Units of the Nonlinear Universe

Abstract

The late time evolution of the gravitational clustering in an expanding universe is described based on the nonlinear scaling relations (NSR) which connect the nonlinear and linear two point correlation functions at different length scales. The existence of critical indices for the NSR suggests that the evolution may proceed towards a universal profile which does not change its shape at late times. If the evolution should lead to a halo profile which preserves the shape at late times, then the correlation function should grow as $a^2$ (in a $\varOmega =1$ universe) even at nonlinear scales. We prove that such exact solutions do not exist; however, there exists a class of solutions (“psuedo-linear profiles”, PLPs for short) which evolve as $a^2$ to a good approximation related to halo profiles of isothermal spheres. They are also configurations of mass in which the nonlinear effects of gravitational clustering is a minimum and hence can act as building blocks of the nonlinear universe.