non-Gaussianities in the matter power-spectrum and bispectrum: the time-RG approach

We apply the time-renormalization group approach to study the effect of pri- mordial non-Gaussianities in the non-linear evolution of cosmological dark matter density perturbations. This method improves the standard perturbation approach by solving renor- malization group-like equations governing the dynamics of gravitational instability. The primordial bispectra constructed from the dark matter density contrast and the velocity fields represent initial conditions for the renormalization group flow. We consider local, equi- lateral and folded shapes for the initial non-Gaussianity and analyze as well the case in which the non-linear parameter fNL parametrizing the strength of the non-Gaussianity de- pends on the momenta in Fourier space through a power-law relation, the so-called running non-Gaussianity. For the local model of non-Gaussianity we compare our findings for the power-spectrum with those of recent N-body simulations and find that they accurately fit the N-body data up to wave-numbers k ∼ 0.25h/Mpc at z = 0. We also present predictions for the (reduced) matter bispectra for the various shapes of non-Gaussianity.