We use very large cosmological N–body simulations to obtain accurate predictions for the two-point correlations and power spectra of mass-limited samples of galaxy clusters .
We consider two currently popular cold dark matter ( CDM ) cosmogonies , a critical density model ( \tau CDM ) and a flat low density model with a cosmological constant ( \Lambda CDM ) .
Our simulations each use 10 ^ { 9 } particles to follow the mass distribution within cubes of side 2 h ^ { -1 } Gpc ( \tau CDM ) and 3 h ^ { -1 } Gpc ( \Lambda CDM ) with a force resolution better than 10 ^ { -4 } of the cube side .
We investigate how the predicted cluster correlations increase for samples of increasing mass and decreasing abundance .
Very similar behaviour is found in the two cases .
The correlation length increases from r _ { 0 } = 12 – 13 h ^ { -1 } Mpc for samples with mean separation d _ { c } = 30 h ^ { -1 } Mpc to r _ { 0 } = 22 – 27 h ^ { -1 } Mpc for samples with d _ { c } = 100 h ^ { -1 } Mpc .
The lower value here corresponds to \tau CDM and the upper to \Lambda CDM .
The power spectra of these cluster samples are accurately parallel to those of the mass over more than a decade in scale .
Both correlation lengths and power spectrum biases can be predicted to better than 10 % using the simple model of Sheth , Mo & Tormen ( 2000 ) .
This prediction requires only the linear mass power spectrum and has no adjustable parameters .
We compare our predictions with published results for the APM cluster sample .
The observed variation of correlation length with richness agrees well with the models , particularly for \Lambda CDM .
The observed power spectrum ( for a cluster sample of mean separation d _ { c } = 31 h ^ { -1 } Mpc ) lies significantly above the predictions of both models .