Estimating acoustic peak positions in the cosmic microwave background anisotropy power spectrum

Abstract We present a simple formula for estimating the positions of acoustic peaks in the temperature power spectrum of the cosmic microwave background anisotropies: l = (n -1 /4)π/θ * , where l is the multipole moment in spherical harmonics, n is a positive integer, and θ * is the angular acoustic scale. Using published cosmological parameters, we calculate θ * = 1/96.35. Our estimates for the first seven acoustic peaks positions agree with the 2018 results of ESA's Planck mission within a 3% of relative error.