All-sky reconstruction of the primordial scalar potential from WMAP
  temperature data
  An essential quantity required to understand the physics of the early
Universe, in particular the inflationary epoch, is the primordial scalar
potential $\Phi$ and its statistics. We present for the first time an all-sky
reconstruction of $\Phi$ with corresponding $1\sigma$-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
$\Phi$ 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 $\Phi$ projected onto a sphere with
corresponding distance. Furthermore, we present an advanced method for
inferring $\Phi$ 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.
