The topology of large-scale structure in galaxy redshift surveys

The topology of large-scale structure is investigated by consideration of two recently completed redshift surveys: the 2-degree Field Galaxy Redshift Survey (2dFGRS) and the Las Campanas Redshift Survey (LCRS). Minkowski functionals---a family of statistical measures based on geometric descriptors of the content, shape, and connectivity of spatial sets, and on the topological Euler characteristic---are presented as effective tools for discriminating between galaxy distributions that display different topologies. The redshift surveys are examined using Minkowski functionals, taking in to account their individual selection effects. The results are compared with the predictions of three inflation-based models of structure formation: the standard cold dark matter model (SCDM), an open cold dark matter model (OCDM), and a cold dark matter model containing a cosmological constant (LCDM). In the case of the 2dFGRS, the statistics are shown to be able to discriminate between the predictions of the models with high significance. The Minkowski functionals for the north Galactic cap are consistent with the currently favored LCDM paradigm. Those for the south Galactic cap show significant disagreement with all theoretical models; however, this deviation is thought to reflect the presence of a supercluster in the region of the 2dFGRS studied. The Minkowski functional statistics of the relatively smaller LCRS are found to be consistent with the predictions of both the OCDM and LCDM models. It is concluded that the Minkowski functionals are useful statistical discriminators when applied to large enough sample sets, such as the 2dFGRS. Amongst the measures, the integrated mean curvature statistic has the greatest discriminatory power, followed by the genus statistic.