Curvature dependence of peaks in the cosmic microwave background distribution

Abstract

The widely cited formula ${l}_{1}\ensuremath{\simeq}200{\ensuremath{\Omega}}_{0}^{\ensuremath{-}1/2}$ 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 ${\ensuremath{\Omega}}_{M}$ fixed at 0.3, the position of any Doppler peak varies as ${\ensuremath{\Omega}}_{0}^{\ensuremath{-}1.58}$ near ${\ensuremath{\Omega}}_{0}=1.$