Large galaxy redshift surveys have long been used to constrain cosmological models and structure formation scenarios. In particular, the largest structures discovered observationally are thought to carry critical information on the amplitude of large
-scale density fluctuations or homogeneity of the universe, and have often challenged the standard cosmological framework. The Sloan Great Wall (SGW) recently found in the Sloan Digital Sky Survey (SDSS) region casts doubt on the concordance cosmological model with a cosmological constant (i.e. the flat LCDM model). Here we show that the existence of the SGW is perfectly consistent with the LCDM model, a result that only our very large cosmological N-body simulation (the Horizon Run 2, HR2) could supply. In addition, we report on the discovery of a void complex in the SDSS much larger than the SGW, and show that such size of the largest void is also predicted in the LCDM paradigm. Our results demonstrate that an initially homogeneous isotropic universe with primordial Gaussian random phase density fluctuations growing in accordance with the General Relativity, can explain the richness and size of the observed large-scale structures in the SDSS. Using the HR2 simulation we predict that a future galaxy redshift survey about four times deeper or with 3 magnitude fainter limit than the SDSS should reveal a largest structure of bright galaxies about twice as big as the SGW.
We measure the 3D genus topology of large scale structure using Luminous Red Galaxies (LRGs) in the Sloan Digital Sky Survey and find it consistent with the Gaussian random phase initial conditions expected from the simplest scenarios of inflation. T
his studies 3D topology on the largest scales ever obtained. The topology is sponge-like. We measure topology in two volume-limited samples: a dense shallow sample studied with smoothing length of 21h^{-1}Mpc, and a sparse deep sample studied with a smoothing length of 34h^{-1}Mpc. The amplitude of the genus curve is measured with 4% uncertainty. Small distortions in the genus curve expected from non-linear biasing and gravitational effects are well explained (to about 1-sigma accuracy) by N-body simulations using a subhalo-finding technique to locate LRGs. This suggests the formation of LRGs is a clean problem that can be modeled well without any free fitting parameters. This bodes well for using LRGs to measure the characteristic scales such as the baryon oscillation scale in future deep redshift surveys.
