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 reproduce small features in $P(k)$ with good accuracy. To take the observational errors into account, we perform Monte Carlo simulations with fixed values of the cosmological parameters. As a result, we obtain an oscillatory $P(k)$. We confirm that thus reconstructed $P(k)$ recovers the WMAP angular power spectrum with the resolution of $\Delta \ell \simeq 5$. However, a very similar oscillatory behavior is found in test calculations using artificial CMB data generated from a scale-invariant primordial spectrum by adding random numbers which mimic the observational errors. Thus, the oscillation found in $P(k)$ for the WMAP data may be simply caused by the dispersion of data