= Peebles primordial-plasma predictions
{c}
<P. J. E. Peebles> made the connection between microscopic processes and cosmological observables quantitative. His 1968 paper treated <cosmological recombination> as a kinetic problem. Capturing an <Electron> directly into the <hydrogen> <ground state> releases a <photon> that can ionize another atom. Net neutralization depends on escape of resonance radiation through <cosmological redshift> and on <two-photon spontaneous emission> from the $2s$ state. An equilibrium <Saha equation> alone does not give that history.<Recombination of the Primeval Plasma by P. J. E. Peebles>[Peebles, Recombination of the Primeval Plasma (1968), §§IIb–IId, pp.3–6]{ref}
This matters for an acoustic prediction because the <hydrogen ionization fraction> fixes the supply of free <Electrons> for <Thomson scattering>. In physical units the scattering rate per <photon> is $\Gamma_T=n_e\sigma_Tc$. The <cosmological visibility function> describes the distribution of last-scattering times. Thus <atomic physics> helps determine when the <photon-baryon acoustic oscillator> is read out, as well as how rapidly <tight coupling> fails.
In 1970 <P. J. E. Peebles> and <J. T. Yu> followed <adiabatic cosmological perturbations> by numerically integrating the <photon> collision equation through <cosmological recombination>. Their calculation connected acoustic evolution and dissipation to residual matter structure and microwave brightness fluctuations. It did not assume that a perfect <photon-baryon fluid> remained valid throughout last scattering. Their illustrative cosmological models and normalization were historical choices, rather than the present <Lambda-CDM model>; their predicted brightness variance versus angular resolution should not be relabelled as a modern measured $C_\ell$ spectrum.<Primeval Adiabatic Perturbation in an Expanding Universe by P. J. E. Peebles and J. T. Yu>[Peebles and Yu, Primeval Adiabatic Perturbation in an Expanding Universe (1970), pp.815–816; §VI, pp.829–833, Figs.4–9]{ref}
The continuing idea is a forward prediction: specify <initial conditions>, evolve the coupled matter and radiation, project onto the sky, and compare the result with an instrument's readout. <Coherent initial phases are needed for acoustic variance peaks> explains why a collection of oscillating modes does not automatically produce a peaked <power spectrum>. The <BOOMERANG acoustic-peak measurement> provides a later observational test of this physical programme.
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