Large-N expansions applied to gravitational clustering

Free access article

Issue		A&A Volume 465, Number 3, April III 2007


Page(s)		725 - 747
Section		Cosmology (including clusters of galaxies)
DOI		http://dx.doi.org/10.1051/0004-6361:20066832

A&A 465, 725-747 (2007)
DOI: 10.1051/0004-6361:20066832

Large-N expansions applied to gravitational clustering

P. Valageas

Service de Physique Théorique, CEA Saclay, 91191 Gif-sur-Yvette, France
e-mail: valageas@spht.saclay.cea.fr

(Received 28 November 2006 / Accepted 26 January 2007)

Abstract
We develop a path-integral formalism to study the formation of large-scale structures in the universe. Starting from the equations of motion of hydrodynamics (single-stream approximation) we derive the action which describes the statistical properties of the density and velocity fields for Gaussian initial conditions. Then, we present large-N expansions (associated with a generalization to N fields or with a semi-classical expansion) of the path-integral defined by this action. This provides a systematic expansion for two-point functions such as the response function and the usual two-point correlation. We present the results of two such expansions (and related variants) at one-loop order for a SCDM and a $\Lambda$ CDM cosmology. We find that the response function exhibits fast oscillations in the non-linear regime with an amplitude which either follows the linear prediction (for the direct steepest-descent scheme) or decays (for the 2PI effective action scheme). On the other hand, the correlation function agrees with the standard one-loop result in the quasi-linear regime and remains well-behaved in the highly non-linear regime. This suggests that these large-N expansions could provide a good framework to study the dynamics of gravitational clustering in the non-linear regime. Moreover, the use of various expansion schemes allows one to estimate their range of validity without the need of N-body simulations and could provide a better accuracy in the weakly non-linear regime.

Key words: gravitation -- cosmology: theory -- cosmology: large-scale structure of Universe

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