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We propose the zero-point of the cluster-cluster correlation function as asensitive test for the shape of the power spectrum of initial fluctuations. Itis now possible to go beyond the power law description to measure the point atwhich the correlation function becomes zero. Four independent measurementsindicate 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 conventionalCDM 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 theUniverse 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 ofclusters in an $\Omega=1$ cosmological model with a mixture of cold plus hotdark matter (CHDM). The correlation function we determined for the simulatedclusters has a zero-point, $r_0=55h^{-1}$Mpc that accurately matches the zeropoint of the observed function.Comment: 16 pages, tex, UNLV/93/3

The zero-point of the cluster-cluster correlation function: A key test of cosmological power spectra