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

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 primarily due to cosmic variance. We assume the concordance Λ cold dark matter (ΛCDM) cosmology, utilize 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 = 4.52 × 10 −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 per cent (92 per cent), a dip at 0.001 < k < 0.003 Mpc −1 at 87.2 per cent (98 per cent) and a bump at 0.003 < k < 0.004 Mpc −1 at 90.3 per cent (55.5 per cent) 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 cut‐off of the estimated power spectrum to be about 2.5σ away from the n s = 0.97 model, while in the Bayesian analysis the model is about 1.5σ away from the estimated spectrum. (The σ values are different for the two different methods.)