Cosmic Cartography of the Large-Scale Structure with Sloan Digital Sky
  Survey Data Release 6
  We present the largest Wiener reconstruction of the cosmic density field made
to date. The reconstruction is based on the Sloan Digital Sky Survey data
release 6 covering the northern Galactic cap. We use a novel supersampling
algorithm to suppress aliasing effects and a Krylov-space inversion method to
enable high performance with high resolution. These techniques are implemented
in the ARGO computer code. We reconstruct the field over a 500 Mpc cube with
Mpc grid-resolution while accounting both for the angular and radial selection
functions of the SDSS, and the shot noise giving an effective resolution of the
order of ~10 Mpc. In addition, we correct for the redshift distortions in the
linear and nonlinear regimes in an approximate way. We show that the commonly
used method of inverse weighting the galaxies by the corresponding selection
function heads to excess noise in regions where the density of the observed
galaxies is small. It is more accurate and conservative to adopt a Bayesian
framework in which we model the galaxy selection/detection process to be
Poisson-binomial. This results in heavier smoothing in regions of reduced
sampling density. Our results show a complex cosmic web structure with huge
void regions indicating that the recovered matter distribution is highly
non-Gaussian. Filamentary structures are clearly visible on scales up to ~20
Mpc. We also calculate the statistical distribution of density after smoothing
the reconstruction with Gaussian kernels of different radii r_S and find good
agreement with a log-normal distribution for ~10 Mpc < r_S < ~30 Mpc.
