We measure the topology ( genus curve ) of the galaxy distribution in a very large cosmological simulation designed to resemble closely results from the upcoming Sloan Digital Sky Survey ( SDSS ) .
The mock survey is based on a large N-body simulation that uses 54,872,000 particles in a periodic cube 600 h ^ { -1 } \mbox { Mpc } on a side .
The adopted inflationary cold dark matter ( CDM ) model has parameters \Omega _ { CDM } = 0.4 , \Omega _ { \Lambda } = 0.6 , h = 0.6 , b = 1.3 .
We “ observe ” this simulation to produce a simulated redshift catalog of \sim 10 ^ { 6 } galaxies over \pi steradians , mimicking the ancitipated spectroscopic selection procedures of the SDSS in some detail .
Sky maps , redshift slices , and 3-D contour maps of the mock survey reveal a rich and complex structure , including networks of voids and superclusters that resemble the patterns seen in the CfA redshift survey and the Las Campanas Redshift Survey ( LCRS ) .
The 3-D genus curve can be measured from the simulated catalog with superb precision ; this curve not only has the general shape predicted for Gaussian , random phase initial conditions , but the error bars are small enough to demonstrate with high significance the subtle departures from this shape caused by non-linear gravitational evolution on a 10 h ^ { -1 } \mbox { Mpc } smoothing scale ( where \sigma _ { gal } = 0.4 ) .
These distortions have the form predicted by Matsubara ’ s ( 1994 ) perturbative analysis , but they are smaller in amplitude .
We also measure the 3-D genus curve of the radial peculiar velocity field measured by applying distance-indicator relations ( with realistic errors ) to the mock catalog .
The genus curve is consistent with the Gaussian random phase prediction , though it is of relatively low precision because of the large smoothing length required to overcome noise in the measured velocity field .
Finally , we measure the 2-D topology in redshift slices , similar to those which will become available early in the course of the SDSS and to those already observed in the LCRS .
The genus curves of these slices are consistent with the observed genus curves of the LCRS , suggesting that our inflationary CDM model with \Omega _ { CDM } \sim 0.4 is a good choice .
Our mock redshift catalog is publicly available for the use of other researchers .