A&A 382, 477-487 (2002)

DOI: 10.1051/0004-6361:20011584

## Dynamics of gravitational clustering

##### V. Subleading corrections in the quasi-linear regime

**P. Valageas**

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

(Received 24 September 2001 / Accepted 7 November 2001 )

** Abstract **

We investigate the properties of the standard perturbative expansions which describe the early stages of the dynamics of gravitational
clustering. We show that for hierarchical scenarios with no small-scale cutoff perturbation theory always breaks down beyond
a finite order
*q*_{+}. Furthermore, the degree of divergence increases with the order of the perturbative terms so that renormalization procedures
cannot be applied. Nevertheless, we explain that despite the divergence of these subleading terms the results of perturbation
theory are correct at leading order because they can be recovered through a steepest-descent method which does not use such
perturbative expansions. Finally, we investigate the simpler cases of the Zel'dovich and Burgers dynamics. In particular,
we show that the standard Burgers equation exhibits similar properties. This analogy suggests that the results of the standard
perturbative expansions are valid up to the order
*q*_{+} (i.e. until they are finite). Moreover, the first "non-regular" term of a large-scale expansion of the two-point correlation
function should be of the form
. At higher orders the large-scale expansion should no longer be over powers of
but over a different combination of powers of
1/*R*. However, its calculation requires new non-perturbative methods.

**Key words:**cosmology: theory

**--**large-scale structure of Universe

**©**

*ESO 2002*