  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 affect the nonlinear propagator. In the case of
positive skewness, the onset of the nonlinearity is advanced with a given
comoving wavenumber. On the other hand, the negative skewness gives the
opposite result.
