Reconstruction of the primordial power spectrum using temperature and polarisation data from multiple experiments

We develop a method to reconstruct the primordial power spectrum, P(k), using both temperature and polarisation data from the joint analysis of a number of Cosmic Microwave Background (CMB) observations. The method is an extension of the Richardson-Lucy algorithm, first applied in this context by Shafieloo & Souradeep [1]. We show how the inclusion of polarisation measurements can decrease the uncertainty in the reconstructed power spectrum. In particular, the polarisation data can constrain oscillations in the spectrum more effectively than total intensity only measurements. We apply the estimator to a compilation of current CMB results. The reconstructed spectrum is consistent with the best-fit power spectrum although we find evidence for a 'dip' in the power on scales k approximate to 0.002 Mpc(-1). This feature appears to be associated with the WMAP power in the region 18 <= l <= 26 which is consistently below best-fit models. We also forecast the reconstruction for a simulated, Planck-like [2] survey including sample variance limited polarisation data.