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

Gaussian cosmological models, typified by the inflationary cold dark mattermodels, and non-Gaussian topological defect based cosmological models, such asthe texture seeded model, differ in the origin of large-scale cosmicstructures. In the former it is believed that peaks at appropriate scales inthe initial high density field are the sites onto which matter accretes andcollapses to form the present galaxies and clusters of galaxies, whereas in thelatter these structures can form around the density perturbation seeds (whichare textures in the texture model). Textures initially are randomly distributedon scales larger than their size, in sharp contrast to the initial high densitypeaks in the Gaussian models which are already strongly clustered before anygravitational evolution has occured. One thus expects that the resultantcorrelation of large cosmic objects such as clusters of galaxies in the texturemodel should be significantly weaker than its Gaussian counterpart. We show that an $\Omega_0=1$ biased $b=2$ (as required by cluster abundanceobservations) texture model (or any random seed model) predicts a two-pointcorrelation length of $\le 6.0h^{-1}$Mpc for rich clusters, independent ofrichness. On the other hand, the observed correlation length for rich clustersis $\ge 10.0h^{-1}$Mpc at an approximately $2\sigma$ confidence level. It thusappears that the global texture cosmological model or any random seedcosmological models of this sort are ruled out at a very high confidence($>3\sigma$).Comment: ApJ in press, 17 tex pages and 1 figur