Stability of scale-invariant cosmological correlation functions in the strongly nonlinear clustering regime

We have investigated the stability of the scale-invariant solutions of the BBGKY equations for two-point spatial correlation functions of the density fluctuations in the strongly nonlinear regime. In the case in which the background skewness of the velocity held equals 0, we found that there is no local instability; i.e., the perturbations do not grow nor decay, the solutions are marginally stable. This result means that no special values 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.