In this talk we will present a novel formalism to study the gravitational clustering of dark matter particles, in particular when this process enters a nonlinear regime. In this transition other ways to approach the problem are not accurate enough for the next era of precision cosmology. Conversely, Renormalized Perturbation Theory shows a remarkable good agreement with measurements from simulations. We therefore employ it to study accurately the nonlinear evolution of the matter two-point correlation function, and its Fourier transform, the power spectrum, at the scales imprinted with the baryon acoustic signature. This signature, matter counterpart of the famous acoustic peaks in the Cosmic Microwave Background, is considered as potentially one of the best proves to understand the late time acceleration of the Hubble expansion rate.

Physics Department, New York University