Fluctuations in the Cosmic Microwave Background I: Form Factors and their Calculation in Synchronous Gauge

Abstract

It is shown that the fluctuation in the temperature of the cosmic microwave background in any direction may be evaluated as an integral involving scalar and dipole form factors, which incorporate all relevant information about acoustic oscillations before the time of last scattering. A companion paper gives asymptotic expressions for the multipole coefficient $C_\ell$ in terms of these form factors. Explicit expressions are given here for the form factors in a simplified hydrodynamic model for the evolution of perturbations.Comment: 35 pages, no figures. Improved treatment of damping, including both Landau and Silk damping; inclusion of late-time effects; several references added; minor changes and corrections made. Accepted for publication in Phys. Rev. D1