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Issue A&A
Volume 421, Number 1, July I 2004
Page(s) 23 - 40
Section Cosmology (including clusters of galaxies)
DOI http://dx.doi.org/10.1051/0004-6361:20040125



A&A 421, 23-40 (2004)
DOI: 10.1051/0004-6361:20040125

A new approach to gravitational clustering: A path-integral formalism and large-N expansions

P. Valageas

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

(Received 20 June 2003 / Accepted 4 March 2004)

Abstract
We show that the formation of large-scale structures through gravitational instability in the expanding universe can be fully described through a path-integral formalism. We derive the action S[f] which gives the statistical weight associated with any phase-space distribution function $f({\vec x},{\vec p},t)$. This action S describes both the average over the Gaussian initial conditions and the Vlasov-Poisson dynamics. Next, applying a standard method borrowed from field theory we generalize our problem to an N-field system and we look for an expansion over powers of 1/N. We describe three such methods and we derive the corresponding equations of motion at the lowest non-trivial order for the case of gravitational clustering. This yields a set of non-linear equations for the mean $\overline{f}$ and the two-point correlation G of the phase-space distribution f, as well as for the response function R. These systematic schemes match the usual perturbative expansion on quasi-linear scales but should also be able to treat the non-linear regime. Our approach can also be extended to non-Gaussian initial conditions and may serve as a basis for other tools borrowed from field theory.


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




© ESO 2004

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