A LINE-OF-SIGHT INTEGRATION APPROACH TO COSMIC MICROWAVE BACKGROUND ANISOTROPIES

We present a new method for calculating linear cosmic microwave backgr ound (CMB) anisotropy spectra based on integration over sources along the photon past light cone. In this approach the temperature anisotrop y is written as a time integral over the product of a geometrical term and a source term. The geometrical term is given by radial eigenfunct ions, which do not depend on the particular cosmological model. The so urce term can be expressed in terms of photon, baryon, and metric pert urbations, all of which can be calculated using a small number of diff erential equations. This split clearly separates the dynamical from th e geometrical effects on the CMB anisotropies. More importantly, it al lows us to significantly reduce the computational time compared to sta ndard methods. This is achieved because the source term, which depends on the model and is generally the most time-consuming part of calcula tion, is a slowly varying function of wavelength and needs to be evalu ated only in a small number of points. The geometrical term, which osc illates much more rapidly than the source term, does not depend on the particular model and can be precomputed in advance. Standard methods that do not separate the two terms require much higher number of evalu ations. The new method leads to about 2 orders of magnitude reduction in CPU time when compared to standard methods and typically requires a few minutes on a workstation for a single model. The method should be especially useful for accurate determinations of cosmological paramet ers from CMB anisotropy and polarization measurements that will become possible with the next generation of experiments. A program implement ing this method can be obtained from the authors.