Reconstructing the Primordial Spectrum fromWMAPData by the Cosmic Inversion Method

We reconstruct the primordial spectrum of the curvature perturbation, $P(k)$,from the observational data of the Wilkinson Microwave Anisotropy Probe (WMAP)by the cosmic inversion method developed recently. In contrast to conventionalparameter-fitting methods, our method can potentially reproduce small featuresin $P(k)$ with good accuracy. As a result, we obtain a complicated oscillatory$P(k)$. We confirm that this reconstructed $P(k)$ recovers the WMAP angularpower spectrum with resolution up to $\Delta \ell \simeq 5$. Similaroscillatory features are found, however, in simulations using artificial cosmicmicrowave background data generated from a scale-invariant $P(k)$ with randomerrors that mimic observation. In order to examine the statistical significanceof the nontrivial features, including the oscillatory behaviors, therefore, weconsider a method to quantify the deviation from scale-invariance and apply itto the $P(k)$ reconstructed from the WMAP data. We find that there are possibledeviations from scale-invariance around $k \simeq 1.5\times10^{-2}$ and$2.6\times10^{-2}{\rm Mpc}^{-1}$.Comment: 20 pages, 16 figures, version to be published in Ap