The Zero-Point of the Cluster-Cluster Correlation Function: A Key Test of Cosmological Power Spectra

Abstract

We propose the zero-point of the cluster-cluster correlation function as a sensitive test for the shape of the power spectrum of initial fluctuations. It is now possible to go beyond the power law description to measure the point at which the correlation function becomes zero. Four independent measurements indicate that the zero point, $r_0$, should be in the range (40-60)$h^{-1}$Mpc. The large value of $r_0$ at which the zero-point occurs rules out conventional CDM models independently of the assumed amplitude. Models with $\Omega < 0.25$ should be rejected because they predict too large $r_0$. If the age of the Universe is assumed to be larger than 15 Gyr, models with either $\Omega<0.5$ or $h> 0.55$ are rejected. We present the results of numerical simulations of clusters in an $\Omega=1$ cosmological model with a mixture of cold plus hot dark matter (CHDM). The correlation function we determined for the simulated clusters has a zero-point, $r_0=55h^{-1}$Mpc that accurately matches the zero point of the observed function.