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Comptes Rendus Physique
Volume 7, n° 3-4
pages 350-359 (avril-mai 2006)
Doi : 10.1016/j.crhy.2006.01.010
Challenges in nonlinear gravitational clustering
Défis de lʼaggrégation gravitationnelle non-linéaire
 

Thanu Padmanabhan
Inter-University Centre for Astronomy and Astrophysics, Post Bag 4, Ganeshkhind, Pune 411 007, India 

Abstract

This article addresses some issues related to the statistical description of gravitating systems in an expanding backgrounds. In particular, I describe (a) how the nonlinear mode-mode coupling transfers power from one scale to another in the Fourier space if the initial power spectrum is sharply peaked at a given scale and (b) what are the asymptotic characteristics of gravitational clustering that are independent of the initial conditions. The analysis uses a new approach based on an integro-differential equation for the evolution of the gravitational potential in the Fourier space. I show how this equation allows one to understand several aspects of nonlinear gravitational clustering and provides insight in to the transfer of power from one scale to another through nonlinear mode coupling. Numerical simulations as well as analytic work shows that power transfer leads to a universal power spectrum at late times, somewhat reminiscent of the existence of Kolmogorov spectrum in fluid turbulence. To cite this article: T. Padmanabhan, C. R. Physique 7 (2006).

The full text of this article is available in PDF format.
Résumé

Cet article présente quelques problèmes concernant la description statistique de systèmes gravitants dans un univers en expansion. En particulier, je décris (a) comment le couplage non-linéaire des modes transfère la puissance dʼune échelle à lʼautre dans lʼespace de Fourier, si le spectre de puissance initial est très concentré sur une seule échelle et (b) quelles sont les caractéristiques asymptotiques de lʼaggrégation gravitationnelle qui sont indépendantes des conditions initiales. Lʼanalyse utilise une nouvelle approche basée sur une équation integro-differentielle pour lʼévolution du potentiel gravitationnel dans lʼespace de Fourier. Je montre comment cette équation permet de comprendre plusieurs aspects de lʼaggrégation gravitationnelle non-linéaire et fournit une meilleure connaissance du transfert de puissance dʼune échelle à lʼautre par le couplage non-linéaire des mode. Les simulations numériques de même que le travail analytique montrent que le transfert de puissance conduit à un spectre de puissance universel, qui rappelle le spectre de Kolmogorov en turbulence des fluides. Pour citer cet article : T. Padmanabhan, C. R. Physique 7 (2006).

The full text of this article is available in PDF format.

Keywords : Gravity, Clustering, Power spectrum, Kolmogorov spectrum, Statistical mechanics, Cosmological expansion

Mots-clés : Pesanteur, Aggrégation, Spectre de puissance, Spectre de Kolmogorov, Mécanique statistique, Expansion cosmique




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