EDP Sciences
Free access
Volume 379, Number 1, November III 2001
Page(s) 8 - 20
Section Cosmology
DOI http://dx.doi.org/10.1051/0004-6361:20011309

A&A 379, 8-20 (2001)
DOI: 10.1051/0004-6361:20011309

Dynamics of gravitational clustering

I. Building perturbative expansions
P. Valageas

Service de Physique Théorique, CEN Saclay, 91191 Gif-sur-Yvette, France

(Received 28 May 2001 / Accepted 13 September 2001)

We develop a systematic method to obtain the solution of the collisionless Boltzmann equation which describes the growth of large-scale structures as a perturbative series over the initial density perturbations. We give an explicit calculation of the second-order terms which are shown to agree with the results obtained from the hydrodynamical description of the system. Then, we explain that this identity extends to all orders of perturbation theory and that the perturbative series actually diverge for hierarchical scenarios. However, since the collisionless Boltzmann equation provides the exact description of the dynamics (including the non-linear regime) these results may serve as a basis for a study of the non-linear regime. In particular, we derive a non-perturbative quadratic integral equation which explicitly relates the actual non-linear distribution function to the initial conditions (more precisely, to the linear growing mode). This allows us to write an explicit path-integral expression for the probability distribution of the exact non-linear density field.

Key words: cosmology: theory -- large-scale structure of universe

Offprint request: P. Valageas, valageas@spht.sacaly.cea.fr

© ESO 2001