  We study the off-equilibrium effects of inflaton on the dynamics of
primordial perturbations in the O(N) model. A self-consistent off-equilibrium
formalism is employed to investigate the evolution of the inflationary
background field and its fluctuations with the back-reaction effects. We find
two observable remains left behind the off-equilibrium processes: the running
spectral index of primordial density perturbations and the correlations between
perturbation modes in phase space, which would serve as the imprints to probe
the epoch of inflation, even beyond.
