The intermittent behavior and hierarchical clustering of the cosmic mass field

The hierarchical clustering model of the cosmic mass field is examined in t he context of intermittency. We show that the mass field satisfying the cor relation hierarchy xi (n) similar or equal to Q(n)(xi (2))(n-1) is intermit tent if kappa < d, where d is the dimension of the field and <kappa> is the power-law index of the nonlinear power spectrum in the discrete wavelet tr ansform (DWT) representation. We also find that a field with singular clust ering can be described by hierarchical clustering models with scale-depende nt coefficients Q(n) and that this scale dependence is completely determine d by the intermittent exponent and kappa. Moreover, the singular exponents of a field can be calculated by the asymptotic behavior of Q(n) when n is l arge. Applying this result to the transmitted flux of HS 1700 Ly alpha fore sts, we find that the underlying mass field of the Ly alpha forests is sign ificantly intermittent. On physical scales less than about 2.0 h(-1) Mpc, t he observed intermittent behavior is qualitatively different from the predi ction of the hierarchical clustering with constant Q(n).The observations, h owever, do show the existence of an asymptotic value for the singular expon ents. Therefore, the mass field can be described by the hierarchical cluste ring model with scale-dependent Q(n). The singular exponent indicates that the cosmic mass field at redshift similar to2 is weakly singular at least o n physical scales as small as 10 h(-1) kpc.