Non-parametric reconstruction of the primordial power spectrum at horizon scales from WMAP data

Domenico Tocchini-Valentini, Yehuda Hoffman, Joseph Silk

Published 2005-09-16, updated 2006-01-17Version 2

We extend to large scales a method proposed in previous work that reconstructs non-parametrically the primordial power spectrum from cosmic microwave background data at high resolution. The improvement is necessary to account for the non-gaussianity of the Wilkinson Microwave Anisotropy Probe (WMAP) likelihood due primarily to cosmic variance. We assume the concordance LambdaCDM cosmology, utilise a smoothing prior and perform Monte Carlo simulations around an initial power spectrum that is scale-free and with spectral index n_s=0.97, very close to the concordance spectrum. The horizon scale for the model we are considering corresponds to the wavenumber k_h=4.52X10^{-4} Mpc^{-1}. We find some evidence for the presence of features and we quantify the probabilities of exceeding the observed deviations in WMAP data with respect to the fiducial models. We detect the following marginal departures from a scale-free (spectral index n_s=0.97) initial spectrum: a cut-off at 0.0001<k<0.001 Mpc^{-1} at 79.5% (92%), a dip at 0.001<k<0.003 Mpc^{-1} at 87.2% (98%) and a bump at 0.003<k<0.004 Mpc^{-1} at 90.3% (55.5%) confidence level. These frequentist confidence levels are calculated by integrating over the distribution of the Monte Carlo reconstructions built around the fiducial models. The frequentist analysis finds the low k cutoff of the estimated power spectrum to be about 2.5 sigma away from the n_s=0.97 model, while in the Bayesian analysis the model is about 1.5 sigma away from the estimated spectrum. (The sigma's are different for the two different methods.)