Adiabatic acoustic-peak spacing
= Adiabatic acoustic-peak spacing
{title2=$\ell_n\simeq n\pi\chi_*/r_s(\eta_*)$}
<Adiabatic initial conditions> select coherent cosine phases of the <photon-baryon acoustic oscillator>. Its extrema at last scattering satisfy $kr_s\simeq n\pi$ and project to $\ell\simeq k\chi_*$. Thus $\ell_n\simeq n\pi\chi_*/r_s(\eta_*)$, with comoving <sound horizon> $r_s=\int d\eta/\sqrt{3(1+R)}$. Projection, driving and finite last-scattering width modify the exact peak locations.