Stability of Scale-Invariant Cosmological Correlation Functions in the Strongly Non-Linear Clustering Regime

We investigate stability of the scale-invariant solutions of the BBGKY equations for two-point spatial correlation functions of the density fluctuations in the strongly non-linear regime. In the case that the background skewness of the velocity field is equal to 0, we found that there is no local instability in the strongly non-linear regime. The perturbation does not grow nor does it decay. It has an only marginal stable mode. This result means that no special value of the power index of the two-point spatial correlation function are favored in terms of the stability of the solutions. In other words, the argument about the stability does not determine the power index of the two-point spatial correlation functions in the strongly non-linear regime.