Probing Hierarchical Clustering by Scale-Scale Correlations of Wavelet Coefficients

It is of fundamental importance to determine if and how hierarchical clustering is involved in large-scale structure formation of the universe. Hierarchical evolution is characterized by rules that specify how dark-matter halos are formed by the merging of halos at smaller scales. We show that scale-scale correlations of the matter density field are direct and sensitive measures to quantify this merging tree. Such correlations are most conveniently determined from discrete wavelet transforms. Analyzing two samples of Lyα forests of QSOs absorption spectra, we find significant scale-scale correlations whose scale dependence is typical for branching processes. Therefore, models that predict a "history-independent" evolution are ruled out, and the halos hosting the Lyα clouds must have gone through a "history-dependent" merging process during their formation.