Reconstructing the primordial spectrum with CMB temperature and polarization

We develop a new method to reconstruct the power spectrum of primordial curvature perturbations P (k) by using both the temperature and polarization spectra of the cosmic microwave background (CMB). We test this method using several mock primordial spectra having nontrivial features including the one with an oscillatory component, and find that the spectrum can be reconstructed with a few percent accuracy by an iterative procedure in an ideal situation in which there is no observational error in the CMB data. In particular, although the previous ``cosmic inversion'' method, which used only the temperature fluctuations, suffered from large numerical errors around some specific values of k that correspond to nodes in a transfer function, these errors are found to disappear almost completely in the new method.