The Oscillating Cluster Correlation Function

According to the traditional view galaxies are clustered on small scales, and on large scales the distribution of galaxies and clusters of galaxies is random (i.e. scale-free). Such a distribution is expected for the currently popular structure formation scenario based on the evolving dynamics of the dark matter during the history of the Universe. Quantitatively this behaviour is described by the correlation function of galaxies and clusters of galaxies which has a high peak at small separations but approaches zero at about 30 h Mpc for galaxies and at about 70 h Mpc for clusters of galaxies (in this paper we express the Hubble constant as H0 = h 100 km s −1 Mpc −1 ). Initially these scales were thought to be the scales of the transition to homogeneity. However, in the distribution of galaxies voids of diameter up to 50 h Mpc were discovered, voids in the distribution of clusters of galaxies are even larger with diameters of 100 h Mpc and more. Thus it was thought that the homogeneity begins on supercluster scale. Recent studies have shown that even on supercluster scale the distribution of galaxies and clusters of galaxies may have some regularity. First clear indication for the presence of periodicity in the distribution of high-density regions in the distribution of galaxies came from the deep pencil-beam survey of redshifts of galaxies by Broadhurst et al (1990). High-density regions in this survey form a regular pattern with a period 128 h Mpc. Nearest peaks in the distribution of high-density regions in this survey coincide in position and redshift with superclusters of galaxies (Bahcall 1991), thus one may think that the distribution of superclusters may have some regularity. However, as no clear periodicity was found in other directions, this result was explained as a statistical anomaly (Kaiser and Peacock 1991). Independent studies have shown that approximately on the same scale the cluster correlation function has a weak secondary maximum (Kopylov et al