Reconstructing the primordial spectrum from WMAP data 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 conventional parameter-fitting methods, our method can potentially reproduce small features in 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 angular power spectrum with resolution up to Deltalsimilar or equal to5. Similar oscillatory features are found, however, in simulations using artificial cosmic microwave background data generated from a scale-invariant P( k) with random errors that mimic observation. In order to examine the statistical significance of the nontrivial features, including the oscillatory behaviors, therefore, we consider a method to quantify the deviation from scale invariance and apply it to the P( k) reconstructed from the WMAP data. We find that there are possible deviations from scale invariance around k similar or equal to 1.5 x 10(-2) and 2.6 x 10(-2) Mpc(-1).