Rapid Calculation of Theoretical CMB Angular Power Spectra

Abstract

We have developed a fast method for predicting the angular power spectrum, C_l, of the cosmic microwave background given cosmological parameters and a primordial power spectrum of perturbations. After pre--computing the radiation temperature and gravitational potential transfer functions over a small sub--space of the total model parameter space, the rest of the model space (six or more cosmological parameters and arbitrarily many primordial power spectrum parameters) is reached via rapid analytic and semi--analytic approximations which are highly accurate on all angular scales for which linear perturbation theory applies. A single power spectrum can be calculated in ~ 1 second on a desktop computer. We discuss applications to cosmological parameter estimation.

Version accepted for publication in ApJ (includes new section on polarization and tensor spectra). Fortran code for calculation of C_l and Likelihood(C_l | current data) is available with documentation at http://www.physics.ucdavis.edu/Cosmology/dash/