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 (SDSS) 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 for both the angular and the radial selection functions of the SDSS, and the shot noise giving an effective resolution of the order of similar to 10 Mpc. In addition, we correct for the redshift distortions in the linear and non-linear 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 of up to similar 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 lognormal distribution for 10 Mpc less than or similar to r(S) less than or similar to 30 Mpc.