Nonlinear gravitational clustering: dreams of a paradigm

Abstract

We discuss the late-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 evolution may proceed toward a universal profile that does not change its shape at late times. We begin by clarifying the relation between the density profiles of the individual halos and the slope of the correlation function, and we discuss the conditions under which the slopes of the correlation function at the extreme nonlinear end can be independent of the initial power spectrum. If the evolution should lead to a profile that preserves the shape at late times, then the correlation function should grow as α² (in a Ω = 1 universe), even at nonlinear scales. We prove that such exact solutions do not exist; however, there exists a class of solutions ("psuedolinear profiles") that evolve as α² to a good approximation. It turns out that pseudolinear profiles are the correlation functions that arise if the individual halos are assumed to be isothermal spheres. They are also configurations of mass in which the nonlinear effects of gravitational clustering are a minimum, and hence they can act as building blocks of the nonlinear universe. We discuss the implications of this result.