically against the same first/second-peak formula ℓ_n = nπD_A/r_s the 3D version reports.