Renormalized Newtonian cosmic evolution with primordial non-Gaussianity

We study Newtonian cosmological perturbation theory from a field theoretical point of view. We derive a path integral representation for the cosmological evolution of stochastic fluctuations. Our main result is the closed form of the generating functional valid for any initial statistics. Moreover, we extend the renormalization group method proposed by Mataresse and Pietroni to the case of primordial non-Gaussian density and velocity fluctuations. As an application, we calculate the nonlinear propagator and examine how the non-Gaussianity affects the memory of cosmic fields to their initial conditions. It turns out that the non-Gaussianity affects the nonlinear propagator. In the case of positive skewness, the onset of the nonlinearity is advanced with a given comoving wave number. On the other hand, the negative skewness gives the opposite result.