  The evolution of high order correlation functions of a test scalar field in
arbitrary inflationary backgrounds is computed. Whenever possible, exact
results are derived from quantum field theory calculations. Taking advantage of
the fact that such calculations can be mapped, for super-horizon scales, into
those of a classical system, we express the expected correlation functions in
terms of classical quantities, power spectra, Green functions, that can be
easily computed in the long-wavelength limit. Explicit results are presented
that extend those already known for a de Sitter background. In particular the
expressions of the late time amplitude of bispectrum and trispectrum, as well
as the whole high-order correlation structure, are given in terms of the
expansion factor behavior. When compared to the case of a de Sitter background,
power law inflation and chaotic inflation induced by a massive field are found
to induce high order correlation functions the amplitudes of which are
amplified by almost one order of magnitude. These results indicate that the
dependence of the related non-Gaussian parameters - such as f_NL - on the
wave-modes is at percent level.
