THE TOPOLOGY OF LARGE-SCALE STRUCTURE IN THE UNIVERSE

The distribution of galaxies in the universe displays a rich structure. Considerable information not contained in the power spectrum can be obtained from the topology of the distribution. A random phase distribution has a "spongelike" topology when regions above or below the mean are considered, and the topology for any threshold value is calculable analytically. The topology may be studied by measuring the curvature of the surface, since this is related to the connectivity by the Gauss-Bonnet theorem. A computer can rapidly evaluate topology on a lattice, and non-Gaussian topologies are usually distinguishable. Although some non-Gaussian topology arises in dynamical evolution, the initial conditions can be recovered by smoothing on an appropriate scale. Although some non-Gaussian features are seen in observational samples, they are probably compatible with the random phase hypothesis for initial conditions. Redshift surveys now underway will considerably enhance the significance of the result. © 1990.