Features in the Primordial Spectrum from WMAP: A Wavelet Analysis

Precise measurements of the anisotropies in the cosmic microwave background enable us to do an accurate study on the form of the primordial power spectrum for a given set of cosmological parameters. In a previous paper (Shafieloo and Souradeep 2004), we implemented an improved (error sensitive) Richardson-Lucy deconvolution algorithm on the measured angular power spectrum from the first year of WMAP data to determine the primordial power spectrum assuming a concordance cosmological model. This recovered spectrum has a likelihood far better than a scale invariant, or, `best fit' scale free spectra (\Delta ln L = 25 w.r.t. Harrison Zeldovich, and, \Delta ln L = 11 w.r.t. power law with n_s=0.95). In this paper we use Discrete Wavelet Transform (DWT) to decompose the local features of the recovered spectrum individually to study their effect and significance on the recovered angular power spectrum and hence the likelihood. We show that besides the infra-red cut off at the horizon scale, the associated features of the primordial power spectrum around the horizon have a significant effect on improving the likelihood. The strong features are localised at the horizon scale.