Nonlinear Gravitational Clustering: Dreams of a Paradigm

We discuss the late time evolution of the gravitational clustering in anexpanding universe, based on the nonlinear scaling relations (NSR) whichconnect the nonlinear and linear two point correlation functions. The existenceof critical indices for the NSR suggests that the evolution may proceed towardsa universal profile which does not change its shape at late times. We begin byclarifying the relation between the density profiles of the individual halo andthe slope of the correlation function and discuss the conditions under whichthe slopes of the correlation function at the extreme nonlinear end can beindependent of the initial power spectrum. If the evolution should lead to aprofile which preserves the shape at late times, then the correlation functionshould grow as $a^2$ [in a $\Omega=1$ universe] een at nonlinear scales. Weprove that such exact solutions do not exist; however, ther e exists a class ofsolutions (``psuedo-linear profiles'', PLP's for short) which evolve as $a^2$to a good approximation. It turns out that the PLP's are the correlationfunctions which arise if the individual halos are assumed to be isothermalspheres. They are also configurations of mass in which the nonlinear effects ofgravitational clustering is a minimum and hence can act as building blocks ofthe nonlinear universe. We discuss the implicatios of this result.Comment: 32 Pages, Submitted to Ap