= Sound-horizon angle in an open matter universe
{title2=$\theta_s\simeq\sqrt{\Omega_m a_*/3}$}
For last scattering well inside <matter domination>, $c_s=c/\sqrt3$ gives physical sound radius $R_s=2ca_*^{3/2}/(\sqrt3H_0\sqrt{\Omega_m})$. Neglecting the early <conformal time> in the observer distance, an open dust cosmology has transverse comoving last-scattering distance $r_*=2c/(H_0\Omega_m)$. Thus $\theta_s=R_s/(a_*r_*)=\sqrt{\Omega_m a_*/3}$ and $\ell\sim\pi/\theta_s$. Radiation, baryon sound-speed evolution and acoustic phase shifts refine this estimate.
// Target: cosmology.bigb
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