Curvature Dependence of Peaks in the Cosmic Microwave Background Distribution

Abstract

The widely cited formula $\ell_1\simeq 200 Ω_0^{-1/2}$ 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 $Ω_M$ fixed at 0.3, the position of any Doppler peak varies as $Ω_0^{-1.58}$ near $Ω_0=1$.