Cosmological constraints from the correlation function of galaxy   clusters
  I compare various semi-analytic models for the bias of dark matter halos with halo clustering properties observed in recent numerical simulations. The best fitting model is one based on the collapse of ellipsoidal perturbations proposed by Sheth, Mo & Tormen (1999), which fits the halo correlation length to better than 8 per cent accuracy. Using this model, I confirm that the correlation length of clusters of a given separation depends primarily on the shape and amplitude of mass fluctuations in the universe, and is almost independent of other cosmological parameters. Current observational uncertainties make it difficult to draw robust conclusions, but for illustrative purposes I discuss the constraints on the mass power spectrum which are implied by recent analyses of the APM cluster sample. I also discuss the prospects for improving these constraints using future surveys such as the Sloan Digital Sky Survey. Finally, I show how these constraints can be combined with observations of the cluster number abundance to place strong limits on the matter density of the universe. 
James Robinson (UC Berkeley)