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) which connect the nonlinear and linear two point correlation functions. 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. We begin by clarifying the relation between the density profiles of the individual halo and the slope of the correlation function and 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 which preserves the shape at late times, then the correlation function should grow as $a^2$ [in a $\Omega =1$ universe] een at nonlinear scales. We prove that such exact solutions do not exist; however, ther e exists a class of solutions (``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 correlation functions which 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 is a minimum and hence can act as building blocks of the nonlinear universe. We discuss the implicatios of this result.

32 Pages, Submitted to ApJ

References in corpus (8)

• The Structure of Cold Dark Matter Halos
• Nonlinear evolution of cosmological power spectra
• Reconstructing the linear power spectrum of cosmological mass fluctuations
• Scaling properties of the gravitational clustering in the nonlinear regime
• Modelling the Nonlinear Gravitational Clustering in the Expanding Universe
• Pattern in Nonlinear Gravatational Clustering: A Numerical Investigation
• The non-linear correlation function and the shapes of virialized halos
• Critical Index and Fixed Point in the Transfer of Power in Nonlinear Gravitational Clustering

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• Dark Energy and Gravity
• Nonlinear density evolution from an improved spherical collapse model
• Why Does Gravity Ignore the Vacuum Energy?
• An Improved Semi-Analytical Spherical Collapse Model for Non-linear Density Evolution
• Scale Invariance of Rich Cluster Abundance: A Possible Test for Models of Structure Formation
• A critique of scaling behaviour in non-linear structure formation scenarios
• Power transfer in nonlinear gravitational clustering and asymptotic universality
• A Universal Profile of the Dark Matter Halo and the Two-point Correlation Function
• A Simple Method for Computing the Non-Linear Mass Correlation Function with Implications for Stable Clustering
• The effects of anti-correlation on gravitational clustering
• Collapsed and Extended Cold Dark Matter Haloes in Softened N-Body Gravity
• Energy Ranking Preservation in a N-Body Cosmological Simulation
• Challenges in Non-Linear Gravitational Clustering