Fast cosmological parameter estimation from microwave background temperature and polarization power spectra

We improve the algorithm of Kosowsky, Milosavljevic, and Jimenez for computing power spectra of the cosmic microwave background. The present algorithm computes not only the temperature power spectrum but also the E- and B-mode polarization and the temperature-polarization cross power spectra, providing the accuracy required for current cosmological parameter estimation. Both unlensed and lensed (with non-linear evolution) power spectra are provided up to $\mathcal{l}=3000\mathrm{}$ for temperature and polarization signals. We refine the optimum set of cosmological parameters for computing the power spectra as perturbations around a fiducial model, leading to an accuracy better than 0.5% for the temperature power spectrum throughout the region of parameter space within the Wilkinson Microwave Anisotropic Probe’s first-year $3\sigma$ confidence region. This accuracy is comparable to the difference between the widely used CMBFAST code of Seljak and Zaldarriaga and Boltzmann codes. Our algorithm (CMBWARP) makes possible a full exploration of the likelihood region for eight cosmological parameters in about one hour on a laptop computer. We provide the code to compute power spectra as well as the Markov chain Monte Carlo algorithm for cosmological parameters estimation at http://www.physics.upenn.edu/∼raulj/CMBwarp.