SCALE-INVARIANT CORRELATION-FUNCTIONS OF COSMOLOGICAL DENSITY-FLUCTUATIONS IN THE STRONG-CLUSTERING REGIME

We investigate the scale-invariant solutions of the BBGKY equations fo r spatial correlation functions of cosmological density fluctuations a nd the mean relative peculiar velocity in the strongly nonlinear regim e. It is found that the solutions for the mean relative physical veloc ity depend on the three-point spatial correlation function and the ske wness of the velocity fields. We find that the stability condition, in which the mean relative physical velocity vanishes on the virialized regions, is satisfied only under the assumptions that Davis & Peebles made in their 1977 paper. It is found, however, that their assumptions may not be general in real systems. The power index of the two-point correlation function in the strongly nonlinear regime depends on the m ean relative peculiar velocity, the three-point correlation function, and the skewness. If self-similar solutions exist, then the power inde x in the strongly nonlinear regime is related to the power index of th e initial power spectrum, and its relation depends on the three-point correlation function and the skewness through the mean relative peculi ar velocity.