Curvature dependence of peaks in the cosmic microwave background distribution

The widely cited formula $\ell_1\simeq 200 \Omega_0^{-1/2}$ for the multipole number of the first Doppler peak is not even a crude approximation in the case of greatest current interest, in which the cosmic mass density is less than the vacuum energy density. For instance, with $\Omega_M$ fixed at 0.3, the position of any Doppler peak varies as $\Omega_0^{-1.58}$ near $\Omega_0=1$.