All-sky reconstruction of the primordial scalar potential from WMAP temperature data

Abstract

An essential quantity required to understand the physics of the early Universe, in particular the inflationary epoch, is the primordial scalar potential $Φ$ and its statistics. We present for the first time an all-sky reconstruction of $Φ$ with corresponding $1σ$-uncertainty from WMAP's cosmic microwave background (CMB) temperature data -- a map of the very early Universe right after the inflationary epoch. This has been achieved by applying a Bayesian inference method that separates the whole inverse problem of the reconstruction into many independent ones, each of them solved by an optimal linear filter (Wiener filter). In this way, the three-dimensional potential $Φ$ gets reconstructed slice by slice resulting in a thick shell of nested spheres around the comoving distance to the last scattering surface. Each slice represents the primordial scalar potential $Φ$ projected onto a sphere with corresponding distance. Furthermore, we present an advanced method for inferring $Φ$ and its power spectrum simultaneously from data, but argue that applying it requires polarization data with high signal-to-noise levels not available yet. Future CMB data should improve results significantly, as polarization data will fill the present $\ell-$blind gaps of the reconstruction.