Cosmic Inversion II --An iterative method for reproducing the primordial spectrum from the CMB data--

Pursuing the original idea proposed in our previous paper (Paper I), we improve the method to determine the shape of the initial curvature perturbation spectrum $P(k)$ from the CMB data. The thickness of the last scattering surface (LSS) and the integrated Sachs-Wolfe (ISW) effect, which we neglect in Paper I, are taken into account and an iterative method is newly developed. The new method can reproduce the primordial power spectra with a high accuracy, given the correct values of the cosmological parameters. Conversely, there appear spurious peaks and dips in the reconstructed power spectrum if we use the cosmological parameters slightly different from the true values, while there appear regions of negative $P(k)$ in some cases if we use substantially different values. In other words, the tacit assumption that the cosmological parameters can be determined for an assumed initial spectrum is verified by our reconstruction method. In addition, it could be a new tool to constrain the cosmological parameters without recourse to models of the primordial power spectra.