Dynamique gravitationnelle non linéaire en cosmologie – NLDyn

In cosmology, the growth of gravitational instability in a dark matter fluid is not fully understood yet. However, with the advent of a new generation of observational cosmology projects - let us mention ground-based or space large-scale cosmic shear surveys or the Square-Kilometer-Array - it is necessary to be able to compute with a great precision the density fluctuation spectra as they develop in the matter fluid. N-body simulations can provide us with some answers but only for a limited number of cosmological parameters. The scientific objectives of those projects, and among them the determination of the dark energy property, make however largely use of our ability to perform such calculations for a large variety of models. It is thus necessary to refine our theoretical knowledge of the behavior of the gravitational instabilities. The aims of this project is to develop computation tools of the density spectrum, its bispectrum (three-point correlation function) for a set a various cosmological models. More precisely we wish - to have at our disposal tools for computing those quantities in a manner that would be fully analytical and predictive in the quasilinear regime (e.g. in a regime that extends the purely linear regime in a way that remains to be defined); - to develop models allowing the description of the matter-halo relations or to tackle the nonlinear regime with well controlled approximations. The fulfillment of the first item of this scientific program takes advantage of recent resummation techniques (initially developed by R. Scoccimarro and his collaborators). They allow the derivation of spectra, and in principle correlation functions of any order, in a fully predictive way without introducing divergences. Those analytical results have still to be extended to various cosmologies and to quantities beyond spectra and tested against numerical simulations. The second item of our program is more speculative. There are however favorable indications.