Acoustic Peak Spacing, Cosmological Density, and Equation of State

Abstract

The spacing of the acoustic peaks in the cosmic microwave background radiation anisotropy multipole spectrum has been claimed to provide the value of the total cosmological density overtly, ``written on the sky.'' Through a semianalytic analysis of the cosmological evolution of the sound horizon and the physics of decoupling we address the robustness of the relation between the peak spacing and the cosmological density. In fact, the asymptotic distance and horizon scalings often used are not good approximations, and the individual densities and equations of state of different components do enter the problem. An observed spacing could be fit by models with different total densities. We investigate the different regions of density-equation of state parameter space and also provide accurate fitting formulas for the peak spacing as a function of matter density, total density, and additional component equation of state (e.g. cosmological constant or cosmic strings). Limits provided by peak spacing measurements on the number of neutrino species and the baryon-photon ratio are also addressed.