Volume 421, Number 1, July I 2004
|Page(s)||23 - 40|
|Section||Cosmology (including clusters of galaxies)|
|Published online||11 June 2004|
A new approach to gravitational clustering: A path-integral formalism and large-N expansions*
Service de Physique Théorique, CEN Saclay, 91191 Gif-sur-Yvette Cedex, France
Corresponding author: firstname.lastname@example.org
Accepted: 4 March 2004
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 which gives the statistical weight associated with any phase-space distribution function . 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 . 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 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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