NONLINEAR GRAVITATIONAL CLUSTERING - DREAMS OF A PARADIGM

We discuss the lace-time evolution of the gravitational clustering in an expanding universe, based on the nonlinear scaling relations (NSR) that connect the nonlinear and linear two-point correlation functions. The existence of critical indices for the NSR suggests that the evolu tion may proceed toward a universal profile that does not change its s hape at late times. We begin by clarifying the relation between the de nsity profiles of the individual halos and the slope of the correlatio n function, and we discuss the conditions under which the slopes of th e correlation function at the extreme nonlinear end can be independent of the initial power spectrum. If the evolution should lead to a prof ile that preserves the shape at late times, then the correlation funct ion should grow as a(2) (in a Omega = 1 universe), even at nonlinear s cales. We prove that such exact solutions do not exist; however, there exists a class of solutions (''psuedolinear profiles'') that evolve a s a(2) to a good approximation. It turns out that pseudolinear profile s are the correlation functions that arise if the individual halos are assumed to be isothermal spheres. They are also configurations of mas s in which the nonlinear effects of gravitational clustering are a min imum, and hence they can act as building blocks of the nonlinear unive rse. We discuss the implications of this result.