Breaking Degeneracy of Dark Matter Models by the Scale-Scale Correlations of Galaxies

Recently, scale-scale correlations have been detected in the distributions of quasar's Ly$\alpha$ absorption lines and the maps of cosmic temperature fluctuations. In this paper, we investigate the scale-scale correlations in galaxy distributions. Using samples of mass field given by N-body simulation, we first show that the scale-scale correlation of 2-D and 3-D mass distributions at present day is capable of breaking the degeneracy between the SCDM (standard cold dark matter model) and OCDM (open CDM model) or LCDM (flat CDM model), and even show the difference between the OCDM and LCDM. Using biased galaxy samples produced in an appropriate bias model, we show that the scale-scale correlation of galaxy distribution at zero redshift is still a powerful tool to break the degeneracy in the parameter space, including both cosmological and biasing parameters. We analyze the scale-scale correlations of the APM bright galaxy catalog, and compare it with the mock catalog in the SCDM, OCDM and LCDM models. We find that all the spectra of local and non-local scale-scale correlations predicted by the OCDM model are in excellent agreement with those of the APM-BGC sample, while the SCDM and LCDM mock catalog appear to have somewhat weaker scale-scale correlations than the observation.