Genus Topology of Structure in the Sloan Digital Sky Survey: Model Testing

We measure the three-dimensional topology of large-scale structure in theSloan Digital Sky Survey (SDSS). This allows the genus statistic to be measuredwith unprecedented statistical accuracy. The sample size is now sufficientlylarge to allow the topology to be an important tool for testing galaxyformation models. For comparison, we make mock SDSS samples using severalstate-of-the-art N-body simulations: the Millennium run of Springel et al.(2005)(10 billion particles), Kim & Park (2006) CDM models (1.1 billionparticles), and Cen & Ostriker (2006) hydrodynamic code models (8.6 billioncell hydro mesh). Each of these simulations uses a different method formodeling galaxy formation. The SDSS data show a genus curve that is broadlycharacteristic of that produced by Gaussian random phase initial conditions.Thus the data strongly support the standard model of inflation where Gaussianrandom phase initial conditions are produced by random quantum fluctuations inthe early universe. But on top of this general shape there are measurabledifferences produced by non-linear gravitational effects (cf. Matsubara 1994),and biasing connected with galaxy formation. The N-body simulations have beentuned to reproduce the power spectrum and multiplicity function but nottopology, so topology is an acid test for these models. The data show a``meatball'' shift (only partly due to the Sloan Great Wall of Galaxies; thisshift also appears in a sub-sample not containing the Wall) which differs atthe 2.5\sigma level from the results of the Millennium run and the Kim & Parkdark halo models, even including the effects of cosmic variance.