Constraining Cosmological Parameters by the Cosmic Inversion Method

We investigate the question of how tightly we can constrain the cosmologicalparameters by using the ``cosmic inversion'' method in which we directlyreconstruct the power spectrum of primordial curvature perturbations, $P(k)$,from the temperature and polarization spectra of the cosmic microwavebackground (CMB). In a previous paper, we suggested that it may be possible toconstrain the cosmological parameters using the fact that the reconstructed$P(k)$ does not depend on how many polarization data we incorporate in ourinversion procedure if and only if the correct values of the cosmologicalparameters are used. The advantage of this approach is that we need noassumption regarding the functional form of $P(k)$. In this paper, we estimatetypical errors in the determination of the cosmological parameters when ourmethod is applied to the PLANCK observation. We investigate constraints on $h$,$\Omega_b$, $\Omega_m$, and $\Omega_\Lambda$ through Monte Carlo simulations.Comment: 18 pages, 15 figures, version to be published in Prog. Theor. Phy