THE CORRELATION FUNCTION OF GALAXY CLUSTERS AND DETECTION OF BARYON ACOUSTIC OSCILLATIONS

We calculate the correlation function of 13,904 galaxy clusters of z <= 0.4 selected from the cluster catalog of Wen et al. The correlation function can be fitted with a power-law model xi(r) = (r/R-0)(-gamma) on the scales of 10 h(-1) Mpc <= r <= 50 h(-1) Mpc, with a larger correlation length of R-0 = 18.84 +/- 0.27 h(-1) Mpc for clusters with a richness of R >= 15 and a smaller length of R-0 = 16.15 +/- 0.13 h(-1) Mpc for clusters with a richness of R >= 5. The power-law index of gamma = 2.1 is found to be almost the same for all cluster subsamples. A pronounced baryon acoustic oscillations (BAO) peak is detected at r similar to 110 h(-1) Mpc with a significance of similar to 1.9 sigma. By analyzing the correlation function in the range of 20 h(-1) Mpc <= r <= 200 h(-1) Mpc, we find that the constraints on distance parameters are D-v (z(m) = 0.276) = 1077 +/- 55(1 sigma) Mpc and h = 0.73 +/- 0.039(1 sigma), which are consistent with the cosmology derived from Wilkinson Microwave Anisotropy Probe (WMAP) seven-year data. However, the BAO signal from the cluster sample is stronger than expected and leads to a rather low matter density Omega(m)h(2) = 0.093 +/- 0.0077(1 sigma), which deviates from the WMAP7 result by more than 3 sigma. The correlation function of the GMBCG cluster sample is also calculated and our detection of the BAO feature is confirmed.