A Critical Test of Topological Defect Models: Spatial Clustering of Clusters of Galaxies

Abstract

Gaussian cosmological models, typified by the inflationary cold dark matter models, and non-Gaussian topological defect based cosmological models, such as the texture seeded model, differ in the origin of large-scale cosmic structures. In the former it is believed that peaks at appropriate scales in the initial high density field are the sites onto which matter accretes and collapses to form the present galaxies and clusters of galaxies, whereas in the latter these structures can form around the density perturbation seeds (which are textures in the texture model). Textures initially are randomly distributed on scales larger than their size, in sharp contrast to the initial high density peaks in the Gaussian models which are already strongly clustered before any gravitational evolution has occured. One thus expects that the resultant correlation of large cosmic objects such as clusters of galaxies in the texture model should be significantly weaker than its Gaussian counterpart. We show that an $\Omega_0=1$ biased $b=2$ (as required by cluster abundance observations) texture model (or any random seed model) predicts a two-point correlation length of $\le 6.0h^{-1}$Mpc for rich clusters, independent of richness. On the other hand, the observed correlation length for rich clusters is $\ge 10.0h^{-1}$Mpc at an approximately $2\sigma$ confidence level. It thus appears that the global texture cosmological model or any random seed cosmological models of this sort are ruled out at a very high confidence ($>3\sigma$).